Factor Quadratics (a > 1) | Math Coach Amy

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Key Ideas Easy Medium Hard Hard 2

What to Remember

Slide and Divide

2x² + 7x + 3

SLIDE, multiply 2*3

2x² + 7x + 3

Solve the Puzzle. What two numbers multiply to 6 and add to 7.

1*6

2*3

2x²

+ 3

Now we divided 7x into two pieces 1x and 6x.

2x² + 1x + 6x + 3

Factor by grouping.

2x² + 1x + 6x + 3

Factor the GCF from each part.

x(2x+1) + 3(2x+1)

(2x+1)(x+3)

Level 1

Easy

Example

Factor. 2x² + 7x + 3

2x² + 7x + 3

SLIDE, multiply 2*3

2x² + 7x + 3

Solve the Puzzle. What two numbers multiply to 6 and add to 7.

1*6

2*3

2x²

+ 3

Now we divided 7x into two pieces 1x and 6x.

2x² + 1x + 6x + 3

Factor by grouping.

2x² + 1x + 6x + 3

Factor the GCF from each part.

x(2x+1) + 3(2x+1)

(2x+1)(x+3)

Answer: (2x+1)(x+3)

Factor. 2x² + 5x + 2

Show Answer

2x² + 5x + 2

SLIDE, multiply 2*2

2x² + 5x + 2

Solve the Puzzle. What two numbers multiply to 4 and add to 5.

1*4

2*2

2x²

+ 2

Now we divided 5x into two pieces 1x and 4x.

2x² + 1x + 4x + 2

Factor by grouping.

2x² + 1x + 4x + 2

Factor the GCF from each part.

x(2x+1) + 2(2x+1)

(2x+1)(x+2)

Answer: (2x+1)(x+2)

Factor. 3x² + 8x + 4

Show Answer

3x² + 8x + 4

SLIDE, multiply 3*4

3x² + 8x + 4

Solve the Puzzle. What two numbers multiply to 12 and add to 8.

1*12

2*6

3*4

3x²

+ 4

Now we divided 8x into two pieces 2x and 6x.

3x² + 2x + 6x + 4

Factor by grouping.

3x² + 2x + 6x + 4

Factor the GCF from each part.

x(3x+2) + 2(3x+2)

(3x+2)(x+2)

Answer: (3x+2)(x+2)

Factor. 2x² + 9x + 4

Show Answer

2x² + 9x + 4

SLIDE, multiply 2*4

2x² + 9x + 4

Solve the Puzzle. What two numbers multiply to 8 and add to 9.

1*8

2*4

2x²

+ 4

Now we divided 9x into two pieces 1x and 8x.

2x² + 1x + 8x + 4

Factor by grouping.

2x² + 1x + 8x + 4

Factor the GCF from each part.

x(2x+1) + 4(2x+1)

(2x+1)(x+4)

Answer: (2x+1)(x+4)

Factor. 3x² + 10x + 3

Show Answer

3x² + 10x + 3

SLIDE, multiply 3*3

3x² + 10x + 3

Solve the Puzzle. What two numbers multiply to 9 and add to 10.

1*9

3*3

3x²

+ 3

Now we divided 10x into two pieces 1x and 9x.

3x² + 1x + 9x + 3

Factor by grouping.

3x² + 1x + 9x + 3

Factor the GCF from each part.

x(3x+1) + 3(3x+1)

(3x+1)(x+3)

Answer: (3x+1)(x+3)

Factor. 2x² + 11x + 5

Show Answer

2x² + 11x + 5

SLIDE, multiply 2*5

2x² + 11x + 5

Solve the Puzzle. What two numbers multiply to 10 and add to 11.

1*10

2*5

2x²

+ 5

Now we divided 11x into two pieces 1x and 10x.

2x² + 1x + 10x + 5

Factor by grouping.

2x² + 1x + 10x + 5

Factor the GCF from each part.

x(2x+1) + 5(2x+1)

(2x+1)(x+5)

Answer: (2x+1)(x+5)

Level 2

Medium

Example

Factor. 2x² + x − 6

2x² + x − 6

SLIDE, multiply 2*(−6)

2x² + x − 6

Solve the Puzzle. What two numbers multiply to −12 and add to 1.

(−1)*12

1*(−12)

(−2)*6

2*(−6)

(−3)*4

3*(−4)

2x²

− 6

Now we divided x into two pieces −3x and 4x.

2x² − 3x + 4x − 6

Factor by grouping.

2x² − 3x + 4x − 6

Factor the GCF from each part.

x(2x−3) + 2(2x−3)

(2x−3)(x+2)

Answer: (2x−3)(x+2)

Factor. 2x² − 5x − 3

Show Answer

2x² − 5x − 3

SLIDE, multiply 2*(−3)

2x² − 5x − 3

Solve the Puzzle. What two numbers multiply to −6 and add to −5.

(−1)*6

1*(−6)

(−2)*3

2*(−3)

2x²

− 3

Now we divided −5x into two pieces 1x and −6x.

2x² + 1x − 6x − 3

Factor by grouping.

2x² + 1x − 6x − 3

Factor the GCF from each part.

x(2x+1) − 3(2x+1)

(2x+1)(x−3)

Answer: (2x+1)(x−3)

Factor. 3x² + 5x − 2

Show Answer

3x² + 5x − 2

SLIDE, multiply 3*(−2)

3x² + 5x − 2

Solve the Puzzle. What two numbers multiply to −6 and add to 5.

(−1)*6

1*(−6)

(−2)*3

2*(−3)

3x²

− 2

Now we divided 5x into two pieces −1x and 6x.

3x² − 1x + 6x − 2

Factor by grouping.

3x² − 1x + 6x − 2

Factor the GCF from each part.

x(3x−1) + 2(3x−1)

(3x−1)(x+2)

Answer: (3x−1)(x+2)

Factor. 2x² − 7x + 3

Show Answer

2x² − 7x + 3

SLIDE, multiply 2*3

2x² − 7x + 3

Solve the Puzzle. What two numbers multiply to 6 and add to −7.

(−1)*(−6)

(−2)*(−3)

2x²

+ 3

Now we divided −7x into two pieces −1x and −6x.

2x² − 1x − 6x + 3

Factor by grouping.

2x² − 1x − 6x + 3

Factor the GCF from each part.

x(2x−1) − 3(2x−1)

(2x−1)(x−3)

Answer: (2x−1)(x−3)

Factor. 2x² + 3x − 9

Show Answer

2x² + 3x − 9

SLIDE, multiply 2*(−9)

2x² + 3x − 9

Solve the Puzzle. What two numbers multiply to −18 and add to 3.

(−1)*18

1*(−18)

(−2)*9

2*(−9)

(−3)*6

3*(−6)

2x²

− 9

Now we divided 3x into two pieces −3x and 6x.

2x² − 3x + 6x − 9

Factor by grouping.

2x² − 3x + 6x − 9

Factor the GCF from each part.

x(2x−3) + 3(2x−3)

(2x−3)(x+3)

Answer: (2x−3)(x+3)

Factor. 3x² − 11x + 6

Show Answer

3x² − 11x + 6

SLIDE, multiply 3*6

3x² − 11x + 6

Solve the Puzzle. What two numbers multiply to 18 and add to −11.

(−1)*(−18)

(−2)*(−9)

(−3)*(−6)

3x²

+ 6

Now we divided −11x into two pieces −2x and −9x.

3x² − 2x − 9x + 6

Factor by grouping.

3x² − 2x − 9x + 6

Factor the GCF from each part.

x(3x−2) − 3(3x−2)

(3x−2)(x−3)

Answer: (3x−2)(x−3)

Level 3

Hard

Example

Factor. 4x² + 8x + 3

4x² + 8x + 3

SLIDE, multiply 4*3

4x² + 8x + 3

Solve the Puzzle. What two numbers multiply to 12 and add to 8.

1*12

2*6

3*4

4x²

+ 3

Now we divided 8x into two pieces 2x and 6x.

4x² + 2x + 6x + 3

Factor by grouping.

4x² + 2x + 6x + 3

Factor the GCF from each part.

2x(2x+1) + 3(2x+1)

(2x+1)(2x+3)

Answer: (2x+1)(2x+3)

Factor. 6x² + 13x + 6

Show Answer

6x² + 13x + 6

SLIDE, multiply 6*6

6x² + 13x + 6

Solve the Puzzle. What two numbers multiply to 36 and add to 13.

1*36

2*18

3*12

4*9

6*6

6x²

+ 6

Now we divided 13x into two pieces 4x and 9x.

6x² + 4x + 9x + 6

Factor by grouping.

6x² + 4x + 9x + 6

Factor the GCF from each part.

2x(3x+2) + 3(3x+2)

(3x+2)(2x+3)

Answer: (3x+2)(2x+3)

Factor. 4x² − 15x + 9

Show Answer

4x² − 15x + 9

SLIDE, multiply 4*9

4x² − 15x + 9

Solve the Puzzle. What two numbers multiply to 36 and add to −15.

(−1)*(−36)

(−2)*(−18)

(−3)*(−12)

(−4)*(−9)

(−6)*(−6)

4x²

+ 9

Now we divided −15x into two pieces −3x and −12x.

4x² − 3x − 12x + 9

Factor by grouping.

4x² − 3x − 12x + 9

Factor the GCF from each part.

x(4x−3) − 3(4x−3)

(4x−3)(x−3)

Answer: (4x−3)(x−3)

Factor. 6x² + 5x − 6

Show Answer

6x² + 5x − 6

SLIDE, multiply 6*(−6)

6x² + 5x − 6

Solve the Puzzle. What two numbers multiply to −36 and add to 5.

(−1)*36

1*(−36)

(−2)*18

2*(−18)

(−3)*12

3*(−12)

(−4)*9

4*(−9)

(−6)*6

6*(−6)

6x²

− 6

Now we divided 5x into two pieces −4x and 9x.

6x² − 4x + 9x − 6

Factor by grouping.

6x² − 4x + 9x − 6

Factor the GCF from each part.

2x(3x−2) + 3(3x−2)

(3x−2)(2x+3)

Answer: (3x−2)(2x+3)

Factor. 4x² − 5x − 6

Show Answer

4x² − 5x − 6

SLIDE, multiply 4*(−6)

4x² − 5x − 6

Solve the Puzzle. What two numbers multiply to −24 and add to −5.

(−1)*24

1*(−24)

(−2)*12

2*(−12)

(−3)*8

3*(−8)

(−4)*6

4*(−6)

4x²

− 6

Now we divided −5x into two pieces 3x and −8x.

4x² + 3x − 8x − 6

Factor by grouping.

4x² + 3x − 8x − 6

Factor the GCF from each part.

x(4x+3) − 2(4x+3)

(4x+3)(x−2)

Answer: (4x+3)(x−2)

Factor. 6x² − 13x + 6

Show Answer

6x² − 13x + 6

SLIDE, multiply 6*6

6x² − 13x + 6

Solve the Puzzle. What two numbers multiply to 36 and add to −13.

(−1)*(−36)

(−2)*(−18)

(−3)*(−12)

(−4)*(−9)

(−6)*(−6)

6x²

+ 6

Now we divided −13x into two pieces −4x and −9x.

6x² − 4x − 9x + 6

Factor by grouping.

6x² − 4x − 9x + 6

Factor the GCF from each part.

2x(3x−2) − 3(3x−2)

(3x−2)(2x−3)

Answer: (3x−2)(2x−3)

Level 3

Hard 2

Factor out a GCF first. Then use Slide and Divide.

Example

Factor. 4x² + 14x + 12

GCF is 2.

2(2x² + 7x + 6)

2x² + 7x + 6

SLIDE, multiply 2*6

2x² + 7x + 6

Solve the Puzzle. What two numbers multiply to 12 and add to 7.

1*12

2*6

3*4

2x²

+ 6

Now we divided 7x into two pieces 3x and 4x.

2x² + 3x + 4x + 6

Factor by grouping.

2x² + 3x + 4x + 6

Factor the GCF from each part.

x(2x+3) + 2(2x+3)

(2x+3)(x+2)

Put the 2 back.

2(2x+3)(x+2)

Answer: 2(2x+3)(x+2)

Factor. 6x² + 27x + 30

Show Answer

GCF is 3.

3(2x² + 9x + 10)

2x² + 9x + 10

SLIDE, multiply 2*10

2x² + 9x + 10

Solve the Puzzle. What two numbers multiply to 20 and add to 9.

1*20

2*10

4*5

2x²

+ 10

Now we divided 9x into two pieces 4x and 5x.

2x² + 4x + 5x + 10

Factor by grouping.

2x² + 4x + 5x + 10

Factor the GCF from each part.

2x(x+2) + 5(x+2)

(2x+5)(x+2)

Put the 3 back.

3(2x+5)(x+2)

Answer: 3(2x+5)(x+2)

Factor. 6x² + 22x + 12

Show Answer

GCF is 2.

2(3x² + 11x + 6)

3x² + 11x + 6

SLIDE, multiply 3*6

3x² + 11x + 6

Solve the Puzzle. What two numbers multiply to 18 and add to 11.

1*18

2*9

3*6

3x²

+ 6

Now we divided 11x into two pieces 2x and 9x.

3x² + 2x + 9x + 6

Factor by grouping.

3x² + 2x + 9x + 6

Factor the GCF from each part.

x(3x+2) + 3(3x+2)

(3x+2)(x+3)

Put the 2 back.

2(3x+2)(x+3)

Answer: 2(3x+2)(x+3)

Factor. 8x² − 28x + 20

Show Answer

GCF is 4.

4(2x² − 7x + 5)

2x² − 7x + 5

SLIDE, multiply 2*5

2x² − 7x + 5

Solve the Puzzle. What two numbers multiply to 10 and add to −7.

(−1)*(−10)

(−2)*(−5)

2x²

+ 5

Now we divided −7x into two pieces −2x and −5x.

2x² − 2x − 5x + 5

Factor by grouping.

2x² − 2x − 5x + 5

Factor the GCF from each part.

2x(x−1) − 5(x−1)

(2x−5)(x−1)

Put the 4 back.

4(2x−5)(x−1)

Answer: 4(2x−5)(x−1)

Factor. 6x² + 9x − 15

Show Answer

GCF is 3.

3(2x² + 3x − 5)

2x² + 3x − 5

SLIDE, multiply 2*(−5)

2x² + 3x − 5

Solve the Puzzle. What two numbers multiply to −10 and add to 3.

(−1)*10

1*(−10)

(−2)*5

2*(−5)

2x²

− 5

Now we divided 3x into two pieces −2x and 5x.

2x² − 2x + 5x − 5

Factor by grouping.

2x² − 2x + 5x − 5

Factor the GCF from each part.

2x(x−1) + 5(x−1)

(2x+5)(x−1)

Put the 3 back.

3(2x+5)(x−1)

Answer: 3(2x+5)(x−1)

Factor. 10x² − 5x − 30

Show Answer

GCF is 5.

5(2x² − x − 6)

2x² − x − 6

SLIDE, multiply 2*(−6)

2x² − x − 6

Solve the Puzzle. What two numbers multiply to −12 and add to −1.

(−1)*12

1*(−12)

(−2)*6

2*(−6)

(−3)*4

3*(−4)

2x²

− 6

Now we divided −x into two pieces 3x and −4x.

2x² + 3x − 4x − 6

Factor by grouping.

2x² + 3x − 4x − 6

Factor the GCF from each part.

x(2x+3) − 2(2x+3)

(2x+3)(x−2)

Put the 5 back.

5(2x+3)(x−2)

Answer: 5(2x+3)(x−2)

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