H Algebra 2/Trig · Unit 2
Set the equation equal to zero. Factor. Set each factor equal to zero. Solve.
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1. Set equal to zero
Move every term so one side is 0. The equation is ready to factor when you see = 0.
2. Factor
Factor the quadratic completely.
3. Set each factor equal to zero
If a product is 0, at least one factor is 0. Set each factor equal to 0.
4. Solve
Solve each linear equation.
Set both factors equal to zero and solve.
x = −7 and x = 3
Set both factors equal to zero and solve.
x = 4 and x = −23
x² + 6x + 5 = 0
(x + 1)(x + 5) = 0
x = −1 and x = −5
x² + 7x + 15 = 5
x² + 7x + 15 − 5 = 5 − 5
x² + 7x + 10 = 0
(x + 2)(x + 5) = 0
x = −2 and x = −5
Already factored and set equal to zero.
Set both factors equal to zero and solve.
Answer: x = −5 and x = 2
Set both factors equal to zero and solve.
Answer: x = 6 and x = −1
Set both factors equal to zero and solve.
Answer: x = −4 and x = 32
Set both factors equal to zero and solve.
Answer: x = −13 and x = 5
Set both factors equal to zero and solve.
Answer: x = −8 and x = −3
The equation is set equal to zero. Difference of squares and a = 1.
x² − 25 = 0
(x − 5)(x + 5) = 0
Answer: x = 5 and x = −5
x² + 8x + 12 = 0
(x + 6)(x + 2) = 0
Answer: x = −6 and x = −2
x² − 16 = 0
(x − 4)(x + 4) = 0
Answer: x = 4 and x = −4
x² − 3x − 10 = 0
(x − 5)(x + 2) = 0
Answer: x = 5 and x = −2
x² + 2x − 15 = 0
(x + 5)(x − 3) = 0
Answer: x = −5 and x = 3
The equation is set equal to zero. a > 1.
2x² + 5x + 2 = 0
(2x + 1)(x + 2) = 0
Answer: x = −12 and x = −2
3x² + 10x + 3 = 0
(3x + 1)(x + 3) = 0
Answer: x = −13 and x = −3
2x² − 7x + 3 = 0
(2x − 1)(x − 3) = 0
Answer: x = 12 and x = 3
3x² − 5x − 2 = 0
(3x + 1)(x − 2) = 0
Answer: x = −13 and x = 2
2x² + x − 6 = 0
(2x − 3)(x + 2) = 0
Answer: x = 32 and x = −2
Set the equation equal to zero first. a = 1.
x² + 9x + 20 = 2
x² + 9x + 20 − 2 = 2 − 2
x² + 9x + 18 = 0
(x + 6)(x + 3) = 0
Answer: x = −6 and x = −3
x² − 2x − 8 = 7
x² − 2x − 8 − 7 = 7 − 7
x² − 2x − 15 = 0
(x − 5)(x + 3) = 0
Answer: x = 5 and x = −3
x² + 5x = −6
x² + 5x + 6 = −6 + 6
x² + 5x + 6 = 0
(x + 2)(x + 3) = 0
Answer: x = −2 and x = −3
x² + 11x + 30 = 6
x² + 11x + 30 − 6 = 6 − 6
x² + 11x + 24 = 0
(x + 8)(x + 3) = 0
Answer: x = −8 and x = −3
x² − 7x = −12
x² − 7x + 12 = −12 + 12
x² − 7x + 12 = 0
(x − 3)(x − 4) = 0
Answer: x = 3 and x = 4
Set the equation equal to zero first. a > 1.
2x² + 7x + 5 = 2
2x² + 7x + 5 − 2 = 2 − 2
2x² + 7x + 3 = 0
(2x + 1)(x + 3) = 0
Answer: x = −12 and x = −3
3x² + 4x = 4
3x² + 4x − 4 = 4 − 4
3x² + 4x − 4 = 0
(3x − 2)(x + 2) = 0
Answer: x = 23 and x = −2
2x² − x = 6
2x² − x − 6 = 6 − 6
2x² − x − 6 = 0
(2x + 3)(x − 2) = 0
Answer: x = −32 and x = 2
4x² + 5x = 6
4x² + 5x − 6 = 6 − 6
4x² + 5x − 6 = 0
(4x − 3)(x + 2) = 0
Answer: x = 34 and x = −2
2x² + 9x + 10 = 3
2x² + 9x + 10 − 3 = 3 − 3
2x² + 9x + 7 = 0
(2x + 7)(x + 1) = 0
Answer: x = −72 and x = −1
Six problems from Easy, Medium, and Hard.
x² − 5x + 6 = 0
(x − 2)(x − 3) = 0
Answer: x = 2 and x = 3
Set both factors equal to zero and solve.
Answer: x = 8 and x = −2
3x² + 5x = 2
3x² + 5x − 2 = 2 − 2
3x² + 5x − 2 = 0
(3x − 1)(x + 2) = 0
Answer: x = 13 and x = −2
x² − 49 = 0
(x − 7)(x + 7) = 0
Answer: x = 7 and x = −7
x² + 8x + 15 = 3
x² + 8x + 15 − 3 = 3 − 3
x² + 8x + 12 = 0
(x + 6)(x + 2) = 0
Answer: x = −6 and x = −2
2x² + 11x + 5 = 0
(2x + 1)(x + 5) = 0
Answer: x = −12 and x = −5
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