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Math Coach Amy
Amy Ferguson Moncure

H Algebra 2/Trig · Unit 3

Divide by a Monomial

Split the fraction and divide each term by the monomial.

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Key Ideas Easy Medium Hard

a + bc = ac + bc

Subtract the exponents.

What to Remember

One term at a time

Split the fraction. Divide the numbers, then subtract the exponents.

A term with a smaller exponent than the divisor stays over x.

Level 1

Easy

Every term divides evenly.

Example
Divide. 6x⁴ + 9x²3x

Divide each term by 3x.

6x⁴3x

= 2x³

9x²3x

= 3x

Put the terms back together.

2x³ + 3x

Answer: 2x³ + 3x

1
Divide. 8x⁵ + 4x³2x
Show Answer

Divide each term by 2x.

8x⁵2x

= 4x⁴

4x³2x

= 2x²

Put the terms back together.

4x⁴ + 2x²

Answer: 4x⁴ + 2x²

2
Divide. 12x⁴ − 6x²6x
Show Answer

Divide each term by 6x.

12x⁴6x

= 2x³

−6x²6x

= −x

Put the terms back together.

2x³ − x

Answer: 2x³ − x

3
Divide. 15x³ + 10x²5x
Show Answer

Divide each term by 5x.

15x³5x

= 3x²

10x²5x

= 2x

Put the terms back together.

3x² + 2x

Answer: 3x² + 2x

4
Divide. −18x⁶ + 9x³9x²
Show Answer

Divide each term by 9x².

−18x⁶9x²

= −2x⁴

9x³9x²

= x

Put the terms back together.

−2x⁴ + x

Answer: −2x⁴ + x

5
Divide. 14x⁵ + 21x²7x
Show Answer

Divide each term by 7x.

14x⁵7x

= 2x⁴

21x²7x

= 3x

Put the terms back together.

2x⁴ + 3x

Answer: 2x⁴ + 3x

Level 2

Medium

A coefficient becomes a fraction.

Example
Divide. 8x⁴ + 2x²4x

Divide each term by 4x.

8x⁴4x

= 2x³

2x²4x

= 12x

Put the terms back together.

2x³ + 12x

Answer: 2x³ + 12x

1
Divide. 6x⁵ + 3x²6x
Show Answer

Divide each term by 6x.

6x⁵6x

= x⁴

3x²6x

= 12x

Put the terms back together.

x⁴ + 12x

Answer: x⁴ + 12x

2
Divide. 10x⁴ − 4x³4x
Show Answer

Divide each term by 4x.

10x⁴4x

= 52x³

−4x³4x

= −x²

Put the terms back together.

52x³ − x²

Answer: 52x³ − x²

3
Divide. 9x³ + 3x6x
Show Answer

Divide each term by 6x.

9x³6x

= 32x²

3x6x

= 12

Put the terms back together.

32x² + 12

Answer: 32x² + 12

4
Divide. 12x⁵ + 8x²8x
Show Answer

Divide each term by 8x.

12x⁵8x

= 32x⁴

8x²8x

= x

Put the terms back together.

32x⁴ + x

Answer: 32x⁴ + x

5
Divide. −15x⁴ + 5x²10x
Show Answer

Divide each term by 10x.

−15x⁴10x

= −32x³

5x²10x

= 12x

Put the terms back together.

−32x³ + 12x

Answer: −32x³ + 12x

Level 3

Hard

A constant, or another low power, stays in the denominator.

Example
Divide. 10x⁴ − 3x² + 42x

Divide each term by 2x.

10x⁴2x

= 5x³

−3x²2x

= −32x

42x

= 2x

Put the terms back together.

5x³ − 32x + 2x

Answer: 5x³ − 32x + 2x

1
Divide. 6x³ + 5x − 23x
Show Answer

Divide each term by 3x.

6x³3x

= 2x²

5x3x

= 53

−23x

= −23x

Put the terms back together.

2x² + 53 − 23x

Answer: 2x² + 53 − 23x

2
Divide. 8x⁵ − 2x² + 64x
Show Answer

Divide each term by 4x.

8x⁵4x

= 2x⁴

−2x²4x

= −12x

64x

= 32x

Put the terms back together.

2x⁴ − 12x + 32x

Answer: 2x⁴ − 12x + 32x

3
Divide. 9x⁴ + 33x
Show Answer

Divide each term by 3x.

9x⁴3x

= 3x³

33x

= 1x

Put the terms back together.

3x³ + 1x

Answer: 3x³ + 1x

4
Divide. 12x⁵ − 8x² + 44x
Show Answer

Divide each term by 4x.

12x⁵4x

= 3x⁴

−8x²4x

= −2x

44x

= 1x

Put the terms back together.

3x⁴ − 2x + 1x

Answer: 3x⁴ − 2x + 1x

5
Divide. 15x³ + 6x − 33x
Show Answer

Divide each term by 3x.

15x³3x

= 5x²

6x3x

= 2

−33x

= −1x

Put the terms back together.

5x² + 2 − 1x

Answer: 5x² + 2 − 1x

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