Lesson
Factoring Polynomials with a CMF (Common Monomial Factor)
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• Slide 1
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Factoring Polynomials with a CMF (Common Monomial Factor)

LESSON NO.1

• Slide 2
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PATTERN NO. 1

• ax + ay = a(x + y)

• bm + bn = b(m + n)

• abx - aby = ab(x - y)

• cdx - cdy = cd(x - y)

• Slide 3
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STEP NO.1

Find the common numerical coefficient.

• Slide 4
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PATTERN NO. 2

• axm + axn = ax(m + n)

• bym - byn = by(m - n )

• dzm + dzn = dz(m + n)

• Slide 5
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STEP NO. 2

Find the common literal coefficient.

• Slide 6
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STEP NO. 3

Apply DPMA or Distributive Property of Multiplication over Addition.

• Slide 7
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SUMMARY

TO FACTOR POLYNOMIALS WITH A COMMON MONOMIAL FACTOR:

1. Find the common numerical coefficient (always express the numerical coefficient in prime factored form);

2. Find the common literal coefficient. (always choose the common variable with the least exponent)

3. Factor out the CMF using DPMA or Distributive Property of Multiplication over Addition.

• Question 8
10 seconds
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Q.

Factor the polynomial: 3x + 3y.

3(x + y)

3(x - y)

x(3 + y)

y(x - 3)

• Question 9
5 seconds
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Q.

What is the common numerical coefficient in 5x - 5y?

x

y

5

-5

• Question 10
10 seconds
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Q.

What is the common literal coefficient of 3xm - 4xn?

3

x

m

n

• Question 11
45 seconds
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Q.

Factor: 2xm + 3xn

m(2x + 3n)

n(2m + 3x)

6(mx + nx)

x(2m + 3n)

• Question 12
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Q.

Factor: 12a - 6b

6(2a - b)

6(2a + b)

12(a - b)

12(a + b)

• Question 13
45 seconds
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Q.

What is the common monomial factor of 15ax - 25bx?

5a

5b

5x

5

• Question 14
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Q.

Factor the polynomial 15ax - 25bx.

5a(3x - 5b)

5b(3x - 5x)

5x(3a - 5b)

5(3ax - 5bx)

• Question 15
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Q.

TRUE or FALSE: The common monomial factor of 21mx + 49my - 63mz is 7m.

True

False

• Question 16
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Q.

TRUE or FALSE: The common monomial factor of 6x2 y + 12xy - 24xy2 is 3xy.

True

False

• Question 17
45 seconds
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Q.

Which of the following has a common monomial factor?

2x - 2y + 3m

12mn + 16m - 15n

20ab + 10ac + 30ad

• Slide 18
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CONGRATULATIONS!

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