Factoring Polynomials with a CMF (Common Monomial Factor)

Factoring Polynomials with a CMF (Common Monomial Factor)

LESSON NO.1

PATTERN NO. 1

• ax + ay = a(x + y)

• bm + bn = b(m + n)

• abx - aby = ab(x - y)

• cdx - cdy = cd(x - y)

STEP NO.1

Find the common numerical coefficient.

PATTERN NO. 2

• axm + axn = ax(m + n)

• bym - byn = by(m - n )

• dzm + dzn = dz(m + n)

STEP NO. 2

Find the common literal coefficient.

STEP NO. 3

Apply DPMA or Distributive Property of Multiplication over Addition.

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.

Multiple Choice

Factor the polynomial: 3x + 3y.

• 3(x + y)

• 3(x - y)

• x(3 + y)

• y(x - 3)

Multiple Choice

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

• x

• y

• 5

• -5

Multiple Choice

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

• 3

• x

• m

• n

Multiple Choice

Factor: 2xm + 3xn

• m(2x + 3n)

• n(2m + 3x)

• 6(mx + nx)

• x(2m + 3n)

Multiple Choice

Factor: 12a - 6b

• 6(2a - b)

• 6(2a + b)

• 12(a - b)

• 12(a + b)

Multiple Choice

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

• 5a

• 5b

• 5x

• 5

Multiple Choice

Factor the polynomial 15ax - 25bx.

• 5a(3x - 5b)

• 5b(3x - 5x)

• 5x(3a - 5b)

• 5(3ax - 5bx)

Multiple Choice

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

• True

• False

Multiple Choice

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

• True

• False

Multiple Select

Which of the following has a common monomial factor?

• 2x - 2y + 3m

• 12mn + 16m - 15n

• 20ab + 10ac + 30ad

CONGRATULATIONS!