Factoring Polynomials with a CMF (Common Monomial Factor) - Quizizz

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Factoring Polynomials with a CMF (Common Monomial Factor)

7th - 9th grade

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Mathematics

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Slide 1
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Factoring Polynomials with a CMF (Common Monomial Factor)
LESSON NO.1
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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)
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Slide 3
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STEP NO.1
Find the common numerical coefficient.
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Slide 4
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PATTERN NO. 2
axm + axn = ax(m + n)
bym - byn = by(m - n )
dzm + dzn = dz(m + n)
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Slide 5
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STEP NO. 2
Find the common literal coefficient.
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Slide 6
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STEP NO. 3
Apply DPMA or Distributive Property of Multiplication over Addition.
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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.
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Question 8
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Q.
Factor the polynomial: 3x + 3y.
answer choices
3(x + y)
3(x - y)
x(3 + y)
y(x - 3)
<p>3(x + y)</p>
alternatives
<p>3(x - y)</p>
<p>x(3 + y)</p>
<p>y(x - 3)</p>
answer explanation
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Question 9
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Q.
What is the common numerical coefficient in 5x - 5y?
answer choices
x
y
5
-5
<p>x</p>
alternatives
<p>y</p>
<p>5</p>
<p>-5</p>
answer explanation
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Question 10
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Q.
What is the common literal coefficient of 3xm - 4xn?
answer choices
3
x
m
n
<p>3</p>
alternatives
<p>x</p>
<p>m</p>
<p>n</p>
answer explanation
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Question 11
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Q.
Factor: 2xm + 3xn
answer choices
m(2x + 3n)
n(2m + 3x)
6(mx + nx)
x(2m + 3n)
<p>m(2x + 3n)</p>
alternatives
<p>n(2m + 3x)</p>
<p>6(mx + nx)</p>
<p>x(2m + 3n)</p>
answer explanation
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Question 12
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Q.
Factor: 12a - 6b
answer choices
6(2a - b)
6(2a + b)
12(a - b)
12(a + b)
<p>6(2a - b)</p>
alternatives
<p>6(2a + b)</p>
<p>12(a - b)</p>
<p>12(a + b)</p>
answer explanation
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Question 13
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Q.
What is the common monomial factor of 15ax - 25bx?
answer choices
5a
5b
5x
5
<p>5a</p>
alternatives
<p>5b</p>
<p>5x</p>
<p>5</p>
answer explanation
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Question 14
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Q.
Factor the polynomial 15ax - 25bx.
answer choices
5a(3x - 5b)
5b(3x - 5x)
5x(3a - 5b)
5(3ax - 5bx)
<p>5a(3x - 5b)</p>
alternatives
<p>5b(3x - 5x)</p>
<p>5x(3a - 5b)</p>
<p>5(3ax - 5bx)</p>
answer explanation
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Question 15
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Q.
TRUE or FALSE: The common monomial factor of 21mx + 49my - 63mz is 7m.
answer choices
True
False
<p>True</p>
alternatives
<p>False</p>
answer explanation
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Question 16
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Q.
TRUE or FALSE: The common monomial factor of 6x²y + 12xy - 24xy² is 3xy.
answer choices
True
False
<p>True</p>
alternatives
<p>False</p>
answer explanation
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Question 17
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Q.
Which of the following has a common monomial factor?
answer choices
2x - 2y + 3m
12mn + 16m - 15n
20ab + 10ac + 30ad
<p>2x - 2y + 3m</p>
alternatives
<p>12mn + 16m - 15n</p>
<p>20ab + 10ac + 30ad</p>
answer explanation
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Slide 18
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CONGRATULATIONS!
Bullet 1
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Bullet 7
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