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Factorize these: a) 2x-12 b) 4x+2x2 c) 17y+51-34 d) -4x-12 e) 10x+15 f) 3x-21+6x

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Answers

6 parts
a

2(x - 6)

b

2x(2 + x)

c

17(y + 1)

d

-4(x + 3)

e

5(2x + 3)

f

3(3x - 7)

Step-by-step solution

14 steps

Here are the factorizations for each expression:

Part a· 2 steps

  1. Find the greatest common factor (GCF) of $2x$ and 12.

    The GCF is 2.

  2. Factor out the GCF.

    2x−12=2(x)−2(6)=2(x−6)2x - 12 = 2(x) - 2(6) = 2(x - 6)

    The factored expression is 2(x−6)\boxed{2(x - 6)}.

Part b2x(2 + x)

  1. Find the GCF of 4x4x and 2x22x^2.

    The GCF is $2x$.

  2. Factor out the GCF.

    4x+2x2=2x(2)+2x(x)=2x(2+x)4x + 2x^2 = 2x(2) + 2x(x) = 2x(2 + x)

    The factored expression is 2x(2+x)\boxed{2x(2 + x)}.

Part c17(y + 1)

  1. Combine the constant terms.

    17y+51−34=17y+1717y + 51 - 34 = 17y + 17

  2. Find the GCF of $17y$ and 17.

    The GCF is 17.

  3. Factor out the GCF.

    17y+17=17(y)+17(1)=17(y+1)17y + 17 = 17(y) + 17(1) = 17(y + 1)

    The factored expression is 17(y+1)\boxed{17(y + 1)}.

Part d-4(x + 3)

  1. Find the GCF of −4x-4x and −12-12.

    The GCF is −4-4.

  2. Factor out the GCF.

    −4x−12=−4(x)−4(3)=−4(x+3)-4x - 12 = -4(x) - 4(3) = -4(x + 3)

    The factored expression is −4(x+3)\boxed{-4(x + 3)}.

Part e5(2x + 3)

  1. Find the GCF of $10x$ and 15.

    The GCF is 5.

  2. Factor out the GCF.

    10x+15=5(2x)+5(3)=5(2x+3)10x + 15 = 5(2x) + 5(3) = 5(2x + 3)

    The factored expression is 5(2x+3)\boxed{5(2x + 3)}.

Part f3(3x - 7)

  1. Combine the like terms ($3x$ and $6x$).

    3x−21+6x=(3x+6x)−21=9x−213x - 21 + 6x = (3x + 6x) - 21 = 9x - 21

  2. Find the GCF of $9x$ and 21.

    The GCF is 3.

  3. Factor out the GCF.

    9x−21=3(3x)−3(7)=3(3x−7)9x - 21 = 3(3x) - 3(7) = 3(3x - 7)

    The factored expression is 3(3x−7)\boxed{3(3x - 7)}.

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