Math  /  Algebra

QuestionFactor by grouping. 6x312x27x+146 x^{3}-12 x^{2}-7 x+14

Studdy Solution

STEP 1

1. The expression is a polynomial with four terms.
2. We can attempt to factor the polynomial by grouping terms.

STEP 2

1. Group the terms in pairs.
2. Factor out the greatest common factor from each pair.
3. Identify and factor out the common binomial factor.

STEP 3

Group the terms in pairs:
(6x312x2)+(7x+14) (6x^3 - 12x^2) + (-7x + 14)

STEP 4

Factor out the greatest common factor from each pair:
For the first pair (6x312x2) (6x^3 - 12x^2) , the greatest common factor is 6x2 6x^2 :
6x2(x2) 6x^2(x - 2)
For the second pair (7x+14) (-7x + 14) , the greatest common factor is 7 -7 :
7(x2) -7(x - 2)

STEP 5

Identify and factor out the common binomial factor (x2) (x - 2) :
6x2(x2)7(x2)=(6x27)(x2) 6x^2(x - 2) - 7(x - 2) = (6x^2 - 7)(x - 2)
The factored form of the polynomial is:
(6x27)(x2) \boxed{(6x^2 - 7)(x - 2)}

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