Wen is factoring the polynomial, which has four terms. 6 x cubed minus 12 x squared plus 7 x minus 14 6 x squared open paren x minus 2 close paren plus 7 times open paren x minus 2 close paren Which is the completely factored form of his polynomial?
Answer
A
open paren 6 x squared plus 2 close paren times open paren x minus 7 close paren
B
open paren 6 x squared minus 2 close paren times open paren x plus 7 close paren
C
open paren 6 x squared minus 7 close paren times open paren x plus 2 close paren
D
open paren 6 x squared plus 7 close paren times open paren x minus 2 close paren
Explanation
Group the terms: (6x³ − 12x²) + (7x − 14). Factoring each group gives 6x²(x − 2) + 7(x − 2), so the common factor is (x − 2). The completely factored form is (6x² + 7)(x − 2), which is choice D.
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