Pascha is factoring the polynomial, which has four terms. 3 x cubed minus 15 x squared plus 8 x minus 40 3 x squared open paren x minus 5 close paren plus 8 times open paren x minus 5 close paren Which is the completely factored form of her polynomial?
Answer
A
open paren 3 x squared plus 8 close paren times open paren x minus 5 close paren
B
open paren 3 x squared minus 5 close paren times open paren x plus 8 close paren
C
open paren 3 x squared minus 8 close paren times open paren x plus 5 close paren
D
open paren 3 x squared plus 5 close paren times open paren x minus 8 close paren
Explanation
Group the terms: 3x³ − 15x² + 8x − 40 = 3x²(x − 5) + 8(x − 5). Both groups contain the common factor (x − 5), so factoring it out gives (3x² + 8)(x − 5). This matches choice A.
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