The factors of 3x3 − 7x2 + 4 are ______.

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KollegeApply · Accepted Answer

The factors of 3x3 − 7x2 + 4 are (x − 1) (x − 2) (3x + 2). Explanation: Let p(x) = 3x3 − 7x2 + 4 Factors of the constant term 4 are $\pm$1, $\pm$2, $\pm$4 Put x = 1; p(1) = 3(1)3 − 7(1)2 + 4 = 3 − 7 + 4 = 0 x − 1 is a factor of p(x). 3x2 − 4x − 4 `x − 1")"overline(3x^3 - 7x^2 + 0x + 4)` 3x3 − 3x2 − + − 4x2 + 0x − 4x2 + 4x + − − 4x2 + 4 − 4x2 + 4 + − x 3x3 − 7x2 + 4 = (x − 1) (3x2 − 4x − 4) = (x − 1) (3x2 − 2x + 2x − 4) = (x − 1) [3x(x − 2) + 2(x − 2)] = (x − 1) (x − 2) (3x + 2)

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