If both (x − 2) and (x + 3) are factors of x³ + ax² + bx − 12, then:

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Accepted Answer

a = 3, b = −4. p(2) = 8 + 4a + 2b − 12 = 0 gives 2a + b = 2, and p(−3) = −27 + 9a − 3b − 12 = 0 gives 3a − b = 13. Adding, 5a = 15, so a = 3 and b = −4. Indeed x³ + 3x² − 4x − 12 = (x − 2)(x + 2)(x + 3).

If both $(x - 2)$ and $(x + 3)$ are factors of $x^{3} + a x^{2} + b x - 12$ , then:

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If both (x−2) and (x+3) are factors of x3+ax2+bx−12, then:

Step-by-Step Solution

Master this topic in 30 minutes a day.

More Algebra practice

If both $(x - 2)$ and $(x + 3)$ are factors of $x^{3} + a x^{2} + b x - 12$ , then: