The polynomials 𝑥3+𝑎 𝑥2−𝑥+𝑏x 3 +a x 2 −x+b and 𝑥3+𝑏 𝑥2−5 𝑥+3 𝑎x 3 +b x 2 −5 x+3 a both have 𝑥+2x+2 as a factor, the values of 𝑎a and 𝑏b are
Question
Solution 1
Given that both polynomials have x+2 as a factor, we can use the Factor Theorem which states that a polynomial f(x) has a factor (x-c) if and only if f(c) = 0.
For the first polynomial, x^3 + ax^2 - x + b, we substitute x = -2:
(-2)^3 + a(-2)^2 - (-2) + b = 0 -8 + 4a + 2 + b = 0 4a + b = 6 ----(1 Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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The polynomials 𝑥3+𝑎 𝑥2−𝑥+𝑏x 3 +a x 2 −x+b and 𝑥3+𝑏 𝑥2−5 𝑥+3 𝑎x 3 +b x 2 −5 x+3 a both have 𝑥+2x+2 as a factor, the values of 𝑎a and 𝑏b are
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