Question

Q4 if (x - 2) be a factor of the polynomial p(x) = 2x3 + 3x2 - 5x + k, find the value of k?
Q5 What is the value of p when px3 + 16x2 + 8x - 32 is divided by (x + 2), leaving a 0 as remainder?
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Answer 1

4. given (x - 2) is a factor of p(x) = 2x³ + 3x² - 5x + k

therefore 2 is a zero of p(x)

p(2) = 2(2)³ + 3(2)² - 5(2) + k = 0

➡ 16 + 12 - 10 + k = 0

➡ 28 - 10 + k = 0

➡ 18 + k = 0

➡ k = -18

5. leaving 0 remainder means (x + 2) is a factor of the polynomial p(x) = px³ + 16x² + 8x - 32 and -2 is a zero of polynomial p(x)

p(-2) = p(-2)³ + 16(-2)² + 8(-2) - 32 = 0

➡ -8p + 32 - 16 - 32 = 0

➡ -8p - 16 = 0

➡ -8p = 16

➡ p = -16/8

➡ p = -2

Answer 2

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