Q4 if (x - 2) be a factor of the polynomial p(x) = 2x3 + 3x2 - 5x + k,

1.	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?
Answer» $\text{[math]}$ 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 $\text{[math]}$

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?

Answer»

$\text{[math]}$

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

$\text{[math]}$