Question

b) Find the value of 'p' for which the polynomial 2x4 + 3x3 + 2px2 + 3x +6
is divided by (x + 2).
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Answer 1

Hope you understand my hand writing

Answer 2

Answer:

value of p is -1

Step-by-step explanation:

p(x) = 2x⁴ + 3x³ + 2px² + 3x + 6

It is given that, Polynomial p(x) is divisible by (x+2), so (x+2) is a factor of polynomial p(x).

(x+2) = 0

=> x = -2

Put x = -2 in polynomial p(x).

2(-2)⁴ + 3(-2)³ + 2p(-2)² + 3(-2) + 6 = 0

=> 2(16) + 3(-8) + 2p(4) + 3(-2) + 6 = 0

=> 32 - 24 + 8p - 6 + 6 = 0

=> 8 + 8p = 0

=> 8p = -8

=> p = -8/8

=> p = -1

Therefore, value of p is -1.