Question

if axcube + bxsquare +x - 6 has (x+2) as a factor and leaves a reminder 4 when divided by (x-2),find the values of 'a' and 'b'​

Answer 1

Step-by-step explanation:

Let p(x) = ax³ + bx²+x-6

A/C to question,

(x + 2) is the factor of p(x), and we know this is possible only when p(-2) = 0 So, p(2)= a(-2)3 + b(-2)² - 2 - 6=0

⇒-8a + 4b-8=0 ⇒ 2a-b+ 2 = 0-(1)

again, question said that if we p(x) is divided by ( x-2) then it leaves remainder 4. so, P(2) = a(2)³ + b(2)² + 2 - 6 = 4

⇒8a + 4b - 4 = 4

2a + b -2 = 0 -----(2)

solve equations (1) and (2), 4a=0⇒a= 0 and b =2

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