Question

Use remainder theorem to prove that x-3 is a factor of x⁴-6x³ + ax + b if 3a+b = 81
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Answer 1

Step-by-step explanation:

Factors of x

2

−3x+2 are (x−1) and (x−2).

Let f(x)=x

4

−px

2

+q

Since, f(x) is divisible by (x−1) and (x−2)

∴f(1)=0 and f(2)=0

⇒f(1)=1

4

−p(1)

2

+q=0

and f(2)=2

4

−p(2)

2

+q=0

1−p+q=0....(i)

and 16−4p+q=0....(ii)

(i)−(ii), we get

−15+3p=0⇒p=5

putting value of p in eq. (i), we get q=4

Thus, we get

p=5 and q=4.