Question

Determine if x - 2 is a factor of p(x) = x^4 - 3x^2 + 2x - 8, and explain why

Answer 1

At First

x-2=0
x=2

P(x)=x⁴-3x²+2x-8
p(2)=(2)⁴-3(2)²+2(2)-8
p(2)= 16-3×4+4-8
= 16-12+4-8
= 0

Answer 2

Yes, (x-2) is a factor of the polynomial p(x)= x⁴-3x²+2x-8.

Given:-

(x-2) is a factor of the polynomial x⁴-3x²+2x-8.

To Find:-

to determine whether (x-2) is factor of p(x)= x⁴-3x²+2x-8

Solution:-

According to Remainder Theorem, if (x-a) is a factor of p(x) then x=a is the root of polynomial p(x) i.e. p(a)=0

Putting (x-2)=0

x=2

Put x=2 in the polynomial

p(x)= x⁴-3x²+2x-8

p(2)= (2)⁴-3(2)²+2(2)-8

p(2)= 16-12+4-8

p(2)=4+4-8

p(2)=8-8=0

So, 2 is the root of the polynomial p(x)=x⁴-3x²+2x-8. Then according to remainder theorem (x-2) is factor of the polynomial.

Hence, (x-2) is the factor of the polynomial p(x)=x⁴-3x²+2x-8.

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