Question

is (x+1) is a factor of x3 - 20²+x-1, verity​

Answer 1

Given:-

• p(x) = x³ - 2x² + x - 1
• g(x) = (x + 1)

To verify:-

• If g(x) is a factor of p(x)

Answer:-

For this problem, we have to use the factor theorem. Factor theorem says that, (x - a) is a factor of p(x) if "a" is a root of p(x) [which means p(a) = 0].

Here,

g(x) = (x + 1)

→ g(x) = x - (-1)

It is now in the form of (x - a), with a = -1. Now we have to check if p(a) = p(-1) = 0

So,

p(x) = x³ - 2x² + x - 1

→ p(-1) = (-1)³ - 2(-1)² + (-1) - 1

→ p(-1) = -1 - 2(1) - 1 - 1

→ p(-1) = -1 - 2 - 1 - 1

→ p(-1) = -5

So,

-5 ≠ 0

→ p(-1) ≠ 0

As p(-1) ≠ 0, that means (-1) is not a zero of p(x) and hence we can conclude that x - (-1) = x + 1 is not a factor of x³ - 2x² + x - 1.

So, g(x) is not a factor of p(x).