Question

Help please

Using the remainder theorem see if (x-2) and (x+5) are factors of the polynomial

X^2+3x-10

Answer 1

See explanations below

Explanation:

Given the polynomial function

P(x) = X^2+3x-10

To check whether x-2 and x+5 are factor, we will find x and then show that P(x) = 0

For x-2

x - 2 = 0

x =2

P(2) = 2²+3(2)-10

P(2) = 4+6 -10

P(2) = 10-10

P(2) = 0

Since the remainder is zero, hence x-2 is a factor of the polynomial

Similarly for x+5;

x+5 = 0

x = -5

P(-5) = (-5)²+3(-5)-10

P(-5) = 25-15-10

P(-5) = 10-10

P(-5) = 0

This also shows that x+5 is a factor