Question

1.
Is (x + 5) a factor of 4x^2 + 23x + 5 ?​

Answer 1

$\sf \Large Solution!!$

$\sf \large Let's\:understand\:the \:question.$

If (x + 5) is a factor of 4x² + 23x + 5, then the remainder will be zero. So let's find out if the remainder is zero and (x + 5) is a factor of the given polynomial or the remainder is not zero and (x + 5) is not a factor of the given polynomial.

$\to$ x + 5 = 0

$\to$ x = -5

$\sf \large Now,$

$\to$ f(x) = 4x² + 23x + 5

$\to$ f(-5) = 4(-5)² + 23(-5) + 5

$\to$ f(-5) = 4(25) - 115 + 5

$\to$ f(-5) = 100 - 115 + 5

$\to$ f(-5) = -10

As we can see that the remainder is not equal to 0, then (x + 5) is not a factor of the given polynomial.