Question

The factors of the polynomial equation P(x) = $4x^3+x^2+5x+8$ is

• A. (x + 1), (4x² – 3x + 8)
• B. (x + 2), (x² – 3x + 8)
• C. (x + 3), (x² + 8x – 3)
• D. (x + 4), (4x² + 3x – 8)

Answer 1

The correct option is A

(x + 1), (4x² – 3x + 8)

The constant term in the given polynomial is 8. But the given polynomial $4x^3+x^2+5x+8$ can also be written as $x^3+\frac{1}{4}{x}^2+\frac{5}{4}x+2$.

So one of the zeros of the polynomial can be obtained by finding the values of given polynomial at the factors of 2 i.e, 1,-1,-2,2.

Here we see that P(-1) = 0, which means that ($x$+1) is a factor of the polynomial P($x$).

The quotient obtained by dividing P($x$) by ($x$+1) is the other factor.