Question

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

• A. x+1 & $4x^2$-3x+8
• B. x-2 & $3x^2$-x+2
• C. x-1 & $4x^2$ + 8

Answer 1

The correct option is A x+1 & $4x^2$-3x+8

The constant term in the given polynomial is 8.

The given polynomial $4x^3+x^2+5x+8$ is divided by 4 to get,

$x^3+\frac{1}{4}{x}^2+\frac{5}{4}x+2$.

We divide the polynomial by 4 to make the coefficient of the highest power as 1. This helps in determining the number of factors in the constant term.

One of the zeros of the polynomial can be found by verifying the factors of 2.
i.e., factors of 2: x = -1, -2, 1 and 2.

$P(-1)=4\times {(-1)}^3+{(-1)}^2+5\times (-1)+8$
$=-4+1-5+8=0$

$P\left(x\right)=0\text{at}x=-1\Rightarrow x+1=0$, which means that $(x+1)$ is a factor of the polynomial $P\left(x\right)$.

Lets divide $P\left(x\right)$ by $(x+1)$ to get the other factor.

$4x^2-3x+8x+1)\overline{4x^3+x^2+5x+8}\underset{–}{{}_{-}4x^3\pm 4x^2}\underset{–}{-3x^2+5x\mp 3x^2\mp 3x}\underset{–}{8x+8{}^{}{}_{-}8x\pm 8}00$

The factors are $x+1\&4x^2-3x+8.$