Question

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

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

Answer 1

The correct option is A $(x+1)$, $(4x^2–3x+8)$

Let us assume that atleast one of the zeroes is an integer. Product of the factors is equal to the constant term (+8). Possible roots are the factors of +8. Hence, possible factors are:
$\pm 1,\pm 2,\pm 4,\pm 8$.

Trying -1, we get:
$p(-1)=4\times {(-1)}^3+{(-1)}^2+5\times (-1)+8$
$p(-1)=-4+1-5+8=0$
So, (x + 1) is a factor of the polynomial P(x).

The quotient obtained when p(x) is divided by (x + 1) is 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 $x+1\&4x^2-3x+8$.