Question

Without performing the long division, showthat 3x^4 + 4x^3-12x^2 - x - 30 is a multiple ofx²+x-6.​

Answer 1

If the polynomial is divisible by $x^2+x-6$

It will be divisible by both $x-2$ and $x+3$.

According to the factor theorem

2 is the zero

Shown below.

-3 is the zero

Shown below.

HENCE SHOWN

CALCULATION

2 is the zero

$3\times 16+4\times 8 -12\times 4 -2-30=48+32-48-32=0$

-3 is the zero

$3^5-4\times3^3-4\times 3^3+(3-30)=3^5-8\times3^3-3^3=3^5-3^5=0$