Question

Is $(x-1),$ a factor of $8x^4+12x^3-18x+14$ ?

• A. Yes
• B. Cannot be determined from given data.
• C. No

Answer 1

The correct option is C No

Factor theorem states if $p\left(x\right)$ is a polynomial of degree $n\ge 1$ and a is any real number then $x–a$ is a factor of $p\left(x\right)$, if and only if $p\left(a\right)=0$

Given equation is $p\left(x\right)=8x^4+12x^3-18x+14$
By using factor theorem, $(x-1)$ is a factor of $p\left(x\right)$ only if $p\left(1\right)=0$

Here, $p\left(1\right)=8(1{)}^4+12(1{)}^3-18\left(1\right)+14$
$=8+12-18+14$
$=34-18=16\ne 0$
Hence, $(x-1)$ is not a factor of $p\left(x\right)$