Question

Write polynomial $P$ as a product of linear factors:$P\left(x\right)=5x^3-2x^2+5x-2$

• A. $P\left(x\right)=(x+i)(x-i)(5x+2)$
• B. $P\left(x\right)=(x+i)(x-i)(5x-2)$
• C. $P\left(x\right)=(x+2i)(x-2i)(x-2)$
• D. $P\left(x\right)=(x+2i)(x-2i)(5x+2)$

Answer 1

The correct option is B $P\left(x\right)=(x+i)(x-i)(5x-2)$

Given the polynomial $P\left(x\right)=5x^3-2x^2+5x-2$

We need to factor $P\left(x\right)$.

First we will rearrange the terms of $P\left(x\right)$.

$\Rightarrow P\left(x\right)=5x^3+5x-2x^2-2$

Now we will factor $5x$ from the first two terms.

$\Rightarrow P\left(x\right)=5x(x^2+1)-2x^2-2$

Now we will factor $-2$ from the last two terms.

$\Rightarrow P\left(x\right)=5x(x^2+1)-2(x^2+1)$

Now we will factor $(x^2+1)$.

$\Rightarrow P\left(x\right)=(x^2+1)(5x-2)$

Now we will factor $(x^2+1)$

Hence, $P\left(x\right)=(x-i)(x+i)(5x-2)$