Question

Please help me factor the following problem.

x^3+2x^2-13x+10

Answer 1

can you find a root a ?

Answer 2

I assume you know how to use the rational root test?

Answer 3

applying the rational root test to the equation, recall that we need to check for factor of the leading coefficient, and the constant

that is the factors of \(\bf \color{red}{1}x^3+2x^2-13x+\color{red}{10}\)

the leading coefficient factors will be used as the denominator
the constant factors are used as numerators

so 1 factors are 1 :)
and 10 factors are, 10, 2, 5, 1

so the likely combinations for a root we can use are \(\bf \pm\cfrac{10}{1}, \pm\cfrac{2}{1}, \pm\cfrac{5}{1}, \pm\cfrac{1}{1}\)

Answer 4

so let us try say..... the x - 2 = 0, that is. x = 2
so let us do some synthetic division on that
\(\large \begin{array}{llllrrrrlll}
2&|&1&2&-13&10\\
&|&&2&8&-10\\
\hline\\
&&1&4&-5&0
\end{array}\)

low and behold,"2" checks out, our remainder is 0, thus x - 2 is a root

and then you'd write the quotient dropping it by 1 exponential

so \(\bf x^3+2x^2-13x+10\implies (x-2)(x^2+4x-5)\)

as to factor out the quadratic...well, that should be simple