Factor f(x)=x^4+x^3-11x^2-9x+18

Factor ${\displaystyle x}$ out of ${\displaystyle x^3}$.

Factor ${\displaystyle x}$ out of ${\displaystyle -9x}$.

Factor ${\displaystyle x}$ out of ${\displaystyle x\cdot x^2+x\cdot -9}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=x}$ and ${\displaystyle b=3}$.

Remove unnecessary parentheses.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 18}$ and whose sum is ${\displaystyle -11}$.

Write the factored form using these integers.

Factor ${\displaystyle (x+3)(x-3)}$ out of ${\displaystyle x(x+3)(x-3)}$.

Factor ${\displaystyle (x+3)(x-3)}$ out of ${\displaystyle (x+3)(x-3)\left(x\right)+(x+3)(x-3)(x^2-2)}$.

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle -2}$ and whose sum is ${\displaystyle 1}$.

Write the factored form using these integers.

Replace all occurrences of ${\displaystyle u}$ with ${\displaystyle x}$.

Remove unnecessary parentheses.