It's x power 3 plus 4x power 2 plus x minus %q

March 20, 2026Mathematics

ScanSolve AI Answer

March 20, 2026

Answer

(x-1)(x+2)(x+3)

Factor $x^3 + 4x^2 + x - 6$ .

Step 1: Apply the rational root theorem. Possible rational roots are $\pm1, \pm2, \pm3, \pm6$ .

Test $x=1$ :

\begin{align*} 1^3 +{}& 4(1)^2 + 1 - 6 \\ ={}& 1 + 4 + 1 - 6 \\ ={}& 0 \end{align*}

$x=1$ is a root, so $(x-1)$ is a factor.

Step 2: Synthetic division of $x^3 + 4x^2 + x - 6$ by $x-1$ :

\begin{array}{r|r} 1 & 1 & 4 & 1 & -6 \\ & & 1 & 5 & 6 \\ \hline & 1 & 5 & 6 & 0 \\ \end{array}

Quotient is $x^2 + 5x + 6$ .

Step 3: Factor $x^2 + 5x + 6$ :

\begin{align*} x^2 +{}& 5x + 6 \\ ={}& (x+2)(x+3) \end{align*}

Step 4: Complete factorization:

x^3 + 4x^2 + x - 6 = (x-1)(x+2)(x+3)

$\boxed{(x-1)(x+2)(x+3)}$

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question