Question

Factor the expression completely.

$x^2+5x-14$

Short answer

Factorized form of $x^2+5x-14$is$\left(x+7\right)\left(x-2\right)$

Step-by-step solution

Step 1. Understanding the concept of factorizing a quadratic equation or expression.

An expression in the form $a{x}^2+bx+c$, we shall find two numbers that multiply to give acand add to give b.

Step 2. Re write the expression after breaking the expression into the numbers.

Here the required numbers are 7 and$-2$

$x^2+5x-14=x^2-2x+7x-14$

Step 3. Factorize the equation taking common terms out.

$\begin{array}{c}{\text{x}}^2-2\text{x}+7\text{x}-14=\text{x}\left(x-2\right)+7\left(x-2\right)\\ =\left(x+7\right)\left(x-2\right)\end{array}$