# How do you factor the expression x^2+4x-21?

Mar 6, 2018

$\left(x + 7\right) \left(x - 3\right)$

#### Explanation:

To factorise any quadratic polynomial , you could use 2 methods.
Here's the easy one
Let the quadratic polynomial be $a {x}^{2} + b x + c$

▪multiply $a \text{ and } c$ , then factorise the result into some factors, say y and z, $y + z = | b |$
${x}^{2} + 4 x - 21$ (a×c=-21=-3×7)

${x}^{2} + 7 x - 3 x - 21$

$x \left(x + 7\right) - 3 \left(x + 7\right)$

$\left(x + 7\right) \left(x - 3\right)$

The other method is a direct application of quadratic formula.

Mar 6, 2018

the answer is $\left(x + 7\right) \left(x - 3\right)$

#### Explanation:

there's an easier way to find this but only when it's ${x}^{2}$. since you know that two numbers have to multiply to give you $- 21$ and add to give you $4$ when you find it, you don't have to go through the whole process and you can just put them in the parenthesis since there's no number in front of $x$