QuestionFactor the expression: $x^{2}+4x+3$ .

Studdy Solution

STEP 1

Assumptions1. The given expression is $x^{}+4x+3$ . We need to factorize this expression

STEP 2

The given expression is a quadratic expression. A quadratic expression of the form $ax^{2}+bx+c$ can be factored as $(x-p)(x-q)$ , where $p$ and $q$ are the roots of the equation $ax^{2}+bx+c=0$ .

STEP 3

To find the roots of the equation, we need to solve the equation $x^{2}+x+3=0$ . The roots of this equation can be found using the formula $x = \frac{-b \pm \sqrt{b^{2}-ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients of $x^{2}$ , $x$ , and the constant term respectively.

STEP 4

In our equation, $a=1$ , $b=4$ , and $c=3$ . Substituting these values into the formula, we get $x = \frac{-4 \pm \sqrt{4^{2}-4(1)(3)}}{2(1)}$

STEP 5

implify the expression under the square root $x = \frac{-4 \pm \sqrt{16-12}}{2}$

STEP 6

Further simplify the expression $x = \frac{-4 \pm \sqrt{4}}{2}$

STEP 7

Calculate the square root $x = \frac{-4 \pm2}{2}$

STEP 8

This gives us two solutions $x = \frac{-4 +2}{2} = -1$ and $x = \frac{-4 -2}{2} = -3$

STEP 9

So, the roots of the equation are - and -3. Therefore, the factored form of the expression $x^{2}+4x+3$ is $(x+)(x+3)$ .
The factored form of $x^{2}+4x+3$ is $(x+)(x+3)$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms