Question

introduction homework (standard 0)
score: 8/28 answered: 8/25
question 9
factor:
$x^2 + 13x + 36 = $
$x^2 + 5x - 36 = $
$x^2 - 5x - 36 = $
$x^2 - 13x + 36 = $
question help: video message instructor post to

Explanation:

For \(x^{2}+13x + 36\)

Step1: Find two numbers that multiply to 36 and add to 13.

The numbers are 4 and 9 since \(4\times9 = 36\) and \(4 + 9=13\).

Step2: Factor the quadratic.

Using the formula \(x^{2}+(a + b)x+ab=(x + a)(x + b)\), we get \((x + 4)(x + 9)\).

For \(x^{2}+5x - 36\)

Step1: Find two numbers that multiply to - 36 and add to 5.

The numbers are 9 and - 4 since \(9\times(-4)=-36\) and \(9+( - 4)=5\).

Step2: Factor the quadratic.

Using the formula \(x^{2}+(a + b)x+ab=(x + a)(x + b)\), we get \((x + 9)(x-4)\).

For \(x^{2}-5x - 36\)

Step1: Find two numbers that multiply to - 36 and add to - 5.

The numbers are - 9 and 4 since \((-9)\times4=-36\) and \(-9 + 4=-5\).

Step2: Factor the quadratic.

Using the formula \(x^{2}+(a + b)x+ab=(x + a)(x + b)\), we get \((x-9)(x + 4)\).

For \(x^{2}-13x + 36\)

Answer:

\(x^{2}+13x + 36=\boldsymbol{(x + 4)(x + 9)}\)

\(x^{2}+5x - 36=\boldsymbol{(x + 9)(x-4)}\)

\(x^{2}-5x - 36=\boldsymbol{(x-9)(x + 4)}\)

\(x^{2}-13x + 36=\boldsymbol{(x-4)(x - 9)}\)