Question

Help with this please

Answer 1

Explanation:

x^2 + 7x + 12 = (x+3)(x+4)

you can use the Quadratic formula if you cannot figure out how to factorize it in your head ... use a =1 b = 7 c = 12 in Quadratic Formula

(x+3)(x+4) = 0

one (either) of the factors need to be zero for this to occur

(x+3) = 0 means x = -3

(x+4) = 0 means x = -4

Answer 2

Part (a)

`x^2+7x+12` factorizes to
`(x+3)(x+4)`

I used the AC method. It is a trial and error process used to factor quadratics. We look for two numbers that multiply to 12 and also add to 7. Those two values are 3 and 4

3*4 = 12

3+4 = 7

The quadratic formula is another method you can use to factor.

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Part (b)

`x^2+7x+12 = 0\\\\(x+3)(x+4) = 0\\\\x+3 = 0 \ \text{ or } \ x+4 = 0\\\\x = -3 \ \text{ or } \ x = -4\\`