# How do you factor #3x ^ { 2} + 8x - 528= 0#?

##### 3 Answers

#### Explanation:

To factor

In

As product is negative, the factors of

Factors of

Now

Hence,

or

or

i.e.

#### Explanation:

This can be factored by completing the square.

Given:

#f(x) = 3x^2+8x-528#

To make the arithmetic less messy, we can premultiply by

We will also use the difference of squares identity:

#a^2-b^2 = (a-b)(a+b)#

with

#3f(x) = 3(3x^2+8x-528)#

#color(white)(3f(x)) = 9x^2+24x-1584#

#color(white)(3f(x)) = (3x)^2+2(3x)(4)+16-1600#

#color(white)(3f(x)) = (3x+4)^2-40^2#

#color(white)(3f(x)) = ((3x+4)-40)((3x+4)+40)#

#color(white)(3f(x)) = (3x-36)(3x+44)#

#color(white)(3f(x)) = 3(x-12)(3x+44)#

Dividing both ends by

#3x^2+8x-528 = (x-12)(3x+44)#

So the given equation can be written:

#(x-12)(3x+44) = 0#

which has zeros

#### Explanation:

The first step is to determine whether there are factors.

We need to find factors of

The smaller the value of

Use some trial and error starting from

Now combine factors of

We have the factors, now add in the signs to get

If we use the factors to solve the equation we get: