Question

Facrtor completely 4x^2-8x-60A.(4x-20)(x+3)B. 4(x-5)(x+3)C. (4x-4)(x+15)D. 4(x-1)(x+15)

Answer 1

`4x^2-8x-60\text{ = 4(x-5)(x+3)}`

Here, we want to factor the given polynomial

The easiest way to go about this is to factor out the highest common factor which is 4 in this case

Thus, we have;

`4x^2-8x-60=4(x^2-2x-15)`

So, we can proceed to factor what we have in the bracket

We can do this by finding two factors which when added gives -2x and when multiplied will give -15x^2

Thus, we have;

`\begin{gathered} x^2-2x-15=x^2-5x+3x-15 \\ =\text{ x(x-5)+3(x-5)} \\ =\text{ (x+3)(x-5)} \end{gathered}`

From here, we proceed to replace the 4 we removed and we get the initial polynomial

Hence;

`4x^2-8x-60\text{ = 4(x-5)(x+3)}`