Question

2xsquare + 17x - 30 Need to factor completelyAnswer is (2x-3)(x+10)But, how to get to that answer??

Answer 1

We are given the following equation

`2x^2+17x-30`

Recall that the standard form of a quadratic equation is given by

`ax^2+bx+c`

By comparing the given equation with the standard form, we see that

 a  =  2

b  =  17

c  = -30

Now to factor the equation, we need to think about two numbers such that

When we multiply them, we get a*c = -60

When we add them, we get b = 17

Can you think of such two numbers?

How about 20 and -3?

When we multiply them we get, 20*-3 = -60 (satisfied)

When we add them together we get, 20 - 3 = 17 (satisfied)

So, our equation becomes

`2x^2+20x-3x-30`

Finally, factor the first two terms and last two terms

`(2x^2+20x)(-3x-30)`

Take 2x common from the first two terms and take -3 common from the last two terms.

`2x(x^{}+10)-3(x+10)`

Finally, take (x + 10) common

`(2x-3)(x+10)`