Question

Factor 5x^2 -7x-6
I know something about how to factor, but I'm not sure what to do because the LC isn't 1.

Answer 1

5x^2-10x +3x - 6
=> 5x(x-2) +3(x-2)
=> (5x+3)(x-2) => x=2, -5/3

Answer 2

Oh ok thank you!!! I've wondered forever how to solve these equations with a leading coefficient that's not one. Thank you!

Answer 3

sorry, it's-3/5. I wrote it wrong. correct it.

Answer 4

when leading coefficient is not one, you have to multiply the first one to the third one.

suppose it is.....

ax^2 + bx +c

you have to multiply a with c

and make b as the sum of two numbers in such a form that the product of of both comes out to be a*b

Answer 5

And then factor by grouping, yes?

Answer 6

see here 5*(-6) = -30

and -10+3 = -7

-10*3 = -30 which is equal to 5*(-6) = -30

Answer 7

and that's it.

Answer 8

i hope you got it @Republican31 did u?

Answer 9

Yep! Thank you!

Answer 10

5x^2 - 7x -6

Product = coeff of sq term and constant term = 5 * -6 = -30
factors of 30 = 2 * 3* 5
factors of -30 = 2 * 3* 5 and odd number of these factors will be negative
like -2, -3, 5, 2, -3, 5, etc

now combine these factors such that their sum is -7 => -2*5 +3 = -7. here the factors used are (-2, 3, 5)

now given eq
= 5x^2 -2*5*x +3x -6 = 5x^2 - 10x + 3x - 6
= 5x(x-2) + 3(x-2)
= (x-2) (5x-2)

done!!!