How can i factor this?

Question

3x^2 + 11x + 10 =


x^2 - 5x - 24 =


please show me how to do it.

Answer 1

you do the inverse of FOIL (first, outer, inner, last)

For x^2 - 5x - 24

we know it's going to be (x+h)(x-b) where h and b are your factors

we know h x b = 24

we also know that xh -xb = -5x

a good guess right off the bat is b=8 and h=3, let's try it

(x + 3)(x - 8) = x^2 +3x -8x - 24 = x^2 - 5x -24

whaddya know (x +3)(x - 8) is your answer

For 3x^2 + 11x + 10

you know (3x + h)(x + b)

you also know hb = 10

and xh + 3xb = 11x

so it could be h=2, b=5 or h=10, b=1 you have to try them to figure it out

I'm gonna go with b=2, h=5 (i'll explain at the end)

SO

(3x + 5)(x + 2) = 3x^2 + 6x + 5x + 10

or in other words

3x^2 + 11x + 10

*I figured I'd save myself some time guessing by noticing that whatever number multiplied against the 3x would had to add to the other factor to equal 11x

or in other words

3x(2) + x(5) = 6x + 5x = 11x

now try this one

2x^2 -4x -6

keep up the good work

Answer 2

3x^2 + 11x + 10
= ( 3x+5)( x+2)
to check multiply 2 outside & 2 inside & add
3x * 2 + 5 * x = 6x + 5x = 11x .middle term


x^2 - 5x - 24
= ( x-8)( x+3)

Answer 3

3x^2 + 11x + 10
= (3x + 5)(x + 2)

x^2 - 5x - 24
= (x - 8)(x + 3)

Hope that helps!

Answer 4

short method:
take 1st number and 3rd one---> 3*10=30 ==> (+6) * (+5)
3x^2+6x+5x+10
[3x(x+2) +5(x+2)]
taking common terms...
(x+2)(3x+5)
so the factor of 3x^2+11x+10 is (x+2)(3x+5)
=================================================
answer for 2 nd question:

take 1st and last number:--->1*(-24)= - 24==>(-8)*(+3)

==> x^2 -8x+3x-24
[x(x-8)+3(x-8)]
take common terms:

(x+3)(x-8)===> answer

Answer 5

3x^2 + 11x + 10

You expect (ax + b)(cx + d)

Choices for a & c are 1 & 3

Choices for b & d are 1 & 10, 2 & 5

(3x + 5)(x + 2) by trial and error

Or see the lesson at the link below


x^2 - 5x - 24

You expect (x + a)(x + b), where a + b = -5 and ab = -24

24 = 2*2*2*3, so -8 and + 3 look good

(x - 8)(x + 3)

Answer 6

3x^2+11x+10= (3x+5)(x+2)

x^2-5x-24= (x-8)(x+3)

Answer 7

1. 3x^2 + 6x + 5x + 10
(3x^2+6x) + (5x+10)
3x(x+2) + 5(x+2)
(3x+5)(x+2)
2. (x-8)(x+3)

Answer 8

1) (3x+_)(x+_)
You need two positive numbers in the blanks. Start trying numbers: (3x+5)(x+2) works.
2)You need two numbers whose difference is 5 and whose sum is 24. 3 and 8 work. (x-8)(x+3)

Answer 9

(3x + 5)(x + 2)

(x - 8)(x + 3)

Answer 10

the second one is (x-8)(x+3) to do this you think of all of the possible factors of 24 that add/subtract to -5