Question

Factor completely 10x^2 + 2x – 8.

(3x + 1)(x + 7)

(3x + 7)(x + 1)

Prime

(3x + 4)(x + 3)

Answer 1

@geerky42 help?

Answer 2

do you want simply to factoriz this eq..?

Answer 3

?

Answer 4

Hint...by looking at the options, do any of those distribute out and make that equation?

Answer 5

not sure xD

Answer 6

For example, that first option

(3x + 1)(x + 7)

If we distribute that out we get

3x^2 + 22x + 7

We multiply the first term in the first parenthesis by each term in the second...and then repeat for the second term in the first parenthesis

Well look how we ended up with 3x^2...This option (and the other 2 you have) will be the same and end up with just 3x^2

We cannot get 10x^2 so no choice here works...except (prime)

Answer 7

Step by step solution:
Step 1:

Simplify \(\color{lime}{\huge\ 10^x2+2x - 8~}\)

Pull out like factors :

\(\color{lime}{\large\ 10x^2 + 2x - 8 = 2 • (5x^2 + x - 4)~}\)

Try to factor by splitting the middle term

Factoring \(\color{blue}{\large\ 5x^2 + x - 4~}\)

The first term is, 5x^2 its coefficient is 5 .
The middle term is, +x its coefficient is 1 .
The last term, "the constant", is -4

Step-1 : Multiply the coefficient of the first term by the constant \(\color{red}{\large\ 5 • -4 = -20~}\)

Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is 1 .
-20 + 1 = -19
-10 + 2 = -8
-5 + 4 = -1
-4 + 5 = 1

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 5
\(\color{purple}{\large\ 5x^2 - 4x + 5x - 4~}\)

Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x-4)
Add up the last 2 terms, pulling out common factors :
1 • (5x-4)
Now add up the four terms of step 3 :
(x+1) • (5x-4)
Which is the desired factorization
Final result :

\(\color{lime}{\huge\cal\ 2 • (5x - 4) • (x + 1)~}\)


\(\color{pink}{\huge\cal\ :)~}\)

Answer 8

@Muzzack thts not an option tho...

Answer 9

simplify it

Answer 10

Thank You! @johnweldon1993

Answer 11

@Muzzack is indeed correct, that would be the correct factorization, however since that is not a given option, we must stick with (prime)

Answer 12

And no problem @camerondoherty :)

Answer 13

\[10x^{2}+2x-8=2( 5x^{2}+x-4)=\2(5x ^{2}+5x-4x-4 )=2(5x(x+1)-4(x+1))=2(5x-4)(x+1)=(5x-4)(2x+2)\]