Algebra Question?

Question

i know how to factor these problems.

x^2 + 10x + 25

you find factors of 25 that add to give you 10.

but whats the trick for these?

3x^2 - 10x - 8

when theres a # behind the first x?

Answer 1

First: multiply the 1st & 3rd term to get -24. find two numbers that give you -24 when multiplied & -10 (2nd term) when added/subtracted. the numbers are (2 & -12). rewrite the expression with the new middle terms.

3x^2 + 2x - 12x - 8

Sec: group "like" terms & factor both sets of parenthesis.

(3x^2 + 2x) - (12x - 8)
x(3x + 2) - 4(3x + 2)

Third: make sure the inner terms match - combine the inner term (once) with the outer term.

(3x+2)(x-4) or, (x-4)(3x+2)

Answer 2

You know that you'll have two parenthesis and that in order to get the first term, the only factors of 3 is 3 and 1

So, your two parenthesis will begin like this:
(3x plus or minus #)(x plus or minus #)

So the last term is -8. The only way to get a negative number is to multiply a neg. and positive. So you know one of the signs will be positive and one will be negative.

Lets try this way:
(3x + #)(x - #)

Now we need to fill in the last numbers.
Factors of 8 are 8 and 1 or 4 and 2. 4 and 2 are your better bet in this case. Let's try them out:
(3x + 4)(x - 2)

Now when you multiply that out you get
3x^2-2x+8

That's not what you wanted to get, so you should probably then switch the 4 and 2

(3x + 2)(x - 4) Now try
3x^2-10x-8
It works. So these are the two factors.

Say you multiplied something out and it was perfect except the term in the middle (in this case -10x) had the wrong sign, then you would switch the negative and positive of each parentheses. Good luck!

Answer 3

i assume you already know how to do the first one.

on the second one, you find two numbers that multiply to -24 and add to -10. (3 x -8 = -24, that is how i got -24 from)

the two numbers are -12 and 2

what you are going to do next is to replace the middle term with the two numbers. (remember to include the variable behind them)

3x^2 - 12x + 2x - 8 (doesn't matter which number is first, you will get the same answer)

factor by groups. Basically means you put the first two term in one group and the last two terms in one group.

(3x^2 - 12x) + (2x - 8)

factor out GCF
3x (x - 4) + 2(x - 4)

(3x + 2) (x - 4)

hope this helps

Answer 4

Multiply the 3 and the -8 together, and find the combination of factors that add up to -10.

3*-8 = -24

-12 + 2 = -10

Answer 5

(3x+2)(x-4)=0 x=-2/3 or 4

You still find factors that will give you a -8 and for the x^2 figures and in this case it is 3 and 1(understood)

Answer 6

3x^2 - 10x - 8 = (3x + 2)(x - 4)#
(-4)(+2) = -8
(-4)(3) + 2 = -10

Answer 7

3x^2 - 10x - 8

= (3x + 2) (x - 4)