Factoring Help?

Question

Hi can someone please tell me how to solve these, i just want to know for these 3 so i am able to solve the rest of them by myself. The questions are

1. 5x^3-10x^2-40x
2. 18x^3 - 98x
3. ax^2 -7ax+12a

i really need help, because i am stuck on my worksheet, i don't know how to solve these,.,,

Answer 1

Factoring was probably the most difficult thing for me when I was in high school math. But now I am taking calculus II and statistics classes in college, so don't worry if it doesn't come easy at first.

Question 1:
5x^3 - 10x^2 - 40x

Start by finding common factors. In this case, each term can be divided by 5x. So now you have,

5x(x^2 - 2x - 8)

Now you have to factor what is in the parenthesis. First, look at the first term, x^2. Decide which two terms will equal this term when multiplied. The only choice is x and x. Next look at the signs. Since there is a negative in the constant, 8, the factored terms will have both a positive and negative factor. Use these two terms to start the factor,

5x(x - _)(x + _)

To find the missing terms, you must find two numbers (one positive and one negative in this case) that add up to the second term (ignore the x), -2, and -8. -4 and 2 will work in this case. This gives the solution,

5x(x - 4)(x + 2)

To check this, simply work backwards.

5x(x - 4)(x + 2) [FOIL the parenthesis terms]
5x(x^2 + 2x - 4x - 8) [Simplify]
5x(x^2 - 2x - 8) [Multiply out the 5x]
5x^3 - 10x^2 - 40x

This same procedure works in the next two problems.


Question 2:

18^3 - 98x
2x^2(9x^2 - 49)

In this problem, there is no middle term. Therefore, the two numbers used must add up to zero and multiply up to -49.

2x^2(3x + 7)(3x - 7)


Question 3:

ax^2 - 7ax + 12a
a(x^2 - 7x + 12)
a(x - 3)(x + 4)


Here are the answers, easy to find:
1) 5x(x - 4)(x + 2)
2) 2x^2(3x + 7)(3x - 7)
3) a(x - 3)(x + 4)

I hope this helps!

Answer 2

1. factor out 5x first to get:
5x(x^2-2x-8)
Then 5x(x-4)(x-2)

2. Factor out 2x first to get:
2x(9x^2-49).
(9x^2-49) is a difference of squares.
Simplified, the whole expression is 2x(3x-7)(3x+7)

3. Factor out "a" first to get:
a(x^2-7x+12)
a(x-4)(x-3)

Remember to take each step slowly and methodically. The more you practice factoring, the quicker you will see these patterns.

Good luck!

Answer 3

1. 5x^3 - 10x^2 - 40x =
5x(x^2 - 2x - 8) =
5x(x - 4)(x + 2)

2. 18x^3 - 98x =
2x(9x^2 - 49) =
2x(3x - 7)(3x + 7)

3. ax^2 - 7ax + 12a =
a(x^2 - 7x + 12) =
a(x - 3)(x - 4)

Answer 4

1. (5x)(x^2 - 2x - 8)
=(5x)(x-4)(x+2)
factors are x=0, x= 4, x= -2

2. (18x) (x^2 - 34/9)
factors are
x=0, x = (squareRoot34)/3, x = -(squareRoot 34)/3

3. a(x^2 - 7x +12)
=a(x-4)(x-3)
factors are x=4, x=3

Answer 5

1. the factor that goes into all three is 5x
so it'll be 5x(x^2-2x-4)
factor that
5x(x-4)(x+2)

2. factor in both is 2x
=2x(9x^2-49)
=2x(3x+7)(3x-7)

3. a(x^2-7x+12)
=a(x-3)(x-4)

Answer 6

1)you can use the ac method
2) just take out a 2x
3)(ax-4)(ax-3)