I have 4 math problems that need to be solved by using factoring. I am unable to figure the following out. I have used the FOIL method but it seems not to be working out. I appreciate any help I can get. Thanks
^ exponet
3x^3-7x^2+2x
x^2-2x+5
x^4-7x^3+2x-14
8x^2-2x=3
3x^3-7x^2+2x
First of all, factor out the x. That gives you
x(3x^2 - 7x +2)
The factors of the term in parentheses must be of the form (3x + a)(x+b), with ab = 2 and a+3b = -7. That means a = -1 and b=-2
x(3x-1)(x-2) is the answer.
To factor the expression 3x^3-7x^2+2x, you can use the method called factoring by grouping. Here are the steps to solve it:
Step 1: Look for the greatest common factor (GCF) of the terms. In this case, the GCF is x.
Step 2: Factor out the GCF from the expression. Divide each term by x:
x(3x^2 - 7x + 2x)
Step 3: Now, you need to factor the trinomial inside parentheses, 3x^2 - 7x + 2. This can be done by finding two numbers whose product is 2 and whose sum is -7.
Step 4: The factors of the last term, 2, are 1 and 2. The sum of these factors is not -7. So, let's try rearranging the terms:
x(3x^2 + 2x - 7x + 2)
Step 5: Group the terms:
x((3x^2 + 2x) - (7x - 2))
Step 6: Factor out the GCF from each group:
x(x(3x + 2) - (7x - 2))
Step 7: Simplify:
x(x - 1)(3x + 2)