SOLUTION: Consider the following polynomial function. f(x)=2x3+3x2−12x+7 Step 1 of 4 : Factor the polynomial completely.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Consider the following polynomial function. f(x)=2x3+3x2−12x+7 Step 1 of 4 : Factor the polynomial completely.      Log On


   

Question 1138498: Consider the following polynomial function.
f(x)=2x3+3x2−12x+7
Step 1 of 4 : Factor the polynomial completely.
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=2x%5E3%2B3x%5E2-12x%2B7
step 1:write 3x%5E2 as 7x%5E2-4x%5E2, and -12x as -14x%2B2x
f%28x%29=2x%5E3%2B7x%5E2-4x%5E2-14x%2B2x%2B7
step 2: group
f%28x%29=%282x%5E3-4x%5E2%29%2B%287x%5E2-14x%29%2B%282x%2B7%29
step 3:factor out common %282x%2B7%29
f%28x%29=%28x%5E2+-+2x%2B1%29%282x+%2B+7%29
step 4: apply rule square of difference
f%28x%29=%28x+-+1%29%5E2+%282x+%2B+7%29


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Substitute x=1 to see if x=1 is a root:

2%2B3-12%2B7+=+0

Yes, x=1 is a root. Use synthetic division to divide out the factor x-1.

 1  |  2  3  -12  7
    |     2    5 -7
    +--------------
       2  5   -7  0

The remainder is 0, so x=1 is a root; (x-1) is a factor.

2x%5E3%2B3x%5E2-12x%2B7+=+%28x-1%29%282x%5E2%2B5x-7%29

(2) Factor the remaining quadratic by whatever method you know.

2x%5E3%2B3x%5E2-12x%2B7+=+%28x-1%29%282x%2B7%29%28x-1%29