You can put this solution on YOUR website! It is not easy, but can be factored as a product of two binomials with integer coefficients.
Some (not all) quadratic polynomials can be factored.
Of the ones than can be factored, some (not all) have factors with integer coefficients.
Here's how to factor .
STEP 1
Multiply the leading coefficient times the independent (constant) term.
STEP 2
Look for pairs of integers that multiply to yield that product, but do not worry about negative signs yet.
There are 6 such pairs of factors.
(You would list them the same way if the product had been -84)
STEP 3
Find the pair of factors (including negative signs as needed) whose product is the product found above, and whose sum equals the coefficient of the term in x.
We are looking for factors whose product is 84 and whose sum is -31.
They will both be negative, so their absolute values will add to 31.
The pair of factors we are looking for is and
STEP 4
Write the factors as coefficients of terms in x, and re-write your polynomial with those two new terms instead of the original term in x.
We write and and using those two expressions to replace in the polynomial to get
STEP 4
Factor by parts, taking out common factors for pairs of the terms. and so to start we write
Then we take out as common factor to finish and we have the factoring as
