Here we have a quadratic trinomial of the form ax2+bx+c, where ∣a∣=1 and there are no common factors. To factor this expression, we will rewrite the middle term, bx, as two terms. The coefficients of these two terms will be factors of ac whose sum must be b.
2x2+x−28⇔2x2+1x+(-28)
We have that a=2,b=1, and c=-28. There are now three steps we need to follow in order to rewrite the above expression.
Find ac. Since we have that a=2 and c=-28, the value of ac is 2×-28=-56.
Find factors of ac. Since ac=-56, which is negative, we need factors of ac to have opposite signs — one positive and one negative — in order for the product to be negative. Since b=1, which is positive, the absolute value of the positive factor will need to be greater than the absolute value of the negative factor, so that their sum is positive.
We can see above that after expanding and simplifying, the result is the same as the given expression. Therefore, we can be sure our solution is correct!
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