To factor the given quadratic trinomial of the form da^2+ea+f, rewrite the middle term, ea, as two terms. The coefficients of these two terms will be factors of df whose sum must be e.
(2a+3)(a-6)
Practice makes perfect
We want to completely factor the given expression. Here we have a quadratic trinomial of the form da^2+ea+f, where |d| ≠1 and there are no common factors. To factor this expression, we will rewrite the middle term, ea, as two terms. The coefficients of these two terms will be factors of df whose sum must be e.
2a^2-9a-18 ⇕ 2a^2+( -9)a+( -18)
We know that d= 2, e= -9, and f= -18. There are now three steps we need to follow in order to rewrite the above expression.
Find d f. Since we have that d= 2 and f= -18, the value of d f is 2* ( -18)=-36.
Find factors of d f. Since d f=-36, which is negative, we need factors of d f to have opposite signs — one positive and one negative — in order for the product to be negative. Since e= -9, which is also negative, the absolute value of the negative factor will need to be greater than the absolute value of the positive factor, so that their sum is negative.
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!
