To factor the given trinomial, think of the process as multiplying two binomials in reverse.
(5x-1)(3x+2)
Practice makes perfect
We have a quadratic trinomial of the form ax^2+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.
15x^2+7x-2 ⇔ 15x^2+ 7x+( - 2)
We have that a= 15, b= 7, and c=- 2. There are now three steps we need to follow in order to rewrite the above expression.
Find a c. Since we have that a= 15 and c= - 2, the value of a c is 15* ( - 2)=- 30.
Find factors of a c. We need factors of a c to have opposite signs — one positive and one negative — in order for the product to be negative. Since b= 7, 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.
