Answer:
- ac = -300
- -20 = -30 +10
- (5x +2)(5x +(-6))
Explanation:
The sequence of required answers provides a step-by-step solution to the problem.
Factors of ac
In the given trinomial, we identify the coefficients as ...
ax² +bx +c = 25x² -20x -12 ⇒ a=25; b=-20; c=-12
Then the ac product is ...
ac = (25)(-12) = -300
The factor pairs that make this product can be listed as ...
-300 = (-300)(1) = (-150)(2) = (-100)(3) = (-75)(4) = (-60)(5) = (-50)(6) = (-30)(10) = (-25)(12) = (-20)(15) . . . . (only pairs with a negative sum are listed)
The sums of these pairs are -299, -148, -97, -71, -55, -44, -20, -13, -5.
The factors of the ac product that add to -20 are -30 and 10.
Factor by grouping
These factors are used to rewrite the -20x term as a sum.
25x² -20x -12 = 25x² -30x +10x -12
Grouping these terms in pairs, we can identify common factors:
= (25x² -30x) +(10x -12)
= 5x(5x -6) +2(5x -6)
= (5x +2)(5x +(-6))