Page 510 - Algebra 1

b. 3x2-11x-4 SOLUTION
Look at the first term of the trinomial. Since 3x2 = (3x)(x), write (3x )(x ).
The last term is -4. List the pairs of factors whose product is -4. (-1)(4) (1)(-4) (-2)(2) (-4)(1) (4)(-1) (2)(-2) Check each of the pairs to see which results in the middle term, -11x.
Possibilities
(3x-1)(x+4) (3x-4)(x+1) (3x+1)(x-4) (3x+4)(x-1) (3x-2)(x+2) (3x+2)(x-2)
Middle Term
11x -x -11x x 4x -4x
Hint
With a negative last term, if the middle term has the wrong sign, reverse the sign in both binomials.
So,3x2 -11x-4=(3x+1)(x-4)
Factoring with Two Variables
Factor 2x2 - 11xy + 5y2 completely.
SOLUTION
Since 2x2 = (2x)(x), write (2x )(x ).
The last term, 5y2, is the product of (-5y) and (-y). Both factors are negative because the second term is negative.
Check the factors to see which order results in -11xy. (2x - 5y)(x - y)
Add the product of the outer and inner terms to see if the sum is -11xy.
(2x)(-y) + (-5y)(x) = -2xy - 5xy
= -7xy
Now check the middle term of (2x - y)(x - 5y).
(2x)(-5y) + (-y)(x) = -10xy - xy
= -11xy ✓
So,2x2 -11xy+5y2 =(2x-y)(x-5y).
Example
4
Hint
If there are two variables in the trinomial, one variable should descend in power while the other ascends.
Lesson 75 495