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Algebra 1
Section 10.5 C
Factoring Quadratic
Trinomials
Factor the trinomial.
1. 3x2 – 7x – 6
= 3x + 2
Outer
-9x
1st terms
-are factors of 3x2
-only choices are 3x and x
x - 3
Inner
+ 2x = -7x
2nd terms
-are factors of – 6
-when you put them in and take the outer
and inner terms of the foil method, combined,
this should make – 7x (the middle term)
2nd term choices include: 3,-2....-3,2....2,-3....-2,3
6,-1....-6,1....1,-6....-1,6
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2. 2x2 – 7x – 9
=
2x - 9
Outer
2x
x + 1
Inner
-9x = -7x
3. 3t2 + 16t + 5
= 3t + 1 t + 5
Outer
15t
Inner
t = 16t
1st terms
-are factors of 2x2
-only choices are 2x and x
2nd terms
-are factors of – 9
-outer and inner terms should make –7x
2nd term choices include: -9,1....9,-1....1,-9....-1,9
3,-3....-3,3
1st terms
-are factors of 3t2
-only choices are 3t and t
2nd terms
-are factors of 5
-outer and inner terms should make 16t
2nd term choices include: 5,1....1,5
© Mr. Sims
4.
6b2
– 11b – 2
= 6b + 1
Outer
-12b
b - 2
Inner
+ b = - 11b
1st terms
-are factors of 6b2
-only choices are 6b, b.......3b,2b
2nd terms
-are factors of – 2
-outer and inner terms should make –11b
2nd term choices include: -2,1....2,-1....1,-2....-1,2
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5.
4x2
+ 27x + 35
= 4x + 7 x + 5
Outer
20x
Inner
7x = 27x
1st terms
-are factors of 4x2
-only choices are 4x, x.......2x,2x
2nd terms
-are factors of 35
-outer and inner terms should make 27x
2nd term choices include: 35,1....1,35....7,5....5,7
© Mr. Sims
6.
14y2
– 15y + 4
= 7y - 4
Outer
-7y
2y - 1
Inner
-8y = -15y
1st terms
-are factors of 14y2
-choices are 14y,y....7y,2y
2nd terms
-are factors of 4
-outer and inner terms should make -15y
-watch negative signs
2nd term choices include: - 4,-1....-1,- 4....-2,-2
both are negative since last term is positive and
middle term is negative (FOIL method)
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7. 2z2 + 19z – 10
= 2z - 1 z + 10
Outer
20z
Inner
-z = 19z
1st terms
-are factors of 2z2
-only choices are 2z and z
2nd terms
-are factors of -10
-outer and inner terms should make 19z
2nd term choices include: 10,-1....-10,1....1,-10....-1,10
5,-2....-5,2....2,-5....-2,5
© Mr. Sims
Algebra 1
Section 10.5 C
Assignment
Factor the trinomial.
1.) 3x2 – 7x – 6
2.) 6x2 – 7x – 5
3.) 3x2 + 8x + 5
4.) 6x2 + 5x – 4
5.) 2x2 – x – 21
6.) 3x2 + 11x + 10
© Mr. Sims
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