Greatest Common Factors and Binomial Products
Multiply the binomial
(3x+4)(3x+4)
9x2+24x+16
Factor the polynomial completely:
24mx + 36m + 30x + 45
3(2x + 3)(4m +5)
Use Split the Middle
30x2 - 67x - 12
(5x - 12) (6x + 1)
What is the quadratic formula?
x= [-b ± √(b2-4ac)]/2a
Solve.
(2x - 9)(x + 8)(6x - 7)= 0
S = {4.5, -8, 1.67}
Write the GCF of the given pair of numbers:
315 and 189
63
Factor the polynomial completely:
6x3 - 6x2 - 24x + 24
6(x - 1)(x + 2)(x - 2)
Use X Factor
48x2 - 40x - 48
8(3x + 2)(2x - 3)
What is the discriminant test? Why is it helpful?
Perfect square --> factor your polynomial to solve
Positive but not perfect square --> must use the quadratic formula to solve
Negative --> no real solutions
It saves you time because it tells you what to do next!
Solve.
x2 - 3x - 10 = 0
S = {-2, 5}
Factor the Polynomial 3x2 - 20x - 7
(x-7)(3x+1)
DOUBLE JEOPARDY!
Factor the polynomial completely:
x2 +6x + 9 - y2
(x + 3 + y)(x + 3 - y)
Use Split the Middle
4x2 + 7x + 18
Prime
Use the Discriminant Test to test factorability.
2x2 + 5x - 10 = 0
-4 No real solution
Solve.
2x2 + 11x + 5 = 0
S= {-0.5, -5)
Write the GCF of the two expressions:
24x2y3z4 and 30x5y4z3
6x2y3z3
Factor the polynomial completely:
10x2 - 7x - 10x + 7
(10x - 7)(x - 1)
Use X Factor
2m2 + 15m - 50
(2m - 5)(m + 10)
Solve using the Quadratic Formula:
2x2 - 15x - 5 = 0
S = {7.82, -0.32}
Solve.
12x2 - 20x + 7 = 0
S = {1/2, 7/6}
or
S = {0.5, 1.17}
Write the GCF of the 3 numbers:
324, 540, 1080
108
Factor the polynomial completely:
4x3+ 24x2 - x - 6
(x + 6)(x + 0.5)(x - 0.5)
Use Split the Middle
8x5 + 2x4 - 3x3
x3(4x + 3)(2x - 1)
What is the converse of the multiplication property of zero? Why do we need to know this?
If a product of real numbers equals zero, then one of its factors equals zero. That is, for real numbers n and p, if np = 0, then n=0 or p = 0.
This concept allows us to solve by setting each factor equal to zero.
Solve. (Hint: split problem in half and factor first)
5x3 - 20x2 - 3x + 12 = 0
S = {4, √(4/3), -√(4/3)}