Factoring!
Factor:
12x^2y^3-9xy^2+18xy^4
3xy^2(4xy-3+6y^2)
Solve: x2+21x = 22
{1, -22}
A triangle has an area of 36 square inches. If the height of the triangle is 6 in more than its base, what are its height and base? Create a polynomial equation and solve by factoring.
1/2 x(x+6) = 36
12ft by 6 ft
Multiply:
(x+3)(x-4)
x^2 -x -12
Is this a polynomial? Explain why or why not. If it is, state the degree and classify it by the number of terms.
3x^2 -4x + (3y)/x -1
It is not a polynomial because 3y/x is not a monomial because it is not a product of numbers and variables and a polynomial is a sum of monomials.
Factor: x2+4x-21
(x+7)(x-3)
Solve: 9x2-1 = 0
{1/3, -1/3}
The length of a rectangular swimming pool is 20 ft greater than its width. The area of the pool is 525 feet. What are the dimensions of the pool? Create a polynomial equation to represent the situation and solve by factoring.
w(w+20) = 525
15 ft by 35 ft
Multiply:
(2xy^2-y^3)^2
4x^2y^4 -4xy^5 +y^6
Is this a polynomial? Explain why or why not. If it is, state the degree and classify it by the number of terms.
4 -3x +4x^3
Yes, it is a polynomial because it is three monomials added together. Third degree (cubic) trinomial
Factor: 6x4-6
6(x2+1)(x+1)(x-1)
Solve:
3k^2=-2k
{0, -2/3}
A rectangular garden is twice as long as it is wide. If its length is increased by 4 ft and its width is decreased by 3 ft, the new rectangle formed has an area of 100 ft2 Find the dimensions of the new rectangle. Create a polynomial equation and solve by factoring.
(2x+4)(x-3) = 100
5ft by 20 ft
Multiply:
(2x-5)(-3x^2+x-4)
-6x^3 +17x^2 -13x +20
Is this a polynomial? Explain why or why not. If it is, state the degree and classify it by the number of terms.
5x^4-1
Yes, it is a polynomial because it is 2 monomials added together. Fourth degree (quartic) binomial
Factor: 12x2+69x +45
3(4x+3)(x+5)
Solve:
x^2 =1
{1, -1}
When Jerald shoots a free throw, the ball is 6 ft from the floor and has an initial upward velocity of 20 feet/s. The hoop is 10 ft from the floor. How long is the basketball in the air before it reaches the hoop? An equation that models the motion is
h = -16t^2+20t +6
1 second
(x^2 + 3x -4)(x^2 + 3x +5)
x^4 +6x^3 + 10x^2 + 3x -20
(3x^2 +5x-2) +(x^2 -2x -3)
4x2+3x-5
Factor:
2d^3-4d^2-8d +16
2(d-2)^2(d+2)
Solve:
4x^2 -9x = -x -3
{ 1/2, 3/2}
Billie dives from a 36ft platform with an initial upward velocity of 14 ft/s. How long will it take Billie to reach the water? An equation that models the motion is
h = -16t^2+14t +36
2 seconds
A 20 ft by 30 ft pool is surrounded by a walkway of uniform width that is x ft wide. Write an expression to find the area of the walkway and the pool.
4x2+ 100x + 600 ft2
(-3x^2 +5x -2) -(x^2 +2x +6)
-4x^2 +3x -8
Factor:
x^32-1
(x^16+1)(x^8+1)(x^4+1)(x^2+1)(x+1)(x-1)
Solve: -4x2+19x = -30
{-5/4, 6}
ECO club is building a garden against the BCB. They want to fence it in but they only need fencing on 3 sides since the side of the BCB will be the fourth side. They have 21 m of fencing and want the garden to have an area of 55 m2. What are the dimensions of the garden? Create a polynomial equation to model the situation and solve.
5 m by 11 m
OR
5.5 m by 10 m
A tennis court is 36ft by 78ft. A path of uniform width x ft surrounds the tennis court. Write an expression to find the area of the path.
4x2+ 228x ft2
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