Variable and Expresssion
Write a mathematical expression for:
5 less than twice a number x
2x-5
Identify each for the polynomial: 4 + 5x - 7x3
a) Degree of the polynomial
b) Leading Term
c) Leading Coefficient
d) Type
a) Degree of the polynomial : 3
b) Leading Term : -7x3
c) Leading Coefficient : -7
d) Type: Trinomial
Perform the following operations:
(3x2 - 5x + 6) - 2(x3 + 5x - 4)
-2x3 + 3x2 - 15x +14
State the method you would use to factor then factor
x2 + 5x - 14
Trial and Error or AC Method
(x+7)(x-2)
Factor the following expression:
-15y7 - 40y6
-5y6 (3y + 8)
Write a phrase for
xy+9
Answers may vary.
The sum of 9 and the product of x and y.
9 more than the product of x and y.
The product of x and y increased by 9.
Identify each for the polynomial: 5x2 - 3
a) Type
b) Constant
c) List all terms
a) Type: binomial
b) Constant: -3
c) List all terms: 5x2, -3
Perform the following operations:
3x(5x2 + 2x - 5) + (x3 + 8x + 4)
16x3 + 6x2 - 7x + 4
State the method you would use to factor then factor
25x2 - 49
Difference of Squares
(5x+7)(5x-7)
Factor the following expression:
2y3 - 6y2 - 7y + 21
(2y2 - 7) (y - 3)
Write a mathematical expression for
8 more than the quotient of 5 and x
5/x + 8
Is the following a polynomial? Explain
4x2 + 1/3 x -2
Yes
Perform the following operation.
(4x2y3)(6x4y)
24x6y4
State the method you would use to factor then factor
5yx2 + 25xy2 - 15xy
Pull out a Greatest Common Factor
5xy(x+5y-3)
Factor the expression:
x2 + 6x - 55
(x + 11) (x - 5)
Write an expression using only one variable and define your variable:
There are two types of balls in the PE bin. There are three more basketballs as there are soccer balls. Write an expression for the total number of balls in the bin.
x = number of soccer balls
x + x + 3
or
2x + 3
Is the following a polynomial. Explain
5sqrt(x) + 2x - 6
No, it has a x under the root which is fraction exponent
Perform the following operation.
(x + 5) (3x2 + 4x - 2)
3x3 + 19x2 +18x - 10
State the method you would use to factor then factor
x3 + 125
Sum of Cubes
(x + 5)(x - 5x + 25)
Factor the expression:
3x2 + 8x - 16
(3x-4)(x+4)
Write an expression using only one variable and define your variable:
There are three types of candy in a bowl. There are twice as many Twix as there are Kit Kats. There are 7 more Hersey's than Twix. Write an expression for the total number of pieces of candy in the bowl.
x = Number of Kit Kats
x + 2x + 2x +7
of
5x + 7
Is the following a polynomial? Explain
(x3-5x2+8)/x2
No, there is an x in the denominator which means negative exponent.
Perform the following operation.
(2x - 3)2
4x2 - 12x + 9
State the method you would use to factor then factor.
4a2b - 25b
GCF and Difference of Squares
b(2a + 5)(2a - 5)
Factor the expression:
8x3 - 27
(2x-3)(4x2 +6x +9)