Use Properties of Exponent
Evaluate and tell which property of Exponent you used.
33 x 32
243: product of Powers property
use direct substitution to evaluate the polynomial funtion for the given value of x.
F(x) = 5x3 - 2x2 + 10x - 15; x= -1
= 5(-1) - 2(1) - 10 - 15
= -15 - 2 - 10 - 15
= -32
Find the product of the polynomial: x(2x2-5x+7)
x(2x2-5x+7x)
2x3-5x+7x
Monomial Factors
3y5-48y3
3y5-48y3
= 3y3(y2-16)
= 3y3(y+4)(y-4)
Scientific notation
(6.3 x 105)(8.9 x 10-12)
=56.07 x 10-7
=5.607 x 101 x 10-7
=5.607 x 10-6
Write in scientific notation.
(4.2 x 103)(1.5 x 106)
6.3 x 109
use direct substitution to evaluate the polynomial funtion for the given value of x.
g(x) = 4x3 - 2x5; x = -3
= 4(-27) - 2(-243)
= -108 + 486
= 378
Find the product of the polynomial: (y-7)(y+6)
(y-7)(y+6)
y2+6y-7y-42
y2-y-42
Factoring by Grouping
4c3+8c2-9c-18
4c3+8c2-9c-18
= 4c2(c+2)-9(c+2)
= (c+2)(2c+3)(2x-3)
Multiplying Polynomials
(2a - 3)(a2 - 10a - 2)
(2a - 3)(a2) - (2a - 3)(10a) - (2a - 3)(2)
2a3 -23a2 + 26a + 6
List at least two Properties of Exponents
Product of powers
Product of a power
Power of a product
Negative exponent
Zero exponent
Quotient of Powers
Power of a Quotient
use direct substitution to evaluate the polynomial funtion for the given value of x.
h(x) = 6x3 - 25x + 20; x = 5
= 6(125) - 125 + 20
=750 - 125 + 20
= 645
Find the product of the polynomial: 5x2(6x+2)
5x2(6x+2)
30x3+10x2
Factor by Grouping
x3+x+x+1
x3+x+x+1
= x2(x+1)+1(x+1)
= (x2+1)(x+1)
Adding and subtracting polynomial: (5b-6b3+2b4)-(9b3+4b4-7)
(5b-6b3+2b4)-(9b3+4b4-7)
2b4-4b4-6b3-9b3+5b+7
-2b4-15b3+5b+7
Evaluate and tell which property you used.
(-5)(-5)4
-3125; product of Powers property
use direct substitution to evaluate the polynomial funtion for the given value of x.
g(x) = 4x5 + 6x3 + x2 - 10x + 5; x = -2
= 4(-32) + 6(-8) + 4 + 20 + 5
= -128 - 48 + 4 + 25
= -147
Find the product: (w-9)2
(w-9)2
w2-(2)9w+92
w2-18w+81
Quadratic Form
x4-25
X4-25
= (x2-5)(x2+5)
Write in scientific notation.
(3.4 x 103) (2.8 x 108)
9.52 x 1011
Simplify tell which Properties of Exponents used.
(22y3)5
1024y15; power of a product property, power of a power property
use direct substitution to evaluate the polynomial funtion for the given value of x.
f(x) = 8x + 5x4 - 3x3; x = 2
= 16 + 5(16) - 3(4) - 8
= 16 + 80 - 12 - 8
=76
Multiply the binomial: (x-5)(x+1)(x+3)
(x-5)(x+1)(x+3)
(x2+1x-5x-5)(x+3)
(x2-4x-5)x+(x2-4x-5)3
x3-4x2-5x+3x2-12x-15
x3-x2-17x-15
Solving Equations
y3-5y2=0
y3-5y2=0
y2(y-5)=0
y=0,5
Simplify equation.
(5b - 6b3 + 2b4) - (9b3 + 4b4 - 7)
2b4 - 4b4 - 6b3 - 9b3 + 5b + 9
-2b4 - 15b3 + 5b + 7