Adding Polynomials
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
Subtract the polynomials:
(g - 4) - (3g - 6)
-2g + 2
Find the perimeter with a rectangle width w and length 2w + 2
6w+4
Multiply the Polynomials:
3x2 (2x4)
6x6
Which of these is in standard form? Why
1. x + 1
2. x3 - 4x + x2
3. 15x + 10x2 - 5x4
#1; order from greatest degree to least degree
True or False
When multiplying monomials the coefficients and exponents are multiplied.
False
The coefficients are multiplied, but the exponents are added together.
Add the polynomials:
(-3a - 2) + (7a + 5)
4a + 3
Subtract the polynomials:
(-5h - 2) - (7h +6)
-12h - 8
Find the area with a width w and length 2w + 2
Area is 2w2 + 2w units2
Multiply the Polynomials:
3x2(2x + 4x2 - 5)
12x4 + 6x3 - 15x2
Write the following in standard form:
-8 - 11x + 3x4 + 12x2
What is the degree and the leading coefficient?
3x4 +12x2 - 11x - 8
degree: 4
Leading coefficient: 3
Name the Rule and how it works
x^0
Zero Exponent Rule
The term equals to 1
Add the polynomials:
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
Subtract the polynomials:
(-x2 - 5) - (-3x2 -x -8)
2x2 + x +3
Find the perimeter of a rectangle with a width of 3wz - 3z and the length of 10z
6wz+14z
Multiply the polynomials
(4x2 - 12)(2x + 5)
8x3 + 20x2 - 24x - 60
Write the following in standard form:
12x - 18 - 5x2 + 17x4
What is the degree and the leading coefficient?
Standard form: 17x4 - 5x2 + 12x - 18
degree: 4 (Quartic)
Leading coefficient: 17
Name the Rule and how it works
x^-1
Negative Exponent Rule
Converts term into a fraction, moves the variable to the denominator while changing the exponent to a positive.
Add the polynomials:
(t2 + 3t3 -3) + (2t2 +7t -2t3)
t3 +3t2 +7t -3
Subtract the Polynomials:
(k2 + 6k3 -4) - (5k3 + 7k -3k2)
k3 + 4k2 -7k -4
Find the perimeter of a square whose side length is 5x + 5
20x + 20 units
Multiply the Polynomials:
(x-2)(x+6)
x2+4x-12
What is the degree of the following term?
-2x
Linear (1)
Name the Rule and how it works
(x^a)/(x^b)
Quotient Rule
Subtracts Exponents
Add the polynomials
(-14x4 + 5x2 + 16) + (12x4 - 3x3 - 12)
-2x4 - 3x3 + 5x2 + 4
Subtract the Polynomials:
(2x - 3x) - (x2 -2x + 4)
-x2 + x - 4
What is the area of a square with a width of
(3r+ 5)
9r2 + 30r + 25
Multiply the Polynomials:
(3x-6)(5x+3)
15x2-21x-18
Put the polynomial in standard form. Classify the polynomial by degree & number of terms:
- 3x - 4x2 - 7
Standard form: - 4x2 - 3x - 7
degree: 2 (quadratic polynomial)
3 terms so it is a trinomial
Name the Rule and how it works
(x^a)^b
Power Rule
Multiplies Exponents
Add the polynomials:
(-1 + x2 + 2x) + (1 -2x + 2x2)
3x2
Subtract the following polynomials
(3 - 6x5 - 8x4) - (-6x4 - 3x - 8x5)
2x5 - 2x4 + 3x + 3
The length of a triangle is given as 3wz and the width is given as 10z. What is the area?
15wz2
Multiply the Polynomials:
(x - 1)(−8x2 − 6x − 12 )
-8x3 - 6x2 - 12x + 8x2 + 6x + 12
-8x3 + 2x2 - 6x + 12 (Correct Answer)
State the degree and name for this polynomial:
3x4- 12x3
Quartic (4); Binomial
Name the Rule and how it works
x^a*x^b
Product Rule
Adds exponents