Add/Subtract Polynomials
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
Factor the polynomial if possible
49x2 - 100
(7x-10)(7x+10)
Find the perimeter of a regular pentagon with a side length of 3w + 2
Perimeter is 15w + 10 units
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 least to greatest exponent
True or False
When multiplying monomials the coefficients and exponents are multiplied.
False
The coefficients are multiplied, but the exponents are added together.
Subtract the polynomials:
(-x2 - 5) - (-3x2 -x -8)
2x2 + x +3
Factor the polynomial if possible:
9x2 + 24x + 16
(3x+4)2
Find the area of a rectangle with a height of 2x +3 and a width of 6x - 2
12x2 + 14x -6 units squared
Multiply the Polynomials:
3x2(2x + 4x2 - 5)
12x4 + 6x3 - 15x2
Write the following in standard form:
-8 - 11x + 3x4 + 12x2
What is the leading degree and the leading coefficient?
3x4 +12x2 - 11x - 8
Leading degree: 4
Leading coefficient: 3
Name the Rule and how it works
x^0
Zero Exponent Rule
The term equals to 1
Subtract the polynomials:
(k2 + 6k3 -4) - (5k3 + 7k -3k2)
k3 + 4k2 - 7k - 4
Factor the polynomial if possible:
8x3 - 40x2 + 50x
2x(2x - 5)2
Find the perimeter of a rectangle with a width of (3wz - 3z) and the length of 10z
Perimeter is 3wz + 7z units
Multiply the polynomials
(4x2 - 12)(2x + 5)
8x3 + 20x2 - 24x - 60
Write the following in standard form:
12x - 18 - 5x2 + 17x4
What is the leading degree and the leading coefficient?
Standard form: 17x4 - 5x2 + 12x - 18
Leading 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
Factor the polynomial if possible:
81x2 + 144
Not possible
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
Factor the Polynomial if possible:
27x3 - 64y3
(3x - 4y)(9x2 + 12xy + 16y2)
What is the area of a square with a width of
(3r + 5)
9r2 + 30r + 25 units squared
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
Leading 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
Combine the polynomials:
(-1 + x2 + 7x) + (5 -2x + 2x2) - (2x2 + 6 - 3x)
x2 +8x - 2
Factor the following polynomials if possible
125x3 + 216y6
(5x+6y2)(25x2 - 30xy2 + 36y4
The height of a triangle is given as 3wz and the base is given as 10z. What is the area?
30wz2
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