Adding Polynomials
Add the Polynomials
(4x + 9) +(x - 4)
5x + 5
Subtract the polynomials:
(g - 4) - (3g - 6)
-2g + 2
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.
Add the polynomials:
(-3a - 2) + (7a + 5)
4a + 3
Subtract the polynomials:
(-5h - 2) - (7h +6)
-12h - 8
Multiply the Polynomials:
3x2(2x + 4x2 - 5)
12x4 + 6x2 - 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
Add the polynomials:
(x2 +3x + 5) + ( -x2 +6x)
9x + 5
Subtract the polynomials:
(-x2 - 5) - (-3x2 -x -8)
2x2 + x +3
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
Subtract the Polynomials:
(k2 + 6k3 -4) - (5k3 + 7k -3k2)
k3 + 4k2 -7k -4
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
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
Add the polynomials:
(-1 + x2 + 2x) + (1 -2x + 2x2)
3x2
Subtract the following polynomials
(3 - 6x5 - 8x4) - (-6x4 - 3x - 8x5)
2x5 - 2x4 + 3x + 3
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