Classify Polynomials
Classify the polynomial by its degree and number of terms.
5x3
Cubic Monomial
Simplify. Write you answer in standard form.
(12y2 + 17y - 4) + (9y2 - 13y + 3)
21y2 + 4y - 1
Multiply. Write you answer in standard form.
-3a(5a2 + 2a)
-15a3 - 6a2
Factor using the GCF.
9x - 36
9(x - 4)
50 pts. Write the polynomial in standard form:
-3x + 5x3 - x5 + 8x2
50 pts. Identify the leading coefficient.
-x5 + 5x3 + 8x2 - 3x
Leading Coefficient = -1
Question: Find the GCF of 30 and 75.
Answer: GCF is 5.
Explain the mistake and state the correct answer.
They didn't take out the GREATEST common factor.
Correct Answer: The GCF is 15.
Classify the polynomial by its degree and number of terms.
2x + 6
Linear Binomial
Simplify. Write you answer in standard form.
(3x2 - x) - (x2 + 3x + 5)
2x2 - 4x - 5
Multiply. Write you answer in standard form.
(x + 6)(x - 3)
x2 + 3x - 18
Factor using the GCF.
−3k3 + 15k2 − 6k
3k(−k2 + 5k − 2)
Simplify. Write your answer in standard form.
6 - 2x(3x - 2) - x
-6x2 + 3x + 6
Question: Factor completely using grouping:
15x^3-10x^4+8x-12
Answer: 5x^3(3-2x)+4(2x-3)
Explain the mistake and state the correct answer.
They did not finish the problem AND they did not write the polynomial in standard form before using grouping.
Correct Answer:
(2x-3)(-5x^3+4)
Classify the polynomial by its degree and number of terms.
4x2 + 4x - 6
Quadratic Trinomial
Simplify. Write you answer in standard form.
(-3m2 + m3) + (4m2 + 6m)
m3 + m2 + 6m
Multiply. Write you answer in standard form.
(3y + 2)(y - 4)
3y2 - 10y - 8
Factor by grouping.
m3 − m2 + 2m − 2
(m2 + 2)(m − 1)
Multiply. Write you answer in standard form.
(x + 8)2
x2 + 16x + 64
Question: Classify the polynomial by the degree and number of terms.
-2x^2+5x^3-13+x
Answer: Quartic (4th degree) Binomial (2 terms)
Explain the mistake and state the correct answer.
They did not write the polynomial in standard form first AND mixed up the words for the degree and number of terms.
Correct Answer: Cubic (3rd degree) Polynomial with 4 Terms.
Classify the polynomial by its degree and number of terms.
-2x5 + 3x2 - 3x + 2
Quintic Polynomial with 4 terms
Simplify. Write you answer in standard form.
(6x3 - 4x2 + x - 9) - (3x2 + 7x + 3)
6x3 - 7x2 - 6x - 12
Multiply. Write you answer in standard form.
(x - 3)2
x2 - 6x + 9
Factor by grouping.
12a3 − 9a2 + 4a − 3
(3a2 + 1)(4a − 3)
Simplify. Write your answer in standard form.
(-3y2 - 4y - 8) - (-3y2 + 3y) - 7y - 3
-14y - 11
Question: Add/subtract the polynomials.
(-3m^2+m^3)+(4m^2+6m)
Answer: 4m^6-12m^4+6m^3-18m^2
Explain the mistake and state the correct answer.
They multiplied the polynomials instead of adding.
Correct Answer:
m^3+m^2+6m
Classify the polynomial by its degree and number of terms.
5x9 + 2x3 - 3x2 - 4x + 1
9th degree Polynomial with 5 terms
Simplify. Write you answer in standard form.
-(3 + 4z) - (6z2 - 2)
-6z2 - 4z - 1
Multiply. Write you answer in standard form.
(2x + 3)(x2 - 4x - 7)
2x3 - 5x2 - 26x - 21
Factor by grouping.
40xy + 30x − 100y − 75
5(2x − 5)(4y + 3)
Multiply. Write you answer in standard form.
(3x2y + 2y)(3xy + 2y + 3x +1)
9x3y2 + 6x2y2 + 9x3y + 3x2y + 6xy2 + 4y2 + 6xy + 2y
Question: Multiply.
6pr(2p-r)
Answer:
6p^2r
Explain the mistake and state the correct answer.
They tried to combine like terms after distributing but these are not like terms.
Correct Answer:
12p^2r-6pr^2