Question

version #1
polynomial equations & factoring
total questions: 20
worksheet title
instructor name: carmen belleza

1. which polynomial is written in standard form?

a) 8x - 11x²
b) 19x + 7x² - 9x³+18
c) 12 + 4x
d) 4x³+7x - 9

1. classify by number of terms: 3x³ - 6x

a) 4 - term polynomial
b) binomial
c) trinomial
d) monomial

1. add the polynomials. (2x + 5y)+(3x - 2y)

a) 5x + 7y
b) 5x + 3y
c) 3x + 5y
d) 7xy+1xy

1. classify by the degree: 4x³ - 5x²+2x - 1

a) quadratic
b) fourth degree
c) linear
d) cubic

1. simplify the expression. (4a³ - 8a - 4a²)+(7a³ - 7 - 6a)

a) 5a³ - 4a² - 14a - 7
b) 11a³ - 4a² - 14a - 7
c) 5a³ - 4a² - 20a - 7
d) 5a³ - 9a² - 20a - 7

1. find the perimeter of the rectangle with sides 3x + 4 and 2x

a) 6x + 8
b) 5x + 12
c) 4x + 6
d) 10x + 8

Explanation:

Step1: Recall standard - form of polynomial

A polynomial in standard form has terms in descending order of exponents.
For a), \(8x - 11x^{2}\) should be \(-11x^{2}+8x\). For b), \(15x + 7x^{2}-9x^{3}+18\) should be \(-9x^{3}+7x^{2}+15x + 18\). For c), \(12 + 4x\) is in standard form as the constant term comes first and then the linear term. For d), \(4x^{3}+7x - 9\) is in standard form.

Step2: Recall number - of - terms classification

The polynomial \(3x^{3}-6x\) has two terms, so it is a binomial.

Step3: Add polynomials

\((2x + 5y)+(3x - 2y)=(2x+3x)+(5y - 2y)=5x + 3y\)

Step4: Determine degree of polynomial

The highest power of \(x\) in \(4x^{3}-5x^{2}+2x - 1\) is 3, so it is a cubic polynomial.

Step5: Simplify polynomial sum

\((4a^{3}-8a - 4a^{2})+(7a^{3}-7 - 6a)=(4a^{3}+7a^{3})-4a^{2}+(-8a-6a)-7 = 11a^{3}-4a^{2}-14a - 7\)

Step6: Calculate rectangle perimeter

The perimeter \(P\) of a rectangle with length \(l = 3x + 4\) and width \(w = 2x\) is \(P=2(l + w)=2((3x + 4)+2x)=2(5x + 4)=10x+8\)

Answer:

1. c) \(12 + 4x\), d) \(4x^{3}+7x - 9\)
2. b) Binomial
3. b) \(5x + 3y\)
4. d) Cubic
5. b) \(11a^{3}-4a^{2}-14a - 7\)
6. d) \(10x + 8\)