Question

1. What is the sum or difference?

4x^10 - 9x^10 (1 point)

(A). -5x^10
(B). -5x^20
(C). -36x^20
(D). -36x^20

2. What is the sum or difference?

6y^5 - 9y^5 (1 point)

(A). -3y^10
(B). 15y^5
(C). -54y^5
(D). -3y^5

3. Write the Polynomial in standard form. Then name the Polynomial based on its degree and number of terms.

2 - 11x^2 - 8x + 6x^2 (1 point)

(A). -5x^2 - 8x + 2; quadratic trinomial
(B). -5x^2 - 8x; quadratic binomial
(C). -6x^2 - 8x - 2; cubic polynomial
(D). 6x^2 - 8x + 2; cubic trinomial

4. A biologist studied the populations of white-sided jackrabbits and black-tailed jackrabbits over a 5-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years.

White-sided jackrabbits: 5.5x^2 - 9.2x + 6.9
Black-tailed jackrabbits: 5.5x^2 + 9.9x + 1.3 (1 point)

(A). 11x^2 + 0.7x + 8.2
(B). 11x^2 - 0.7x + 8.2
(C). 11x^2 - 0.7x - 8.2
(D). -11x^2 + 0.7x - 8.2

Someone please help! Unit 3 Lesson 9, Polynomials and Factoring!

Answer 1

Solving question 1 : What is the sum or difference?

`image`

Hence, option A is correct i.e.
`-5x^(10)`.

Solving question 2 : What is the sum or difference?

`image`

Hence, option D is correct i.e.
`-3x^(5)`.

Solving question 3 : Write the Polynomial in standard form.

2 - 11x² - 8x + 6x²

We can combine like terms, and rewriting it in decreasing power of x's.

⇒ - 11x² + 6x² - 8x + 2

⇒ (-11 + 6)x² - 8x + 2

⇒ -5x² - 8x + 2

Hence, option A is correct i.e. -5x² - 8x + 2; quadratic trinomial.

Solving question 4 :

White-sided jackrabbits: 5.5x² - 9.2x + 6.9

Black-tailed jackrabbits: 5.5x² + 9.9x + 1.3

Total population = White-sided jackrabbits + Black-tailed jackrabbits

Total population = (5.5x² - 9.2x + 6.9 ) + (5.5x² + 9.9x + 1.3)

Total population = (5.5 + 5.5)x² + (9.9 - 9.2)x + (6.9 + 1.3 )

Total population = 11x² + 0.7x + 8.2

Hence, option A is correct i.e. 11x² + 0.7x + 8.2