Polynomials Unit 1 Review

Answer explanation

To find f(-15), substitute -15 into the function: f(-15) = (2/3)(-15) - 8 = -10 - 8 = -18. Thus, f(-15) = -18.

• -11

• -10

Answer explanation

To find p(1/2), substitute x with 1/2 in the polynomial: p(1/2) = -8(1/2)^3 + 8(1/2)^2 - 11 = -8(1/8) + 8(1/4) - 11 = -1 + 2 - 11 = -10. Thus, the correct answer is -10.

Write an expression that is equivalent to (4x^2 - 5x + 1) + (6x^2 + 12x + 3). Enter your answer in the box below. Answer must be in standard form, will be counted incorrect if not.

(a)  

Answer explanation

To combine the expressions, add the coefficients of like terms: (4x^2 + 6x^2) + (-5x + 12x) + (1 + 3) = 10x^2 + 7x + 4. The equivalent expression in standard form is 10x^2 + 7x + 4.

Write an expression that is equivalent to (-3x^2 + 10x - 1) - (8x^2 - 7x - 7). Enter your answer in the box below. Answer must be in standard form or it will be marked incorrect.

(a)  

Answer explanation

To simplify (-3x^2 + 10x - 1) - (8x^2 - 7x - 7), distribute the negative sign: -3x^2 + 10x - 1 - 8x^2 + 7x + 7. Combine like terms: (-3x^2 - 8x^2) + (10x + 7x) + (-1 + 7) = -11x^2 + 17x + 6.

Which expression represents the perimeter of the triangle pictured?

• 20x + 15

• 21x

• 6x + 3

• 6x + 15

Answer explanation

To find the perimeter of the triangle, sum the lengths of all sides. The expression 6x + 15 correctly represents this total, as it combines the side lengths appropriately.

Match each term with its definition.

• 3 terms

• Quadratic

• 2 terms

• Cubic

• 2nd degree

• Monomial

• 1 term

• Binomial

• 3rd degree

• Trinomial

• Quadratic

• Cubic

• Linear

• Quartic

• Quintic

Answer explanation

The expression -7 - 4x^5 - (1/4)x - x^4 is a polynomial of degree 5, as the highest power of x is 5 (from -4x^5). Therefore, it represents a quintic polynomial.

• 1

• 2

• 3

• 4

• 5