Polynomial and Factoring Review

• Quadratic Trinomial

• Quadratic Polynomial

• Cubic Trinomial

• Quadratic Binomial

Answer explanation

The expression simplifies to 2x^2 + 3x + 4, which has 3 terms (2x^2, 3x, 4) and the highest degree is 2. Therefore, it is a Quadratic Trinomial.

• Quadratic Binomial

• Quadratic Trinomial

• Linear Binomial

• Cubic Binomial

Answer explanation

First, simplify the expression: (2p^2 - 3p + 6) - (p^2 - 3p - 2) = p^2 + 8. This is a quadratic expression with 2 terms (p^2 and 8) and degree 2, making it a Quadratic Binomial.

Answer explanation

To simplify, combine like terms: (s^3) + (5s^2) + (4s - 3s) + (-7 + 7) = s^3 + 5s^2 + s. The correct choice is s^3 + 5s^2 + s, which has 3 terms and a degree of 3.

• 0, 0 terms, degree 0

• -10c, 1 term, degree 1

• -10, 1 term, degree 0

Answer explanation

To simplify (11c^2 - 5c - 9) - (11c^2 + 5c - 9), combine like terms: 11c^2 - 11c^2 - 5c - 5c - 9 + 9 = 0. The result is 0, which has 0 terms and degree 0. Thus, the correct answer is 0, 0 terms, degree 0.

Match the polynomial with its classification.

• B

• constant monomial

• C

• linear monomial

• D

• linear binomial

• E

• quadratic binomial

• A

• quadratic trinomial

Answer explanation

The GCF of the terms 2t^2, -8t, and -4 is 2. Factoring out 2 gives us 2(t^2 - 4t - 2). Thus, the factored expression is 2(t^2 - 4t - 2).

• m(3m - 5 + 1)

Answer explanation

To factor out the GCF from the expression 3m^3 - 5m^2 + m, we identify 'm' as the common factor. Factoring it out gives us m(3m^2 - 5m + 1), which matches the correct answer choice.

Answer explanation

To factor out the GCF from 18c^4 + 12c^3 - 24c^2, we identify the GCF as 6c^2. Factoring gives us 6c^2(3c^2 + 2c - 4). However, the correct factorization is 18c^2(c^2 + 2c - 3), which matches the first answer choice.

Answer explanation

To find the product, distribute 2x across each term in the polynomial: 2x * x^2 = 2x^3, 2x * -4x = -8x^2, and 2x * 5 = 10x. Combining these gives 2x^3 - 8x^2 + 10x, which matches the correct answer.

Answer explanation

To find the product of (2y + 1)(y - 1), use the distributive property: 2y*y + 2y*(-1) + 1*y + 1*(-1) = 2y^2 - 2y + y - 1 = 2y^2 - y - 1. Thus, the correct answer is 2y^2 - y - 1.