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Back to Exercise: Perform polynomial operations

Exercises: Add, Subtract, and Multiply Polynomials

Work through each section in order. Show your work where indicated. For multi-step problems, write each step clearly.

Grade 9·22 problems·~35 min·Common Core Math - HS Algebra·standard·hsa-apr-a-1
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A

Recall / Warm-Up

1

Which expression shows the degree and leading coefficient of 4x3−2x2+7x−14x^3 - 2x^2 + 7x - 1?

2

Which pair of terms are like terms that can be combined?

3

Which of the following is NOT a polynomial?

B

Fluency Practice

1

Add the polynomials: (3x2−2x+5)+(x2+4x−3)(3x^2 - 2x + 5) + (x^2 + 4x - 3).

What is the coefficient of x2x^2 in the simplified result?

2

Subtract: (5x2−3x+7)−(2x2+x−4)(5x^2 - 3x + 7) - (2x^2 + x - 4).

What is the coefficient of xx in the simplified result?

3

Subtract: (4x3−2x2+x)−(x3−2x2+5)(4x^3 - 2x^2 + x) - (x^3 - 2x^2 + 5).

What is the constant term of the simplified result?

4

Multiply: (x+4)(x−3)(x + 4)(x - 3).

Bracket diagram showing how each term of (2x − 1) distributes across the three terms of the trinomial, with all six partial products labeled.
5

Multiply: (2x−1)(x2+3x−5)(2x - 1)(x^2 + 3x - 5).

What is the coefficient of x2x^2 in the product?

6

Without fully expanding, predict the degree of the product (3x4−x)(2x3+5)(3x^4 - x)(2x^3 + 5).

What is the degree of the product?

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