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Polynomial Operations Practice

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Polynomial Operations Practice

Simplify each expression. For written questions, show your steps and explain your reasoning.

Multiple Choice

1.To simplify \((4x^2-x+2)+(x-3)(x+2)\), which operation should you do first?

Combine the terms in the first polynomial
Multiply the two binomials
Subtract the second polynomial
Combine all the x-terms

2.When you expand \((3x+2)(x-4)\), what is the coefficient of the x-term in the simplified result?

-10
-4
2
10

3.Which statements are correct when simplifying polynomial expressions? Select all that apply.

Expand products before combining terms across a sum.
A minus sign before parentheses changes the sign of every term inside.
Only terms with the same variable and exponent can be combined.
You can combine an \(x^2\) term with an x-term.

4.Simplify \((2x^2+5x-3)-(x^2-2x+6)\).

\(x^2+7x-9\)
\(3x^2+3x+3\)
\(x^2+3x+3\)
\(x^2+7x+3\)

Simplify and Show Your Work

5.Simplify \((3x^2-2x+4)+(x+3)(x-2)\).

6.Simplify \((5x^2+x-7)-(2x^2-3x+1)+(x-4)(2x+1)\).

7.A rectangular patio has length \((2x+5)\) feet and width \((x+2)\) feet. A surrounding paved strip adds \((x^2+4x+3)\) square feet. Write and simplify an expression for the patio area plus the strip area.

Explain Your Reasoning

8.A student expands \((x+3)^2-(x-2)(x+4)\) and writes \(3x+17\). Show the expansions, simplify the expression, and decide whether the student's result is correct.

9.Give one realistic situation that could be modeled by adding two polynomial expressions and multiplying two polynomial expressions. Name what the variable represents and describe what each expression measures.

10.In what order should you work when an expression includes polynomial products, subtraction, and like terms?