Adding, Subtracting and Multiplying Polynomials: Algebra 1 Math Test – PDF Download

Question 1: Standard form and degree (2 points)

Let \(P=2x-5x^{3}+4-x^{2}\).

1. Write \(P\) in standard form. (1 point)
2. State the degree and the leading coefficient of \(P\). (1 point)

Question 2: Add and subtract (2 points)

Simplify.

1. \((6x^{2}-4x+9)+(-2x^{2}+7x-3)\) (1 point)
2. \((3x^{3}+5x-8)-(x^{3}-2x^{2}+5x+1)\) (1 point)

Question 3: Subtract with two variables (2 points)

Subtract \((7a^{2}b-3ab+4b^{2})-(2a^{2}b+ab-6b^{2})\).

Question 4: Multiply polynomials (2 points)

Multiply.

1. \(-4x(3x^{2}-2x+6)\) (1 point)
2. \((x-6)(x^{2}+4x-2)\) (1 point)

Question 5: Multiply two binomials (2 points)

Multiply \((3x+4)(x-5)\). Complete the area model first, then write the product in standard form.

Question 6: Special products (2 points)

Expand.

1. \((4x-3)^{2}\) (1 point)
2. \((6x+5)(6x-5)\) (1 point)

Question 7: Community garden (3 points)

A community garden is a rectangle that is \(2x+3\) feet long and \(x+5\) feet wide.

1. Write a polynomial in standard form for the area. (1 point)
2. Find the area when \(x=6\). (1 point)
3. Write a polynomial in standard form for the perimeter. (1 point)

Question 8: Bakery profit (3 points)

A bakery sells \(x\) boxes of muffins. Its revenue is \(R=-x^{2}+60x\) dollars and its cost is \(C=12x+150\) dollars. Profit is revenue minus cost.

1. Write a simplified polynomial for the profit. (2 points)
2. Find the profit when 10 boxes are sold. (1 point)

Question 9: Explain the error (2 points)

Liam writes \((x+4)^{2}=x^{2}+16\).

1. Show that his result is wrong by substituting \(x=1\). (1 point)
2. Write the correct expansion. (1 point)

⬇ Download the Algebra 1 Adding, Subtracting and Multiplying Polynomials test (PDF, 88 KB)

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