Algebra 1 Adding, Subtracting and Multiplying Polynomials Quiz: 10 Questions with Explanations

A 3B 4C 2D 9

The degree is the greatest exponent, which is 4. The leading coefficient is 3.

A \(5x^{2} + 3x\)B \(5x^{4} + 3x\)C \(5x^{2} + 7x\)D \(6x^{2} + 3x\)

Combine like terms: 2x² + 3x² = 5x² and 5x – 2x = 3x. Exponents do not change when adding.

A \(5x + 5\)B \(5x – 13\)C \(9x – 13\)D \(5x – 5\)

Distribute the negative: 7x – 4 – 2x + 9 = 5x + 5.

A \(x^{2} + 12\)B \(x^{2} + 7x + 12\)C \(x^{2} + 7x + 7\)D \(2x + 7\)

The cells are x², 4x, 3x, and 12. Combining 4x + 3x gives 7x.

A \(x^{2} + 2x – 24\)B \(x^{2} – 24\)C \(x^{2} + 10x – 24\)D \(x^{2} + 2x + 24\)

x² + 6x – 4x – 24 = x² + 2x – 24.

A \(x^{2} + 49\)B \(x^{2} + 7x + 49\)C \(x^{2} + 14x + 49\)D \(x^{2} + 14x + 14\)

The middle term is 2(7)x = 14x. Squaring each term only misses it.

A \(x^{2} + 81\)B \(x^{2} – 18x – 81\)C \(x^{2} – 18\)D \(x^{2} – 81\)

The inner and outer terms cancel, leaving the difference of squares.

A \(2x + 14\)B \(x^{2} + 10\)C \(x^{2} + 7x + 7\)D \(x^{2} + 7x + 10\)

(x + 5)(x + 2) = x² + 2x + 5x + 10 = x² + 7x + 10. The expression 2x + 14 is the perimeter.

A \(3x^{3} – 2x + 4\)B \(3x^{3} – 6x^{2} + 4\)C \(3x^{3} – 6x^{2} + 12x\)D \(x^{3} – 6x^{2} + 12x\)

Multiply 3x by every term in the parentheses.

A Yes, because it has two termsB No, because it has a negative exponentC Yes, because 1 is a constantD No, because it has a constant term

Polynomial terms have whole-number exponents. A negative exponent means division by a power of x.