Algebra 2 Polynomial Operations and Identities Quiz: 10 Questions with Explanations

A \(5x – 4\)B \(5x + 14\)C \(6x – 45\)D \(5x^{2} – 4\)

Combine like terms: 2x + 3x = 5x and 5 – 9 = -4. Multiplying or squaring variables is not needed when adding.

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

x² – 3x + 4x – 12 = x² + x – 12. Forgetting the middle terms or mixing the signs gives the other choices.

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

The cells are x², 5x, 2x, and 10, which combine to x² + 7x + 10.

A \(a^{2} – b^{2}\)B \(a^{2} + b^{2}\)C \(a^{2} – 2ab – b^{2}\)D \(a^{2} – 2ab + b^{2}\)

The square of a difference has a middle term -2ab and a positive b². a² – b² is the difference of squares.

A \(36x^{2} + 1\)B \(12x^{2} – 1\)C \(36x^{2} – 1\)D \(36x^{2} – 12x – 1\)

The product of a sum and a difference of the same terms is a difference of squares: (6x)² – 1².

A \(x^{2} + 16\)B \(x^{2} + 4x + 16\)C \(2x + 8\)D \(x^{2} + 8x + 16\)

The four regions are x², 4x, 4x, and 16, so the total is x² + 8x + 16.

A 2,601B 2,501C 2,611D 2,550

(50 + 1)² = 2500 + 100 + 1 = 2601. Using a² + b² only gives 2501.

A \(x = 2, y = 3\)B \(x = 3, y = 2\)C \(x = 5, y = 2\)D \(x = 4, y = 1\)

With x = 3 and y = 2: 9 – 4 = 5, 2·3·2 = 12, and 9 + 4 = 13.

A 6B 5C 3D 2

The degree of a product is the sum of the degrees: 2 + 3 = 5. Multiplying the degrees gives 6.

A \((x + 3)^{2} = x^{2} + 9\)B \((x + 3)^{2} = x^{2} + 3x + 9\)C \((x + 3)^{2} = x^{2} + 6x + 9\)D \((x + 3)^{2} = 2x + 6\)

Only the first is an identity. Test x = 1: (1 + 3)² = 16 and 1 + 6 + 9 = 16, while 1 + 9 = 10 shows the second is false.