Algebra Test Polynomials and Factoring

Question 1

Simplify: (3x² + 2x - 1) + (x² - 4x + 5).

Accepted Answer

4x² - 2x + 4

Answer

Combine like terms: (3+1)x² + (2-4)x + (-1+5) = 4x² - 2x + 4.

Question 2

What is the degree of the polynomial 5x⁴ - 3x² + 7x - 2?

Accepted Answer

4

Answer

The degree is the highest power of the variable, which is 4.

Question 3

Multiply: (x + 3)(x - 2).

Accepted Answer

x² + x - 6

Answer

Use FOIL: x² - 2x + 3x - 6 = x² + x - 6.

Question 4

Factor out the GCF: 6x³ + 9x².

Accepted Answer

3x²(2x + 3)

Answer

The GCF of 6x³ and 9x² is 3x², giving 3x²(2x + 3).

Question 5

Expand: (2x + 1)².

Accepted Answer

4x² + 4x + 1

Answer

Using (a + b)² = a² + 2ab + b²: (2x)² + 2(2x)(1) + 1² = 4x² + 4x + 1.

Algebra Test Practice Test