ALGEBRA PRACTICE – FULL ANSWER KEY (Problems 1–18 + Bonus)
1) Factor: 5x^2 - 14x - 3
Work:
Multiply 5 * -3 = -15.
Numbers that multiply to -15 and add to -14: -15 and +1.
Rewrite: 5x^2 - 15x + x - 3
Group: 5x(x - 3) + 1(x - 3)
Answer: (x - 3)(5x + 1)
2) Factor: x^3 - 2x^2 - 4x + 8
Group: (x^3 - 2x^2) + (-4x + 8)
Factor: x^2(x - 2) - 4(x - 2)
Answer: (x - 2)^2 (x + 2)
3) Subtract: (8x^2 - 9x + 13) - (-7x^2 - 6x + 8)
Distribute negative: 8x^2 - 9x + 13 + 7x^2 + 6x - 8
Combine: 15x^2 - 3x + 5
Answer: 15x^2 - 3x + 5
4) Simplify: 5a^4 b / (10a^7 b^-2)
Numbers: 1/2
Exponents: a^(4-7) = a^-3, b^(1 - (-2)) = b^3
Answer: b^3 / (2a^3)
5) Multiply: (3x^2 y^-3)(-2x^2 y^2)
Multiply: -6
x exponents: x^4
y exponents: y^-1
