ACT — mathMedium1 min read

Polynomials and Rational Expressions

Add, subtract, multiply, and divide polynomials for the ACT. Simplify rational expressions.

Tutor AI Team
Tutor AI Team

Polynomial and rational expression questions test your algebra skills on the ACT. You need to add, subtract, multiply, divide, and simplify.

Polynomial Operations

Adding/Subtracting

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

Multiplying

Distribute (FOIL for binomials). (2x+3)(x−4)=2x2−8x+3x−12=2x2−5x−12(2x + 3)(x - 4) = 2x^2 - 8x + 3x - 12 = 2x^2 - 5x - 12

Dividing

Long division or synthetic division.

Rational Expressions

Simplifying

Factor numerator and denominator, cancel common factors.

x2−9x+3=(x+3)(x−3)x+3=x−3\frac{x^2 - 9}{x + 3} = \frac{(x+3)(x-3)}{x+3} = x - 3

Adding/Subtracting

Find common denominator.

2x+3x+1=2(x+1)+3xx(x+1)=5x+2x(x+1)\frac{2}{x} + \frac{3}{x+1} = \frac{2(x+1) + 3x}{x(x+1)} = \frac{5x + 2}{x(x+1)}

Multiplying/Dividing

Factor, cancel, multiply. To divide: flip and multiply.

Practice Problems

    1. Simplify x2−4x2+x−6\frac{x^2 - 4}{x^2 + x - 6}.
    1. Multiply (x+2)(x2−2x+4)(x + 2)(x^2 - 2x + 4).
    1. Add 1x−1+2x+2\frac{1}{x-1} + \frac{2}{x+2}.

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Key Takeaways

  • ✓

    Factor before simplifying rational expressions.

  • ✓

    Common denominator for adding/subtracting.

  • ✓

    FOIL for multiplying binomials.

  • ✓

    Check for restrictions (denominator ≠ 0).

Tags:
#act#math#algebra#polynomials#rational-expressions

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