GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A civil engineer is calculating the stress on a beam. The stress (S) in Pascals is given by the expression 3(x + 2)^2 - 5(x + 2) + 7, where x is a variable representing a load factor. Simplify this expression.
- A3x^2 + 2x + 9
- B3x^2 + 7x + 7
- C3x^2 + 2x + 7
- D3x^2 + 7x + 9
Show answer & explanationAnswer & explanation
Correct answer: D. 3x^2 + 7x + 9
To simplify the expression, we need to expand (x+2)^2, distribute the -5, and then combine like terms. This process involves polynomial expansion and basic algebraic simplification.
Why the other options are wrong
- A. This option has an incorrect coefficient for the 'x' term.
- B. This option has an incorrect constant term.
- C. This option has incorrect coefficients for both the 'x' and constant terms.
Simplifying Algebraic Expressions (Polynomials)
The process of rewriting an algebraic expression in a more compact and understandable form by performing operations like distribution, combining like terms, and expanding products.
- Follow the order of operations (PEMDAS/BODMAS).
- Distribute multiplication over addition/subtraction.
- Combine terms with the same variable and exponent.
Memory trick: Expand, Distribute, Combine Clearly.