Question

Create your own question that could appear on the test for this unit. The question can be about adding, subtracting, multiplying, or factoring polynomials. Solve your own problem to make sure that the question has a solution. What are two pieces of mathematical advice you have for a classmate who’s about to take an assessment on the content you learned in this unit? Think about what types of mistakes are common when adding, subtracting, multiplying, or factoring polynomials.

Answer 1

Question:
Simplify the expression: (2x - 3)(x + 4) + (x - 5)(x + 2)

Solution:
Expanding each product of binomials, we get:
(2x - 3)(x + 4) + (x - 5)(x + 2)
= 2x² + 8x - 3x - 12 + x² + 2x - 5x - 10
= 3x² + 2x - 22

Mathematical advice for a classmate:

1. Carefully distribute and combine like terms when adding or subtracting polynomials. One common mistake is forgetting to distribute the negative sign when subtracting binomials or omitting like terms.

2. When factoring polynomials, always look for common factors first. Factoring out the greatest common factor helps simplify the expression and makes it easier to factor further, if needed. Additionally, double-check your factoring by expanding the obtained factors to ensure you have factored correctly.