Question

For each polynomial operation, write the letter that corresponds to the resulting expression from the list..

a. (5x² + 2x + 1) + (6x² − 3x + 9) is equivalent to expression.
b. (-3x²+6x-12) + (5x+9) is equivalent to expression
c. (8x+16) - (3x² - 3x - 15) is equivalent to expression.
d. (5x² + 23x-7) - (x² - 4x+21) is equivalent to expression.

Answer 1

Polynomials are added or subtracted by combining like terms. Expression a results in 11x² - x + 10, expression b is -3x² + 11x - 3, expression c is -3x² + 11x + 1, and expression d is 4x² + 27x - 28.

Step-by-step explanation:

When adding or subtracting polynomials, we simply combine like terms, where terms in each polynomial with the same variable to the same power are like terms. For example, when we add (5x² + 2x + 1) and (6x² − 3x + 9), we combine the x² terms, the x terms, and the constant terms individually: (5x² + 6x²) + (2x - 3x) + (1 + 9) which simplifies to 11x² - x + 10. Similarly, for subtraction of polynomials like (8x+16) - (3x² - 3x - 15), each term of the subtracted polynomial changes sign before they are combined with the corresponding terms from the first polynomial, leading to 8x - (-3x²) + 16 - 3x - 15.

Now, let's perform the operations and match them to their corresponding expressions as listed in the question:

1. (5x² + 2x + 1) + (6x² − 3x + 9) results in 11x² - x + 10, equivalent to expression a.
2. (-3x²+6x-12) + (5x+9) simplifies to -3x² + 11x - 3, equivalent to expression b.
3. (8x+16) - (3x² - 3x - 15) simplifies to -3x² + 11x + 1, equivalent to expression c.
4. (5x² + 23x-7) - (x² - 4x+21) simplifies to 4x² + 27x - 28, equivalent to expression d.