Question

Select the correct answer.

Simplify the following expression. Classify the resulting polynomial.

3x(x − 3) + (2x + 6)(-x − 3)


quadratic monomial

quadratic binomial

quadratic trinomial

linear binomial

Answer 1

9514 1404 393

Answer:

• x² -21x -18
• quadratic trinomial

Explanation:

Eliminating parentheses, we get ...

= (3x)(x) -(3x)(3) +(2x)(-x -3) +6(-x -3)

= 3x² -9x +(2x)(-x) +(2x)(-3) +(6)(-x) +(6)(-3)

= 3x² -9x -2x² -6x -6x -18

= x²(3 -2) +x(-9-6-6) -18

= x² -21x -18

The highest power is 2, so this is a quadratic.

There are 3 terms, so this is a trinomial.

Answer 2

quadratic trinomial

Explanation:

3x(x − 3) + (2x + 6)(-x − 3)

Distribute

3x^2 -9x + (2x + 6)(-x − 3)

FOIL

3x^2 -9x + -2x^2 -6x -6x -18

Combine like terms

x^2-21x-18

This has 3 terms so it is a trinomial

The highest power of x is 2 so it is quadratic