Math Math Algebra and Functions 2

Question 1

Factor the expression x² − 9.

Accepted Answer

(x + 3)(x − 3)

Answer

x² − 9 is a difference of squares: (x + 3)(x − 3).

Question 2

If f(x) = 2x + 5, what is f(−3)?

Accepted Answer

-1

Answer

f(−3) = 2(−3) + 5 = −6 + 5 = −1.

Question 3

Solve the system: x + y = 8 and x − y = 2.

Accepted Answer

x = 5, y = 3

Answer

Adding equations: 2x = 10, x = 5; then y = 8 − 5 = 3.

Question 4

What is the y-intercept of the line 3x + 2y = 12?

Accepted Answer

6

Answer

Set x = 0: 2y = 12, y = 6, so the y-intercept is 6.

Question 5

Simplify: 3x² + 5x − 2x² + x

Accepted Answer

x² + 6x

Answer

Combine like terms: (3x² − 2x²) + (5x + x) = x² + 6x.

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