Math 8 Exam 1 Solutions

You will not receive full credit if you do not clearly show work as demonstrated
in class. Show all work in the space provided on this exam. Circle your answers .

1. Add , subtract, or multiply as directed.
Express your answer as a single polynomial in standard form.

(16 points)

2. Use synthetic division to find the quotient and remainder when 2x⁴ − 3x² + 2
is divided by x − 2.

(5 points)

So the quotient is 2x³ + 4 x² + 5x +10 and the remainder is 22.

3. Simplify each expression . Assume that all variables are positive when they appear. (15 points)

4. Factor completely each polynomial. If the polynomial cannot be factored, say it is prime. (20 points)

5. Use synthetic division to determine whether x + 4 is a factor of x⁶ −16x⁴ + x² −16 . (5 points)

Since the remainder is zero , x + 4 is a factor of x⁶ −16x⁴ + x² −16

6. Perform the indicated operation and simplify the result.
Leave your answer in factored form .

(20 points)

6. Continued from the previous page .

7. Find the quotient and remainder when 2x⁴ − 3x³ + x +1 is divided by 2x² + x +1. (5 points)

So the quotient is and the remainder is .

8. Simplify each expression .

(10 points)

9. Find the value of

when x = 3 and y = −2.

(4 points)