Question 1
simplify the following expression: (5x2 + 3x + 4) − (2x2 − 6x + 3). if the final answer is written in the form ax2 + bx + c, what is the value of b?

question 2
simplify: (3x2 − 2) + (2x2 − 6x + 3)

5x2 − 6x + 1

5x2 − 6x − 1

x2− 6x + 1

5x2 − 8x + 3

question 3
a sports company conducted a road test of a new model of a geared bike. the test rider cycled (3x - 2) miles on a flat road, (x2 - 5) miles uphill, and (2x + 7) miles downhill. which simplified expression is equivalent to the total distance, in miles, for which the bike was tested?

x2 - x

x2 + 5x

x2 − x + 14

x2 + 5x + 14

question 4
simplify: (4x − 6) − (5x + 1)

x + 7

−x + 7

x − 7

−x − 7

question 5
simplify the following expression: (x + 6y) - (3x − 10y). if the final answer is written in the form ax + by, what is the value of a?

question 6
simplify: (3x − 5) + (3x + 6)

6x − 1

1

6x − 11

Question 1 Simplify the following expression: (5x2 + 3x + 4) − (2x2 − 6x + 3). If the final answer is written in the form Ax2 + Bx + C, what is the value of B?

Solution:

5x^2 + 3x + 4 - 2x^2 + 6x - 3 = 3x^2 + 9x + 1

Then, B = 9

Question 2
Simplify: (3x2 − 2) + (2x2 − 6x + 3)

5x2 − 6x + 1

5x2 − 6x − 1

x2− 6x + 1

5x2 − 8x + 3

Solution:

3x^2 - 2 + 2x^2 - 6x + 3 = 5x^2 - 6x + 1

Question 3
A sports company conducted a road test of a new model of a geared bike. The test rider cycled (3x - 2) miles on a flat road, (x2 - 5) miles uphill, and (2x + 7) miles downhill. Which simplified expression is equivalent to the total distance, in miles, for which the bike was tested?

x2 - x

x2 + 5x

x2 − x + 14

x2 + 5x + 14

(3x - 2) + (x2 - 5) + (2x + 7) = 3x - 2 + x^2 - 5 +2x + 7 = x^2 + 5x

Question 4
Simplify: (4x − 6) − (5x + 1)

x + 7

−x + 7

x − 7

−x − 7

(4x − 6) − (5x + 1) = 4x - 6 - 5x - 1 = -x -7

Question 5
Simplify the following expression: (x + 6y) - (3x − 10y). If the final answer is written in the form Ax + By, what is the value of A?

(x + 6y) - (3x − 10y) = x + 6y - 3x + 10y = -2x + 16y

A = -2

Question 6
Simplify: (3x − 5) + (3x + 6)

6x − 1

1

6x − 11

(3x − 5) + (3x + 6) = 3x - 5 + 3x + 6 = 6x + 1

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