Question

Question 1 (1 point) Divide using any method. -3x3 + 4.x2 + 2x – 5) (x - 2)

Answer 1

Answer:Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of

0

.

x

+

1

4

x

2

-

2

x

-

5

Divide the highest order term in the dividend

4

x

2

by the highest order term in divisor

x

.

4

x

x

+

1

4

x

2

-

2

x

-

5

Multiply the new quotient term by the divisor.

4

x

x

+

1

4

x

2

-

2

x

-

5

+

4

x

2

+

4

x

The expression needs to be subtracted from the dividend, so change all the signs in

4

x

2

+

4

x

4

x

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

4

x

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

Pull the next terms from the original dividend down into the current dividend.

4

x

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

Divide the highest order term in the dividend

−

6

x

by the highest order term in divisor

x

.

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

Multiply the new quotient term by the divisor.

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

-

6

x

-

6

The expression needs to be subtracted from the dividend, so change all the signs in

−

6

x

−

6

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

+

6

x

+

6

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

4

x

-

6

x

+

1

4

x

2

-

2

x

-

5

-

4

x

2

-

4

x

-

6

x

-

5

+

6

x

+

6

+

1

The final answer is the quotient plus the remainder over the divisor.

4

x

−

6

+

1

x

+

1

Step-by-step explanation: