Synthetic Division

If the factors of a polynomial function include (x-4)(x-3)(x+2)(x-1). Which of the following can be a possible polynomial function that has been factorized?

• x⁴+9x³+5x²-10

• x⁴+9x³+5x²+24

• x⁴+12x³+6x²-7

• x⁴+10x³+5x²-2

If the factors of a polynomial function include (x-2)(x+13)(x-1). Which of the following can be a possible polynomial function that has been factorized?

• x⁴+9x³+5x²-10

• x⁴+9x³+5x²+26

• x⁴+12x³+6x²-7

• x⁴+10x³+5x²-2

If the factors of a polynomial function include (x-7)(x+2)(x-1). Which of the following can be a possible polynomial function that has been factorized?

• x⁴+9x³+5x²-14

• x⁴+9x³+5x²+21

• x⁴+12x³+6x²-28

• all of the above

Which of the following can be a factor of x⁴-29x²+100 = 0.

• x-5

• x-20

• x+13

• x-1

• (x-5) , (x-20) and (x-1)

Which of the following cannot be considered as a factor of x⁴-29x²+100 = 0.

• x-5

• x-20

• x+13

• x-1

The function: x⁴+9x³+5x²-10= 0 translates into whcih synthetic division.

• 1 9 5 -10 0 divided by -1

• 1 9 5 -10 divided by 6

• 1 9 5 -10 divided by 4

• 1 9 5 -10 divided by 3

If I solve a synthetic division and it has 3 steps.

Starts: 1 -8 23 -28 12 divided by 3

Solution: 1 -5 8 -4 0

Then in the second synthetic division.

Starts : 1 -5 8 -4 divided by 2

Solution: 1 -3 2 0

Then in the third step.

Starts: _____________________________

• 1 -3 2 divided by 1

• 1 -3 2 divided by -1

• 1 -3 2 divided by 2

• All of the above

• None of the above

If I solve a synthetic division and it has 3 steps.

Starts: 1 -8 23 -28 12 divided by 3

Solution: 1 -5 8 -4 0

Then in the second synthetic division.

Starts : 1 -5 8 -4 divided by 2

Solution: 1 -3 2 0

Then in the third step.

Starts: _____________________________

• It means (x+3) and (x+2) are two of its factors.

• It means (x-3) and (x-2) are two of its factors.

• It means (x-3) and (x-2) are all of its factors.

• It means (x-3) and (x-2) are not its factors.

If I solve a synthetic division and it has 3 steps.

Starts: 1 -8 23 -28 12 divided by 3

Solution: 1 -5 8 -4 0

Then in the second synthetic division.

Starts : 1 -5 8 -4 divided by 2

Solution: 1 -3 2 0

Then in the third step.

Starts: _____________________________

• The third step can be avoided because there is no solution.

• The third step could be avoided by factoring x²-3x+2 = 0.

• The polynomial function has no factors.

• The polynomial function has other factors not expressed yet.

If I solve a synthetic division and it has 3 steps.

Starts: 1 -8 23 -28 12 divided by 3

Solution: 1 -5 8 -4 0

Then in the second synthetic division.

Starts : 1 -5 8 -4 divided by 2

Solution: 1 -3 2 0

Then in the third step.

Starts: _____________________________

• The original polynominal equation is a fifth degree function

• The original polynominal equation is a fourth degree function

• The original polynominal equation is a third degree function

• The original polynominal equation is a second degree function