Factor Theorem and Long Division

Finish dividing p(x)=5x^3+34x^2+26x+C by x+6. Determine what value C must equal if x+6 is a factor of p(x).

• C would need to be equal to 0.

• C would need to be equal to 12.

• C would need to be equal to -12.

• C would need to be equal to 300.

• Yes, x-3 is a factor of p(x) since the remainder is 0.

• No, x-3 is not a factor of p(x) since the remainder is 0.

Match the following appropriately. It is important you can recognize the connection between factors and solutions.

• 5 is a solution of p(x).

• x - 5 is a factor of p(x).

• -3 is a solution of p(x).

• x + 3 is a factor of p(x).

• 5/3 is a solution of p(x).

• x + 5 is a factor of p(x).

• -5 is a solution of p(x).

• 3x - 5 is a factor of p(x).

• 1 is a solution of p(x)

• 1 is not a solution of p(x)

• x -1 is a factor of p(x)

• x+1 is not a factor of p(x)

Match the following:

• The work provided shows the polynomial 5x² - 10x - 40 being divided by...

• x + 2...

• x+2

• -2...

• 0

• The remainder is...

• x-7 is a factor of p(x).

• x+7 is a factor of p(x).

• -7 is a solution of p(x).

• 7 is a solution of p(x).

Which statement accurately describes what this work demonstrates?

• 5 is a solution of p(x) since the remainder is 0.

• 5 is a solution of p(x) since the remainder is 100.

• 5 is not a solution of p(x) since the remainder is 0.

• 5 is not a solution of p(x) since the remainder is 100.

• x-5 is a factor of p(x) since 5 was a solution.

• x-5 is not a factor of p(x) since 5 was not a solution.

• x+5 is not a factor of p(x) since 5 was not a solution.

• x+5 is a factor of p(x) since 5 was a solution.