Understanding the Remainder Theorem

The video tutorial explains the remainder theorem, which states that if a polynomial f(x) is divided by x-k, the remainder is f(k). The instructor demonstrates this using synthetic division and evaluates the polynomial to show that the remainder is zero when the divisor is a factor. The video also highlights the importance of the theorem in determining factors of polynomials without division.

What does the Remainder Theorem state?

• If a polynomial is divided by a linear factor, the remainder is the value of the polynomial evaluated at the root of the factor.

• If a polynomial is divided by a linear factor, the remainder is always zero.

• If a polynomial is divided by a linear factor, the remainder is the value of the polynomial evaluated at zero.

• If a polynomial is divided by a quadratic factor, the remainder is the value of the polynomial evaluated at the root of the factor.

Tags

CCSS.HSA.APR.D.6

In the example provided, what are the coefficients used for synthetic division?

• 5, -7, 24

• 5, 7, -24

• 5, -7, -24

• 5, 7, 24

Tags

CCSS.HSA.APR.B.2

What is the resulting factor when the polynomial is divided by x + 3?

• 5x + 8

• 5x - 8

• 5x - 3

• 5x + 3

Tags

CCSS.HSA.APR.D.6

What is the final step in synthetic division?

• Drop down the first coefficient.

• Subtract the last coefficient from the previous result.

• Add the last coefficient to the previous result.

• Multiply the last coefficient by the divisor.

Tags

CCSS.HSF.IF.A.2

What is the value of f(-3) for the polynomial 5x^2 + 7x - 24?

• 0

• 10

• -10

• 24

Tags

CCSS.7.EE.B.3

What is the result of 5 times (-3)^2 in the verification example?

• 15

• 30

• 45

• 60

Tags

CCSS.HSA.APR.B.2

Why is the Remainder Theorem important?

• It helps in finding the degree of a polynomial.

• It helps in simplifying polynomials.

• It helps in determining if a factor evenly divides a polynomial.

• It helps in finding the roots of a polynomial.

Tags

CCSS.HSA.APR.B.2

What is the purpose of evaluating a polynomial at a specific value according to the Remainder Theorem?

• To find the constant term of the polynomial.

• To find the remainder when the polynomial is divided by a linear factor.

• To determine the leading coefficient.

• To find the degree of the polynomial.

Tags

CCSS.HSF.IF.A.2

What is the value of f(2) for the polynomial 5x^2 + 7x - 24?

• 24

• 34

• 10

• 0

Tags

CCSS.HSA.APR.B.2

What is the remainder when the polynomial 5x^2 + 7x - 24 is divided by x - 2?

• 0

• 10

• 34

• 24

Tags

CCSS.HSA.APR.B.2