Remainder Theorem & Factor Theorem

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of this division is equal to f(c).

Tags

CCSS.HSA.APR.B.2

Front

What is the Factor Theorem?

Back

The Factor Theorem states that (x - c) is a factor of the polynomial f(x) if and only if f(c) = 0.

Tags

CCSS.HSA.APR.B.2

Front

How do you determine if (x - c) is a factor of a polynomial?

Back

To determine if (x - c) is a factor of a polynomial f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

Tags

CCSS.HSA.APR.B.2

Front

What is the remainder when p(x) = x^3 - 5x^2 + 2x - 10 is divided by (x - 5)?

Back

The remainder is 0.

Tags

CCSS.HSA.APR.B.2

Front

Is (x - 3) a factor of 3x^3 + 10x^2 - x - 12?

Back

No, it is not a factor.

Tags

CCSS.HSA.APR.B.2

Front

What is the remainder when (9x^4 - 45x^3 + 37x^2 + x + 2) is divided by (x - 2)?

Back

The remainder is -64.

Tags

CCSS.HSA.APR.B.2

Front

If f(x) = x^2 - 4, what is f(2)?

Back

f(2) = 0, so (x - 2) is a factor.

Tags

CCSS.HSF.IF.A.2

Front

What does it mean if the remainder is 0 when dividing a polynomial?

Back

If the remainder is 0, it means that the divisor is a factor of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

What is the significance of the Remainder Theorem in polynomial division?

Back

The Remainder Theorem allows us to quickly find the remainder without performing long division.

Tags

CCSS.HSA.APR.B.2

Front

How can you use synthetic division to find the remainder?

Back

Synthetic division can be used to divide a polynomial by a linear factor and find the remainder efficiently.

Tags

CCSS.HSA.APR.D.6