section 4-3 the remainder and factor theorems. remainder theorem remainder theorem – if a...

Section 4-3

The Remainder and Factor Theorems

Remainder Theorem

Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant, P(r), and where Q(x) is a polynomial with degree one less than the degree of P(x).

Example 1

Synthetic Divisionby x+3

62 xxRemainder 13

534 23 xxx

Divide using synthetic division.

yyyy 234 246 By y+2

Divide using synthetic division.

yyyy 234 246 By y+2

- 2 -1 0 4 0 3 2 0 2 -4 0 0 -6 8 -1 2 0 0 3 -4 8

432 45 yyy Remainder of 8

Divide using synthetic division. By (x+2)8102 xx

Divide using synthetic division. By (x-1)143 23 xxx

Divide using synthetic division. By (x+1)533 xx

Divide using synthetic division. By (x-4)4372 234 xxxx

Example 3

Example 4

Use the remainder and factor theorem to find the remainder for each division. State whether

the binomial is a factor of the polynomialby (x+1)

822 xx1624 23 xxx

Use the remainder and factor theorem to find the remainder for each division. State whether

the binomial is a factor of the polynomialby (x+4)

822 xx8102 xx

Use the remainder and factor theorem to find the remainder for each division. State whether

the binomial is a factor of the polynomialby (x-1)

822 xx123 x

Use the remainder and factor theorem to find the remainder for each division. State whether

the binomial is a factor of the polynomialby (x-4)

822 xx164 24 xx

Example 5