section 2-2 synthetic division; the remainder and factor theorems

Section 2-2 Synthetic Division; The Remainder and Factor Theorems

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Section 2-2

Synthetic Division; The Remainder and Factor Theorems

Recall…

Polynomial long division is like long division with numbers.

Page 3: Section 2-2 Synthetic Division; The Remainder and Factor Theorems

The Remainder Theorem

When a polynomial P(x) is divided by x – a, the remainder is P(a).

Synthetic Division

Since synthetic substitution gives not only the remainder but also the quotient, we can use it in place of long division, this is called synthetic division.

The Factor Theorem

For a polynomial P(x), x – a is a factor if and only if P(a) = 0.

Page 6: Section 2-2 Synthetic Division; The Remainder and Factor Theorems

Example

Find the quotient and remainder when

is divided by x + 4 81023 xxx

Page 7: Section 2-2 Synthetic Division; The Remainder and Factor Theorems

Example

If x = 2 is a root of

find the remaining roots.

0102352 23 xxx

Page 8: Section 2-2 Synthetic Division; The Remainder and Factor Theorems

Example

When a number is divided by 5 the quotient is 7 and the remainder is 2. Find the number.

Page 9: Section 2-2 Synthetic Division; The Remainder and Factor Theorems

Example

When a polynomial P(x) is divided by 3x – 4, the quotient is and the remainder is -1. Find P(x).

223 xx

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