POLYNOMIAL OPERATIONS

INTEGRATED MATHEMATICS

TYPES OF POLYNOMIALSName # Terms Example

Monomial

Binomial

Trinomial

Polynomial

LIKE TERMS• Same Variable• Same Exponent

Example: and

DEGREE: LARGEST EXPONENT ON POLYNOMIAL

DESCENDING ORDER: HIGHEST DEGREE FIRST

DESCENDING ORDER:

EXAMPLE 1(3 𝑥2+2 𝑥−2 )+(−2𝑥2+5 𝑥+5)

EXAMPLE 2(31𝑚4+𝑚2+2𝑚−1 )+(−7𝑚4+5𝑚2−2𝑚+2)

EXAMPLE 3(4 𝑎2𝑏−5𝑎+2 )+(−2𝑎2𝑏−2𝑎−4 )

EXAMPLE 4(3𝑛3−3𝑚3𝑛2−5𝑛−3 )+(5𝑛3+2𝑚3𝑛2−3𝑚−2𝑛−2)

EXAMPLE 5(−2𝑚3−5𝑚2−2𝑚−4 )+(𝑚4−6𝑚2+7𝑚−10)

EXAMPLE 6(−2𝑥4 𝑦3−5𝑥𝑦+2 )+(𝑥4 𝑦3+𝑥2+2𝑥𝑦+5)

Subtract

(𝑎3−2𝑎2+4 )−(𝑎4−4 𝑎3−3𝑎2)EXAMPLE 7

(4 𝑥3 𝑦+2 𝑥2 𝑦 2−3 𝑥𝑦+6 )−(𝑥3 𝑦−2𝑥2 𝑦2−2𝑥𝑦−3)

EXAMPLE 8

(3 𝑥3 𝑦2−4 𝑥𝑦+1 )−(−4 𝑥3 𝑦2−3𝑥2 𝑦2+3 𝑥𝑦−5)

EXAMPLE 9

(5𝑝2−3𝑝+6 )−(9𝑝2−5𝑝−3)EXAMPLE 10

(4 𝑥3+2𝑥2−2 𝑥−3 )−(2𝑥3−3 𝑥2+2)

EXAMPLE 11

MULTIPLYING POLYNOMIALS• SIMPLIFY USING THE

DISTRIBUTIVE PROPERTYExample 1 2x ( 5x + 3 )

• SIMPLIFY USING THE DISTRIBUTIVE PROPERTYExample 2

• SIMPLIFY USING THE DISTRIBUTIVE PROPERTYExample 3

• SIMPLIFY USING THE DISTRIBUTIVE PROPERTYExample 4

8p

• SIMPLIFY USING THE DISTRIBUTIVE PROPERTYExample 5

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MULTIPLYING BINOMIALS

HOW WOULD YOU USE THE DISTRIBUTIVE PROPERTY TO SIMPLIFY THIS?( x + 1) ( x + 5 )

binomial binomial

HOW WOULD YOU USE THE DISTRIBUTIVE PROPERTY TO SIMPLIFY THIS?Example 6

( x + 1) ( x + 5 )

Example 6( 2n + 3) ( n - 6 )

Example 7

Example 8

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SPECIAL CASESExample 9

SPECIAL CASESExample 10

SPECIAL CASESExample 11

SPECIAL CASESExample 12

SPECIAL CASESExample 13

SPECIAL CASESExample 14

SPECIAL CASESExample 15

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BINOMIALS & TRINOMIALS

Example 1

BINOMIALS & TRINOMIALS

Example 2

BINOMIALS & TRINOMIALS

Example 3

BINOMIALS & TRINOMIALS

Example 4

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