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Real Numbers

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Inequalities & Absolute Value

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Rational Expressions 1

Rat'l. Exp. 2 - mult&div

Rat'l. Exp. 3 - add&subt

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jdsmathnotes

 


UNIT 1 : PRECALCULUS PREP

LESSON 4: OPERATIONS WITH POLYNOMIALS

 

Addition and Subtraction:

 

Example 1: + sign preceding brackets simply drop the brackets and collect like terms

 

a) (3x2 2x + 5) + (5x2 3x 6) = 3x2 2x + 5 + 5x2 3x 6 ** drop brackets

= 3x2 + 5x2 2x 3x +5 6 ** Collect like terms

= 8x2 5x 1

 

Example 2: - sign preceding brackets multiply each term in the bracket by -1 and collect like terms

 

(5x2 3x + 6) (2x2 7x + 8) = (5x2 3x + 6) 1(2x2 7x + 8) ** multiply 2nd bracket by -1

= 5x2 3x + 6 2x2 + 7x - 8

= 5x2 2x2 3x + 7x + 6 8 ** collect like terms

= 3x2 + 4x - 2

 

Example 3:

 

a) (7a2 3ab 5b2) + ( 4a2 8ab 2b2) = 7a2 3ab 5b2 + 4a2 8ab 2b2

= 7a2 + 4a2 3ab 8ab 5b2 2b2

= 11a2 11ab 7b2

b) (8x + 3y 5xy) (4x 7y 6xy) = (8x + 3y 5xy) 1(4x 7y 6xy) ** multiply 2nd bracket by -1

= 8x + 3y 5xy 4x + 7y + 6xy

= 8x 4x + 3y + 7y 5xy + 6xy ** collect like terms

= 4x + 10y + xy

Multiplying with Polynomials (Expanding):

 

Example 1: Monomial x Polynomial multiply each term in bracket by the monomial

 

a) 3x(2x2 5x + 7) = -3x(2x2) 3x(-5x) 3x(7) ** multiply each term by -3x

= -6x3 + 15x2 21x

b) 2x(5x 3) 5(2x + 7) = 10x2 6x 10x 35 ** multiply each term in 1st bracket by 2x and 2nd bracket by -5

= 10x2 16x 35 ** collect like terms

 

Example 2: Polynomial x Polynomial multiply each term in 1st bracket by each term in 2nd bracket

 

a) (3x + 5)(2x 7) = 3x(2x 7) + 5(2x 7) ** multiply each term in 1st bracket by each term in 2nd bracket

= 6x2 21x + 10x 35 ** expand as in previous example

b) (2x + 3)(3x2 5x 2) = 2x(3x2 5x 2) + 3(3x2 5x 2) ** multiply each term in 1st bracket by each term in 2nd bracket

= 6x3 10x2 4x + 9x2 15x 6 ** expand

= 6x3 x2 19x 6 ** collect like terms

c) 2(5x 3)2 3(2x 1)(3x + 2) = 2(5x 3)(5x 3) 3(2x 1)(3x + 2)

= 2(25x2 15x 15x + 9) 3(6x2 + 4x 3x 2)

= 50x2 30x 30x + 18 18x2 12x + 9x + 6

= 32x2 63x + 24

 

 

 

 

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