Page 7 - 8-Math-5 Polynomials

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= 20 x2+3 (Law of exponents)
= 20 x5

Example 2: Find the product of 3x2 + 2x - 4 and 5x2 - 3x + 3

Solution: Horizontal Method
(3x2 + 2x - 4) (5x2 - 3x + 3)
= 3x2(5x2 - 3x + 3) + 2x (5x2 - 3x + 3) - 4(5x2 - 3x + 3)
= 15x4 - 9x3 + 9x2 + 10x3 - 6x2 + 6x - 20x2 + 12x - 12
= 15x4 + (10 - 9)x3 + (9 - 6 - 20)x2 + (6 + 12)x -12
= 15x4 + x3 - 17x2 + 18x - 12

Example 3: Multiply 2x - 3 with 5x + 6

Solution: Vertical Method

5x + 6

x 2x - 3

10x2 + 12x

- 15x - 18

10x2 - 3x - 18

Note: The product of two polynomials is also a polynomial whose degree is equal to the
sum of the degrees of the two polynomials.

5.3.2 Division of Polynomials

Division is the reverse process of multiplication.
The method of division of polynomials is explained through examples.

Example 1: Divide (- 8x5 ) by ( - 4x3 )

Solution: (- 8x5 ) ' ( - 4x3 ) = ( - 8x5 ) x 1
-4x3

= 2x 5 - 3

= 2x2

version: 1.1

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