College Algebra (Abridged)

( ) = 8 4 + 3 2 − 17 + 10 If we wish to add or subtract these two expressions, then we combine the coefficients of the like terms. The addition for these expressions is given as follows: ( ) = 4 3 – 6 2 + 9 + 12 + 8 4 + 3 2 − 17 + 10 ( ) = 8 4 + 4 3 + (– 6 2 + 3 2 ) + (9 − 17 ) + (12 + 10) ( ) = 8 4 + 4 3 − 3 2 − 8 + 22 Similarly, subtraction of these polynomials will be done as follows: ( ) = 4 3 – 6 2 + 9 + 12– (8 4 + 3 2 − 17 + 10) ( ) = − 8 4 + 4 3 + (– 6 2 − 3 2 ) + (9 + 17 ) + (12 − 10) ( ) = − 8 4 + 4 3 − 9 2 + 26 + 2 The rules for multiplication and division of polynomials are different. The coefficients are multiplied or divided while the exponents of the variables are added (in the case of multiplication) or subtracted (in the case of division). For instance, if we wish to multiply the above equations ( ) and ( ) , we will be multiplying each and every term of both the equations. ( ) = (4 3 – 6 2 + 9 + 12) ∙ (8 4 + 3 2 − 17 + 10) ( ) = 8 4 (4 3 – 6 2 + 9 + 12) + 3 2 (4 3 – 6 2 + 9 + 12) − 17 (4 3 – 6 2 + 9 + 12) + 10(4 3 – 6 2 + 9 + 12) ( ) = (32 7 – 48 6 + 72 5 + 96 4 ) + (12 5 – 18 4 + 27 3 + 36 2 ) +( − 68 4 + 102 3 − 153 2 – 204 ) + (40 3 – 60 2 + 90 + 120) Simplifying the terms as per the rule of addition and subtraction ( ) = 32 7 − 48 6 + (72 5 + 12 5 ) + (96 4 – 18 4 − 68 4 ) +(27 3 + 102 3 + 40 3 ) + (36 2 − 153 2 – 60 2 ) +( − 204 + 90 ) + 120 ( ) = 32 7 – 48 6 + 84 5 + 10 4 + 169 3 – 177 2 − 114 + 120 1.10 Solving Quadratic Equations The system of equations with a maximum leading power of two is termed as a quadratic equation, while the system of equations with a maximum leading power of three are known as cubic equations. The graphs for quadratic equations are generally a U-shaped curve. The general form of a quadratic equation is:

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