Given: X = r 2, Y = 2r - 9, and Z = r2 17r 30.
Simplify [X Y - Z] X.
(r+2)(2r-9)-(r^(2)+17r+30)/(r+2)... For a polynomial of the form x^(2)+bx+c, find two factors of c (30) that add up to b (17). [ [ In this problem 15*2=30 and 15+2=17, so insert 15 as the right hand term of one factor and 2 as the right-hand term of the other factor. (r+2)(2r-9)-((r+15)(r+2))/(r+2)... Reduce the expression by canceling out the common factor of (r+2) from the numerator and
denominator. (r+2)(2r-9)-((r+15) (r+2) )/( (r+2) )... Reduce the expression by canceling out the common factor of (r+2) from the numerator and denominator. (r+2)(2r-9)-(r+15) Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group. (r*2r+r*-9+2*2r+2*-9)-(r+15)... Simplify the FOIL expression by multiplying and combining all like terms. (2r^(2)-5r-18)-(r+15)... Multiply -1 by each term inside the parentheses. (2r^(2)-5r-18)+-r-15... Since -5r and -r are like terms, subtract r from -5r to get -6r. 2r^(2)-6r-18-15... Subtract 15 from -18 to get -33. 2r^(2)-6r-33 is the answer. ] ]
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