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X^2+6x+9 is divided by x+3 |
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Answer» 1.1 Factoring x2 + 6X + 9 The first term is, x2 its coefficient is 1 . The middle term is, +6x its coefficient is 6 . The last term, "the constant", is +9 Step-1 : Multiply the coefficient of the first term by the constant 1 • 9 = 9 Step-2 : Find two factors of 9 whose SUM equals the coefficient of the middle term, which is 6 . -9 + -1 = -10 -3 + -3 = -6 -1 + -9 = -10 1 + 9 = 10 3. + 3 = 6 That's it Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 3 x2 + 3x + 3x + 9 Step-4 : Add up the first 2 TERMS, pulling out like factors : x • (x+3) Add up the last 2 terms, pulling out common factors : 3 • (x+3) Step-5 : Add up the four terms of step 4 : (x+3) • (x+3) Which is the desired factorization 1.2 Cancel out (x+3) which appears on both sides of the fraction line. Final answer is (x+3) |
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