Simplify (x^2 + 8x + 12)/(x + 2) multiply by 6/(x + 6)
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(x + 6)
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1.1 Factoring x2 - 8x - 12
The first term is, x2 its coefficient is 1 .
The middle term is, -8x its coefficient is -8 .
The last term, "the constant", is -12
Step-1 : Multiply the coefficient of the first term by the constant 1 • -12 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -8 .
-12 + 1 = -11 -6 + 2 = -4 -4 + 3 = -1 -3 + 4 = 1 -2 + 6 = 4 -1 + 12 = 11
Observation : No two such factors can be found !!
1.2 Polynomial Long Division
Dividing : x2-8x-12
("Dividend")
By : x+6 ("Divisor")
dividend x2 - 8x - 12 - divisor * x1 x2 + 6x remainder - 14x - 12 - divisor * -14x0 - 14x - 84 remainder 72
Quotient : x-14
Remainder : 72
Answer:
Multiply the coefficient of the first term by the constant 1 • 12 = 12