- (x + 2)^2 + 9
why did my teacher factorize it into this
9(1 - (x + 2)^2/9)
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answers:
moondog say: first move the nine in front 9-(X+2)^2
second remove nine from the equation....9(1-((X+2)^2)/9)....either you or teacher missed a set of parenthesis
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az_lender say: It's easy to show that the two expressions are equivalent, and other responders have done so. Your error lies in calling this "factorization." There was some other reason for rewriting the expression as
9[1 - (x+2)^2/9],
and that reason would be revealed if you had shown us what the teacher did NEXT!
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cidyah say: -(x+2)^2 + 9
factor out 9
9(-(x+2)^2 / 9 + 1)
= 9 ( 1 - (x+2)^2 / 9 )
= 9 ( 1- (x+2) /3) ( 1+ (x+2) /3)
a^2-b^2 = (a-b)(a+b)
a= 1
b= (x+2) /3
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doctormcgoveran say: factoring is the other direction and it is tough. the direction you are going is called multiplication it is easy.In applied amth we first build an equation to fit a physical idea x^2 then we have to solve for X. secondly the second term is incorrect becasue you went from pencil to computer (x+2)^2/9 is not the same as ((x+2)^2)/9
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Mathias say: Why did my teacher factorize it into this:
9 {1 - [(x + 2)^2] / 9} <--- This is quite right but useless at all levels. Your teacher has poor skills.
This is the way I would do it:
- (x + 2)^2 + 9 = 9 - (x + 2)^2 = 3^2 - (x + 2)^2 <--- Difference of two squares.
3^2 - (x + 2)^2 = [3 - (x + 2)] * [3 + (x + 2)] {Rule: a^2 - b^2 = (a - b) * (a + b)}.
[3 - (x + 2)] * [3 + (x + 2)] = (3 - x - 2) * (3 + x + 2).
(3 - x - 2) * (3 + x + 2) = (1 - x) * (5 + x).
Ans.: (1 - x) * (x + 5).
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Como say: 9 - [ x + 2 ] ²
3 ² - [ x + 2 ] ²
[ 3 - (x + 2) ] [ 3 + (x + 2) ]
[ 1 - x ] [ 5 + x ]
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Pope say: The expressions are equivalent, but I have no guess on your teacher's motives in writing it that way. Did you ask the teacher?
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