Can anyone please explain to me this factorisation question?
x square + 10x +25
=x square +2(5)(x)+5 square
= (x+5 ) square
these are the workings but i still dont understand =(
2007-12-04 04:25:48 · 3 answers · asked by korean_freak_ruii 3 in Education & Reference ➔ Homework Help
x^2 + 10x + 25
.... okay... basically factorizing is the reverse of the FOIL method....
Instead of them giving you the ( )( ) and multiplying to get a resulting polynomial, in this problem, they are giving you the resuliting polynomial and are asking you what should go in the ( ) ( ) 's
You know that you start out with (x + _ ) (x + _)....
because when you multiply the x's (which is what the F in FOIL stands for -- the "first" terms), you get ... x * x = x^2
Now.... to find out what the numbers are that go in the blanks ( _ ' s).... the 25 means that your two numbers (or factors) have to multiply to get a product of 25.... however... the middle term "10x", means that those same to factors that multiply to 25, must ALSO add up to 10....
What are the two factors?
They are 5 and 5..... because 5 * 5 = 25..... and those same to fives also add up to 10.... 5 + 5 = 10
x^2 + 10x + 25 = (x+5)(x+5)
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Now why don't you try this one...
x^2 + 12x + 35....
You see x^2,... so automatically you know you have something like (x + _)(x + _)
Now figure out the factors that go in the blanks....
What are the factors of 35? Write down the pairs...
1, 35 because 1 * 35 = 35
5, 7 because 5 * 7 = 35 .....
BUT you have a middle term of 12x.... which means that the two numbers that give you a product of 35, must also give you a sum of 12.... is it 1 & 35? Or 5 & 7
1 + 35 = ?
5 + 7 = ?
It's 5 and 7.... so x^2 + 12x + 35 = (x + 5)(x + 7)
2007-12-04 04:35:42 · answer #1 · answered by blueskies 7 · 0⤊ 0⤋
What you are doing is factoring a trinomial. (x +5)(x+5) is the answer which is (x + 5)^2.
The square root of x^2 is x..that's where that came from.
Look at the 25. What 2 numbers multiplied together gives you 25 AND added together gives you 10??? That's where the 5 comes in.
2007-12-04 12:32:37 · answer #2 · answered by dpirsq2 5 · 0⤊ 0⤋
x^2+10x+25=
(x +5)^2
x*x=x^2
5*5=25
Since it is (x+5)^2= 5x+5x=10x
x^2+10x+25= (x+5)^2= (x+5)(x+5)
2007-12-04 12:42:04 · answer #3 · answered by Dave aka Spider Monkey 7 · 0⤊ 0⤋