Question 1038004: Hello! :) Can you help me find the factor of the following trinomials? Thank you )
x2 + 6x + 9
x2 + 7x + 10
Found 2 solutions by tutor_paul, Edwin McCravy:
Answer by tutor_paul(519)   (Show Source):
You can put this solution on YOUR website! 
Look at the 3rd term (9). What are the factors of 9, than when added together, give the result of the coefficient of x in the second term(6)?
Factors of 9:
1x9 (sum = 10, not 6)
3x3 (sum = 6) - this is the one you want.
Multiply it out and see that you get the original.
I will leave the 2nd part of the problem to you.
====================
Good Luck,
tutor_paul@yahoo.com
Answer by Edwin McCravy(20065)  (Show Source):
You can put this solution on YOUR website!
x2 + 6x + 9
Go right to left. First the 9, then the sign before it, +,
then the 6 before the x, and then the + before the 6.
See the 9. See the + sign before it.
The + sign says "Think of ADDING"
(If it were a minus or negative - it would say "Think of SUBTRACTING")
See the 6. Think of two positive integers
which multiply to give 9 and ADD to give 6.
They are 3 and 3, because 3×3 = 9 and 3+3 = 6
So write this
(x 3)(x 3)
Now we need to put signs between the x's and
the numbers.
Since we thought of ADDING, that's a SUM, so we
think of "SUM SAME SIGN". So we know that they
have the SAME SIGN.
What "SAME SIGN"? The sign before the x in the
original problem, which is a +, and they both
have the SAME SIGN, so we get.
(x+3)(x+3)
Since they are the same, we write it once with an
exponent of 2:
(x+3)2
-------------------------
x2 + 7x + 10
Go right to left. First the 10, then the sign before it, +,
then the 7 before the x, and then the + before the 7.
See the 10. See the + sign before it.
The + sign says "Think of ADDING"
(If it were a minus or negative - it would say "Think of SUBTRACTING")
See the 7. Think of two positive integers
which multiply to give 10 and ADD to give 7.
They are 2 and 5, because 2×5 = 10 and 2+5 = 7
So write this
(x 2)(x 5)
Now we need to put signs between the x's and
the numbers.
Since we thought of ADDING, that's a SUM, so we
think of "SUM SAME SIGN". So we know that they
have the SAME SIGN.
What "SAME SIGN"? The sign before the x in the
original problem, which is a +, and they both
have the SAME SIGN, so we get.
(x+2)(x+5)
---------------------
Here's one with a -
x2 - 6x + 8
Go right to left. First the 8, then the sign before it, +,
then the 6 before the x, and then the - before the 6.
See the 8. See the + sign before it.
The + sign says "Think of ADDING"
(If it were a minus or negative - it would say "Think of SUBTRACTING")
See the 6. Think of two positive integers
which multiply to give 8 and ADD to give 6.
They are 4 and 2, because 4×2 = 8 and 4+2 = 6
So write this
(x 4)(x 2) <-- It would be just as good to write (x 2)(x 4)
Now we need to put signs between the x's and
the numbers.
Since we thought of ADDING, that's a SUM, so we
think of "SUM SAME SIGN". So we know that they
have the SAME SIGN.
What "SAME SIGN"? The sign before the x in the
original problem, which is a -, and they both
have the SAME SIGN, so we get.
(x-4)(x-2)
---------
Another one with a -
x2 + 5x - 14
Go right to left. First the 14, then the sign before it, -,
then the 5 before the x, and then the + before the 5.
See the 14. See the - sign before it.
The + sign says "Think of SUBTRACTING"
(If it were a plus or positive - it would say "Think of ADDING")
See the 5. Think of two positive integers
which multiply to give 10 and SUBTRACT to give 7.
They are 7 and 2, because 7×2 = 14 and 7-2 = 5
So write this
(x 7)(x 2) <-- it would be just as good to write (x 2)(x 7)
Now we need to put signs between the x's and
the numbers.
Since we thought of SUBTRACTING, that's a DIFFERENCE, so we
think of "DIFFERENT SIGNS". So we know that they
have DIFFERENT SIGNS.
What sign goes in which parentheses? The sign before the x in the
original problem, which is a +, and the 7 is LARGER than the 2, so
the 7 gets the + sign, and the SMALLER 2 gets a DIFFERENT sign -.
(x+7)(x-2)
-----
Another one with two -'s
x2 - 10x - 24
Go right to left. First the 24, then the sign before it, -,
then the 11 before the x, and then the - before the 11.
See the 24. See the - sign before it.
The + sign says "Think of SUBTRACTING"
(If it were a plus or positive, it would say "Think of ADDING")
See the 5. Think of two positive integers
which multiply to give 24 and SUBTRACT to give 10.
They are 12 and 2, because 12×2 = 24 and 12-2 = 10
So write this
(x 12)(x 2) <-- it would be just as good to write (x 2)(x 12)
Now we need to put signs between the x's and
the numbers.
Since we thought of SUBTRACTING, that's a DIFFERENCE, so we
think of "DIFFERENT SIGN". So we know that they
have DIFFERENT SIGN.
What sign goes in which parentheses? The sign before the x in the
original problem, which is a -, and the 12 is LARGER than the 2, so
the 12 gets the - sign, and the SMALLER 2 gets a DIFFERENT sign +.
(x-12)(x+2)
----
That's all four cases of factoring x2±x∓. Learn them.
Edwin
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