Question 388968: Using long division, please solve x^2 + 7x + 10 divided by x + 3 Found 2 solutions by rfer, haileytucki:Answer by rfer(16322) (Show Source):
x +4
___________
x+3/x^(2)+7x+10
***-x^(2)-3x
****---------
***********4x+10
***********-4x-12
***********------
***************-2
(The final answer is the quotient plus the remainder over the divisor)
doing more work to further the answer of x+4 :
x+4-(2)/(x+3)
Multiply each term by a factor of 1 that will equate all the denominators. In this case, all terms need a denominator of (x+3).
x*(x+3)/(x+3)+4*(x+3)/(x+3)-(2)/(x+3)
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of (x+3).
(x(x+3))/(x+3)+4*(x+3)/(x+3)-(2)/(x+3)
Multiply the expression by a factor of 1 to create the least common denominator (LCD) of (x+3).
(x(x+3))/(x+3)+(4(x+3))/(x+3)-(2)/(x+3)
The numerators of expressions that have equal denominators can be combined. In this case, (x(x+3))/((x+3)) and ((4(x+3)))/((x+3)) have the same denominator of (x+3), so the numerators can be combined.
(x(x+3)+(4(x+3))-2)/(x+3)
Simplify the numerator of the expression.
(x^(2)+3x+4x+12-2)/(x+3)
Combine all similar terms in the polynomial x^(2)+3x+4x+12-2.
(x^(2)+7x+10)/(x+3)
In this problem 5*2=10 and 5+2=7, so insert 5 as the right hand term of one factor and 2 as the right-hand term of the other factor.
((x+5)(x+2))/(x+3)
Yet; your origional, long division answer= x+4 (ignore the ***'s)
I had to put them there to show you the work on an even scale.
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