Answers

2014-04-20T21:13:46+05:30
Let P(x) =x^3+13x^2+32x+20
If (x - a) is a factor of P(x) then P(a) = 0
So first lets find the a for which P(a) = 0
Lets try the values 1,-1,0,2,-2 for a.
if a = 1
then P(1) = 1^3+13*1^2+32*1+20 = 1 + 13 + 32 + 20 = 66 not equal to zero
so try a = -1
P(-1) = (-1)^3 +13*(-1)^2 + 32*(-1) +20 = -1 + 13 -32 +20 = -33 + 33 = 0
P(-1) = 0 ==> (x--1) = (x+1) is a factor

So divide P(x) by (x+1)

              x^2 + 12x  +20                     
     x+1 |  x^3+13x^2+32x+20
               x^3+  x^2   
               0   +12x^2 +32x
                      12x^2 +12x
                         0    +20x + 20
                                 20x + 20
                                       0
therefore P(x) = (x+1)*(x^2+12x+20)
now we need to factor x^2+12x+20
we need to find two numbers whose SUM = 12 and PRODUCT = 20
10 + 2 = 12
and 10* 2 = 20
so split the term 12x in x^2+12x+20 as the sum of 10x and 2x
==> x^2+12x+20 = x^2+10x+2x+20
now x is common for the first 2 terms and 2 is common for the last two.
==> x^2+12x+20 = x^2+10x+2x+20 = x(x+10)+2(x+10)
now x+10 is common
==> x(x+10)+2(x+10) = (x+10) (x+2)
so the factors of P(x) are (x+1), (x+2), (x+10)
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2014-04-21T11:06:06+05:30
the factors of x^3+13x^2+32x+20 is 3220
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