I need help factoring the following problem
5x^3-45x^2+70x
I need help factoring the following problem
5x^3-45x^2+70x
5x^3-45x^2+70x
= 5x(x^2-9x+14)
= 5x(x-2)(x-7)
We want to simplify 5x^3-45x^2+70x so first we factor out x and we get
x*[5x^2-45x+70]=(1/5)*x*(5x+a)*(5x+b) where a*b=350 and a+b= -45 by trial we
Get a= -35 and b= -10 so the expression is equal to:(1/5)*x*(5x-35)*(5x-10)then
Pulling out the two 5's out of the () we get: 5x^3-45x^2+70x =5x*(x-7)*(x-2) and that is the final answer.
The first thing you want to do when you approach any factoring question is find the number or number and variable if applicable that is present in every single number. In the question the number would be 5 and then you would look to see how there is also an x present in each number as well. Therefore, you would factor out a 5x. This is the same as dividing each number by 5x.
5x (x^2- 9x +14)
From this point you must look at the function you still have inside the paranthesis and determine whether or not it can continue to be factored down. In this case it can be factored (a lot of times figuring out to factor it consists of guess and check)
your final answer would be
5x(x-2)(x-7)
First thing you want to do is find the highest common multiple, In this case 5x is your common multiple, Since it can be factored from 45x^{2} and 70x ..... ( The highest common Multiple is the smallest value from all the coeficents , 5, 45 , 70 .. and the x with the lowest power x^{3} , x^{2} , x ...... thus... 5x as your multiple)
Therefore when you factore out the 5x you get ...
5x ( x^{2} - 9x + 14 )
Now make sure that if you were to distribute in the 5x to ( x^2 - 9x + 14) you'll get the orginal Polynomial of 5x^{3} - 45x^{2} + 70x ... Just to make sure.
so we have
5x ( x^{2} - 9x + 14 ) , now to factor out ( x^{2} - 9x + 14) you need to find the multiples of 14.
1 x 14 = 14 and 2 x 7 = 14 , now choose of the comination and check if whether you add them or subract them they give you the coefficent - 9.
For example say we choose 1 and 14 .. 1 + 14 = 15 , 1 - 14 = -13 , -1 -14 = -15 , 14-1 = 13.. so it wont work.
Try 2 and 7 2 + 7 = 9 , 2-7 = -5 , -2-7= -9... You found the combination -2 , and -7
5x (x -2)(x-7) Answer.
Just to make sure you may want to distribute, and foil, to check if you get the original polynomial.