could someone help me with this math problem?

Question

Factor the following trinomial completely. Look first for the greatest common factor.
20r⁴-48r³ -36r²

Answer 1

Hi Michael,

 

Factor the following trinomial completely. Look first for the greatest common factor.

20r⁴-48r³-36r²



You have to look for the greatest common factor to all three terms. First factor the terms.

1st term 20r⁴                  1*2*2*5*r*r*r*r
2nd term -48r³              -1*2*2*2*2*3*r*r*r
3rd term -36r²               -1*2*2*2*2*3*r*r

What factor is common to all three? Looks like 2*2*r*r= 4r²

1st term 20r⁴              1*2*2*5*r*r*r*r      =4r² (5r²)
2nd term -48r³          -1*2*2*2*2*3*r*r*r  =4r²(-12r)
3rd term -36r²           -1*2*2*3*3*r*r        =4r²(-9)


The 4r² is factored out and what is left goes in the parentheses.

                  20r⁴-48r³-36r²
              = 4r²(5r²-12r-9)

 

Now we have to factor 5r²-12r-9.

I use the double slide method.  Take the coefficient of the 1st term and multiply it by the 3rd term:

                                               r²-12r-5(9)

                                               r²-12r-45

 

Since the 3rd term is negative, one factor must be negative and one positive.

Since the 2nd term is negative, the largest factor must be negative.

Factors of -45 which sum -12

5     -9    no

15    -3   yes                           Factors    (r+15)(r-3)

 

Since we multiplied by 5 before, now we have to divide by 5:      (r+15/5)(r-3/5)

Since 3/5 cannot be reduced, slide the 5 before the y:               (r+3)(5r-3)

 

For the final response, include the GCF=4r²

 

                                           Therefore the answer is:    4r²(r+3)(5r-3)
             
NOW the expression is fully factored.
Hope this helps you with the process of factoring.
THINK MATH!!