Question 655556
From a/c = 4 we get
a = 4c
which tells us that a is a multiple of 4<br>
From b/d = 4 we get
b = 4d
which tells us that b is a multiple of 4<br>
From a/b = 7/5 we get
5a = 7b
which tells us that a is a multiple of 7 and b is a multiple of 5.<br>
Since b must be a multiple of 5 and 4, we can use 20 for b. With b = 20 and b = 4d, we find that d will be 5. With b = 20 and 5a = 7b we can find that a = 28. And with a = 28 and a = 4c we get c = 7.<br>
So our polynomial is:
{{{28x^3+20x^2+7x+5}}}
To factor this by grouping we start by grouping:
{{{(28x^3+20x^2)+(7x+5)}}}
Then we factor out the greatest common factor (GCF) of each group. The GCF of the first group is {{{4X^2}}}. The GCF of the second group is just 1. (Factoring by grouping is one of the rare times we bother to factor out a 1.) Factoring out each GCF from each group:
{{{4x^2*(7x+5)+1*(7x+5)}}}
As we can see, the two sub-expressions have a common factor: 7x+5. Factoring out the common factor from each sub-expression:
{{{(7x+5)*(4x^2+1)}}}<br>
Neither of these factors will factor further so we are finished factoring.