Since the x2 coefficient is no longer 1 it is not enough to find 2 numbers whose sum is 6 and whose multiplication is 25. We need to check the options for 2 numbers that also considering the x2 coefficient that is 4.
We know that there are 2 options for the factored form so that x2 coefficient will be 4:
Option 1 is (4x±a )(x±b) In this option multiplying the first numbers will get 4*1*x2=4x2.
In this option the coefficient of x is calculated by 4bx+ax, meaning x(4b+a) which is 4 times number b and number a.
Option 2 is (2x±a )(2x±b) In this option multiplying the first numbers will get 2*2*x2=4x2.
In this option the coefficient of x is calculated by 2bx+2ax, meaning x(ab+2a) which is 2 times number b and 2 times number a.
The question asked should be: what are the numbers whose multiplication is 6 and one the following:
4 times number b and number a is 25: 4b+a=25
2 times number b and 2 times number a is 25: 2a+2b=25
The numbers whose multiplication is 6 are 1 and 6 or 2 and 3. For each one of these two options we also need to look at the second criteria and find a match.
If the numbers are 6 and 1 (6*1=6):
4 times number b and number a is 25: 4b+a=25
This is possible since 6*4+1=25, therefore the numbers are 6 and 1 and the coefficients of x2 are 6 and 4. The factored form is (4x+1)(x+6).
Checking the answer by opening brackets with FOIL formula: (4x+1)(x+6)=4x2+24x+x+6=4x2+25x+6.
Let’s check the other option: 2 times number b and 2 times number a is 25: 2a+2b=25
We can’t get this with the numbers 1 and 6 since 2*1+2*6=14 and not 25.
If the numbers are 2 and 3 (2*3=6):
4 times number b and number a is 25: 4b+a=25
We can’t get this with the numbers 2 and 3 since 2*1+3*4=16 and not 25, also 3*1+2*4=11 and not 25.
Let’s check the other option: 2 times number b and 2 times number a is 25: 2a+2b=25
We can’t get this with the numbers 2 and 3 since 2*2+3*2=10 and not 25.