2025 · Q39
Consider:
- I4x+13y is a factor of (3x+y)^2+(3x+y)(x+5y)-20(x+5y)^2.
- IIx+19y is a factor of the same. Which is/are correct?
Elementary MathematicsAlgebra
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Set A=3x+y, B=x+5y: A^2+AB-20B^2=(A+5B)(A-4B). Now A+5B=8x+26y=2(4x+13y) and A-4B=-(x+19y). So (4x+13y) and (x+19y) are both factors: I and II correct. Not spotting the A,B substitution leads to messy expansion.