4x⁶-24x⁵+20x⁴+68x³-44x²-40x+k is a perfect square

find k.

Hello student,
Please find the answer to your question below
As given it is a perfect square
Let given expression =(ax³-bx²+cx+d)²
Expanding above expression we get
=(a²x⁶-2abx⁵+(b²+2ac)x⁴+(2ad-2bc)x³+(c²-2bd)x²+2cdx+d²)
By comparing above expression with given expression we get
a²=4 so a=2
-2ab=-24 so b=6
b²+2ac=20 so c=-4
2ad-2bc=68 so d=5
Asked to find k which is d²=25
So value of k=25