the sum of two polynomials is 40x^5-2x^4+x^3-7x^2-1. if the polynomial is the square of (x^2-7x+1), find the other polynomial

Answer 1

"the sum of two polynomials is 40x^5-2x^4+x^3-7x^2-1. if one polynomial is the square of (x^2-7x+1), find the other polynomial"

Square by find the sum of
1. squares of individual terms,
2. 2 times the product of cross terms
P1=(x^2-7x+1)²
=x^4+49x²+1 -14x^3 -14x + 2x^sup2;
= x^4-14x^3+51x^2-14x+1

Since the given polynomial
P=40x^5-2x^4+x^3-7x^2-1
is the sum of two polynomials P1 and P2, we can find P2 by subtracting P1 from P.

Remember the subtraction can only be done on the coefficients of like terms.

P-P1
=40x^5-2x^4+x^3-7x^2-1 - (x^4-14x^3+51x^2-14x+1)
=40x^5 +(-2x^4-x^4) + (x^3+14x^3) + (-7x^2-51x^2) + 14x + (-1-1)
= ....

Can you take it from here?