Posted by **Anonymous** on Sunday, March 6, 2011 at 7:10am.

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

- algebra -
**MathMate**, Sunday, March 6, 2011 at 7:31am
"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?

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