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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 -

    "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
    =x^4+49x²+1 -14x^3 -14x + 2x^sup2;
    = x^4-14x^3+51x^2-14x+1

    Since the given polynomial
    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.

    =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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