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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
    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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