1)What is the coefficient of \(x^2\) when \(-5x^3 - 5x^2 - 7x + 1\) is multiplied by \(-x^2 - 6x + 1\)and the like terms are combined?
Is the answer \(36\)?
2) Find \(h(x)\), with terms in order of decreasing degree, if \(3x^4+2x-1+h(x)=5x^2-6x-1.\)
THX in advance
+6248 \(1)~\text{you have to inspect the terms in the two polynomials and find which ones, $\\$ when their exponents are added, sum to two}\\ (-5x^2, 1)\\ (-7x,-6x)\\ (1,-x^2)\\ \text{and that's all of them. Performing the multiplication and summing them all we get}\\ (-5 + 42-1)x^2 = 36x^2\\ \text{You are correct, well done!}\)
\(2)~3x^4 + 2x-1 +h(x) = 5x^2 -6x-1\\ h(x) = (5x^2-6x-1) - (3x^4+2x-1)\\ h(x) = -3x^4 + 5x^2 -8x\)
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