what polynomial can be added to x^{2}+5x+1 to get a sum of 4x^{2}-3

Cabiolab 2020-12-03 Answered
what polynomial can be added to x2+5x+1 to get a sum of 4x23
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Expert Answer

Leonard Stokes
Answered 2020-12-04 Author has 98 answers
When adding two polynomials, you need to add the like terms. Therefore, to figure out what polynomial can be added to x2+5x+1x to get a sum of 4x23, you can compare each pair of like terms to see what the missing like terms must be.
Looking at the quadratic terms, you need x2+?=4x2. The quadratic term of the missing polynomial must then be 3x2 since x2+3x2=4x2
Looking at the linear terms, you need 5x+?=0 since the sum 4x23 does not have a linear term. The linear term of the missing polynomial must then be −5x since 5x+(−5x)=0.
Looking at the constant terms, you need 1+?=−31+?=−3. The constant term of the missing polynomial must then be −4 since 1+(−4)=−3.
Since the missing polynomial must have a quadratic term of 3x2, a linear term of −5x, and a constant term of −4, then the polynomial 3x25x4 can be added to x2+5x+1 to get a sum of 4x23

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