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

what polynomial can be added to ${x}^{2}+5x+1$ to get a sum of $4{x}^{2}-3$
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Leonard Stokes
When adding two polynomials, you need to add the like terms. Therefore, to figure out what polynomial can be added to ${x}^{2}+5x+1x$ to get a sum of $4{x}^{2}-3$, you can compare each pair of like terms to see what the missing like terms must be.
Looking at the quadratic terms, you need ${x}^{2}+?=4{x}^{2}$. The quadratic term of the missing polynomial must then be 3x2 since ${x}^{2}+3{x}^{2}=4{x}^{2}$
Looking at the linear terms, you need 5x+?=0 since the sum $4{x}^{2}-3$ 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 $3{x}^{2}$, a linear term of −5x, and a constant term of −4, then the polynomial $3{x}^{2}-5x-4$ can be added to ${x}^{2}+5x+1$ to get a sum of $4{x}^{2}-3$