what polynomial can be added to x2+5x+1 to get a sum of 4x2−3

Question

Leonard Stokes · Accepted Answer

When adding two polynomials, you need to add the like terms. Therefore, to figure out what polynomial can be added to

x^{2} + 5 x + 1 x

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} - 5 x - 4

can be added to

x^{2} + 5 x + 1

to get a sum of

4 x^{2} - 3

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

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