Explain! what polynomial should be subtracted from the polynomial y²–5y+1 to get the difference equal to: 5

Hello from MrBillDoesMath!

y^2-5y -4

Discussion:

The problem asks us to find the  polynomial, g(y), such that

y^2-5y + 1 - g(y) = 5     =>  (add g(y) to both sides)

y^2 -5y + 1 - g(y) + g(y) = 5 + g(y)    =>  

y^2 -5y + 1  + 0  = 5 + g(y)               =>       (as -g(y) + g(y) = 0)

Finally subtract 5 from both sides:

y^2 - 5y + 1  -5 = (5 -5 ) + g(y) =>

y^2-5y -4 = g(y)

Thank you,

MrB

Step-by-step explanation:

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