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What polynomial should be subtracted from 3x^2+4x-1 to get the difference equal to 1

Sagot :

Answer:  3x^2+4x-2

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Explanation:

Assume the polynomial we want to find is in the form Ax^2+Bx+C

The goal is to find the values of A, B, and C.

We start with 3x^2+4x-1, then we subtract off Ax^2+Bx+C. Set this equal to 1 and we get:

(3x^2+4x-1) - (Ax^2+Bx+C) = 1

3x^2+4x-1 -Ax^2-Bx-C = 0x^2 + 0x + 1

(3x^2-Ax^2) + (4x-Bx) + (-1-C) = 0x^2 + 0x + 1

(3-A)x^2 + (4-B)x + (-1-C) = 0x^2 + 0x + 1

From here we equate the coefficients of the x^2 terms together and we see that 3-A = 0 which leads to A = 3.

Do the same for the x terms to get 4-B = 0 leading to B = 4

Finally, we have -1-C = 1 lead to C = -2

The polynomial Ax^2+Bx+C becomes 3x^2+4x-2

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Checking the answer:

(3x^2+4x-1) - (Ax^2+Bx+C)

(3x^2+4x-1) - (3x^2+4x-2)

3x^2+4x-1 - 3x^2-4x+2

(3x^2-3x^2) + (4x-4x) + (-1+2)

0x^2 + 0x + 1

0 + 0 + 1

1

We get a difference of 1, so the answer is confirmed.

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