Which polynomial, when added to the polynomial 5x2–3x–9, is equivalent to x^2–5x+6?
5x^2–3x–9 + f(x) = x^2–5x+6
f(x) = x^2–5x+6 - (5x^2–3x–9)
= .....
5x^2–3x–9 + f(x) = x^2–5x+6
f(x) = x^2–5x+6 - (5x^2–3x–9)
= −4x^2−2x+15
To find the polynomial that, when added to the polynomial 5x^2-3x-9, is equivalent to x^2-5x+6, we need to set up the two polynomials in standard form and perform subtraction.
1. Arrange the polynomials in standard form:
5x^2-3x-9
x^2-5x+6
2. Compare the coefficients of the same degree terms:
5x^2 in the first polynomial and x^2 in the second polynomial
The coefficient of x^2 in the second polynomial is 1, so we have 5x^2 = x^2
3. Subtract the coefficients:
5x^2 - x^2 = 0
4. Continue comparing and subtracting the coefficients of the remaining terms:
-3x - (-5x) = 2x
-9 - 6 = -15
5. Write the resulting polynomial using the subtracted coefficients:
The polynomial that, when added to 5x^2-3x-9, yields x^2-5x+6 is 0x^2 + 2x - 15, or simply 2x - 15.
To find the polynomial that, when added to 5x^2 – 3x – 9, is equivalent to x^2 – 5x + 6, we need to determine the difference between the two polynomials.
We can subtract the given polynomial (x^2 – 5x + 6) from the original polynomial (5x^2 – 3x – 9) to find the missing polynomial.
(5x^2 – 3x – 9) - (x^2 – 5x + 6)
Rearranging the terms:
= 5x^2 – 3x – 9 – x^2 + 5x – 6
Combining like terms:
= (5x^2 – x^2) + (-3x + 5x) + (-9 – 6)
Simplifying:
= 4x^2 + 2x - 15
Therefore, the missing polynomial is 4x^2 + 2x - 15.