Question

Find two equivalent expressions for the opposite of the polynomial -x^2+50x-9

Answer 1

Answer:

-(-x² + 50x - 9); x² -50x + 9

Step-by-step explanation:

You find the opposite of a polynomial P by changing the sign of every term in P.

P = -x² + 50x - 9

One way to get -P is to put a negative sign in front of the whole expression.

-P = -(-x² + 50x - 9)

Another way is to distribute the -1 inside the parentheses.

-P = x² -50x + 9

Answer 2

Equivalent expressions are expressions of equal values.

$\mathbf{x^2 - 50x + 9}$ and $\mathbf{ -(-x^2 + 50x - 9)}$ are equivalent expressions for the opposite of $\mathbf{-x^2 + 50x - 9}$

The expression is given as:

$\mathbf{f(x) = -x^2 + 50x - 9}$

To calculate the opposite, we simply negate the signs of the expression.

So, we have:

$\mathbf{-f(x) = -(-x^2 + 50x - 9)}$

Expand

$\mathbf{-f(x) = x^2 - 50x + 9}$

The above highlights mean that:

$\mathbf{x^2 - 50x + 9}$ and $\mathbf{ -(-x^2 + 50x - 9)}$ are equivalent expressions for the opposite of $\mathbf{-x^2 + 50x - 9}$

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