Question

Adding and subtracting polynomials! What is danielle's mistake

Answer 1

Mistake in setting up subtraction.

-x³ + 3x² - 6

Explanation:

Danielle's Mistake:

Danielle made a mistakes setting up the problem:

If you are told "subtract 4 from 6", you do 6 - 4 = 2. You don't do 4 - 6 = -2.

Here, you are told to "subtract x³ - 2x² from x² - 6."

That means to do the following operation:

x² - 6 - (x³ - 2x²).

She subtracted this way

x³ - 2x² - (x² - 6),

which is incorrect.

Correct Work:

x² - 6 - (x³ - 2x²) =

= x² - 6 - x³ + 2x²

= -x³ + 3x² - 6

Answer 2

-x³ + 3x² - 6

Explanation:

Polynomial subtraction:

Danielle's mistake:

Danielle should write the expression x² - 6 first and then enclose the expression to be subtracted in parenthesis with a negative sign prefixed.

Correct work:

x² - 6 - (x³ - 2x²) = x² - 6 - x³ + 2x²

= -x³ + x² + 2x² - 6

Now, Combine like terms.

= -x³ + 3x² - 6