Question

Take 2y 2 - 3y - 5 from y 3 - 6y 2 + 5y. Select the correct answer.

y3 - 2y2 + 3y + 5
y3 - 4y2 + 2y - 5
y3 - 4y2 + 2y + 5
y3 - 8y2 + 8y + 5

Answer 1

`y^3-8y^2+8y+5`

Explanation:

Take one polynomial from the other means to perform the sub.traction of them. Recall that it is better to use grouping symbols when subtracting polynomials, so we get the signs right when combining like terms:

The indicated subtraction is:
`y^3-6y^2+5y - (2y^2-3y-5)`

Make sure that before removing the grouping symbol (parenthesis) that is preceded by a negative sign, we change the signs of every term inside it. Then combine like terms to get the final answer:

`y^3-6y^2+5y - (2y^2-3y-5)=\\=y^3-6y^2+5y-2y^2+3y+5=\\=y^3-6y^2-2y^2+5y+3y+5=\\=y^3-8y^2+8y+5`

Which is the last option shown in the question