Question

Simplify the following polynomial expression. (3x^(2)-x-7)-(5x^(2)-4x-2)+(x+3)(x+2) The polynomial simplifies to an expression that is ________ ________ a with a degree of ________.

Answer 1

To simplify the given polynomial expression (3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2), we need to perform the operations within the parentheses first. By simplifying each term and combining like terms, the simplified expression is -2x^2 - 4x - 3.

Step-by-step explanation:

To simplify the given polynomial expression, we need to perform the operations within the parentheses first. By simplifying each term, we get:

(3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2)

Expanding the last term using the distributive property, we have:

(3x^2 - x - 7) - (5x^2 - 4x - 2) + x^2 + 5x + 6

Combining like terms, we get:

-2x^2 - 4x - 3

The simplified polynomial expression is -2x^2 - 4x - 3, which is a quadratic polynomial with a degree of 2.

Answer 2

To simplify the given polynomial expression, distribute the terms and combine like terms. The simplified polynomial expression is
`-x^2 + 8x + 1,`and it is a polynomial of degree 2.

Step-by-step explanation:

To simplify the given polynomial expression:

1. Distribute the terms in the parentheses:
   `(3x^2 - x - 7) - (5x^2 - 4x - 2) + (x + 3)(x + 2)`
2. Combine like terms:
   `3x^2 - x - 7 - 5x^2 + 4x + 2 + x^2 + 5x + 6`
3. Add or subtract the coefficients of the like terms:
   `(3x^2 - 5x^2 + x^2) + (-x + 4x + 5x) + (-7 + 2 + 6)`
4. Simplify each group of like terms:
   `-x^2 + 8x + 1`

Therefore, the simplified polynomial expression is
`-x^2 + 8x + 1`. It is a polynomial of degree 2.