Question

5
select the correct answer from each drop-down menu.
simplify the following polynomial expression.
(3x² - x - 7) - (5x² - 4x - 2) + (x + 3)(x + 2)
the polynomial simplifies to an expression that is a drop - down drop - down with a degree of drop - down.
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Explanation:

Step1: Expand and simplify terms

First, expand the subtraction and the multiplication:

• For \((3x^2 - x - 7) - (5x^2 - 4x - 2)\), distribute the negative sign: \(3x^2 - x - 7 - 5x^2 + 4x + 2\)
• For \((x + 3)(x + 2)\), use the distributive property (FOIL): \(x^2 + 2x + 3x + 6 = x^2 + 5x + 6\)

Step2: Combine like terms

Now, combine all the terms:

• Combine the \(x^2\) terms: \(3x^2 - 5x^2 + x^2 = -x^2\)
• Combine the \(x\) terms: \(-x + 4x + 5x = 8x\)
• Combine the constant terms: \(-7 + 2 + 6 = 1\)

So the simplified expression is \(-x^2 + 8x + 1\).

Step3: Determine the type and degree

• The expression \(-x^2 + 8x + 1\) is a polynomial (specifically a quadratic trinomial, but generally a polynomial). It has three terms, so it's a trinomial (or just a polynomial). The highest power of \(x\) is 2, so the degree is 2.

Answer:

The polynomial simplifies to an expression that is a \(\text{quadratic}\) (or \(\text{polynomial}\)) \(\text{trinomial}\) (or \(\text{expression}\)) with a degree of \(2\). (Note: The first two drop - downs likely have options like "quadratic", "linear", "monomial", "binomial", "trinomial" etc. Based on the simplified form \(-x^2 + 8x + 1\), it's a quadratic trinomial with degree 2.)