Question

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

Step1: Expand the product term

$(x+3)(x+2) = x^2 + 2x + 3x + 6 = x^2 + 5x + 6$

Step2: Distribute the negative sign

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

Step3: Combine all terms

$3x^2 - x - 7 - 5x^2 + 4x + 2 + x^2 + 5x + 6$

Step4: Combine like terms for $x^2$

$3x^2 - 5x^2 + x^2 = -x^2$

Step5: Combine like terms for $x$

$-x + 4x + 5x = 8x$

Step6: Combine constant terms

$-7 + 2 + 6 = 1$

Step7: Combine all simplified terms

$-x^2 + 8x + 1$

Step8: Identify polynomial type and degree

The expression has 3 terms, so it is a trinomial; the highest power of $x$ is 2, so degree is 2.

Answer:

The polynomial simplifies to an expression that is a trinomial (first dropdown) polynomial (second dropdown) with a degree of $\boldsymbol{2}$ (third dropdown).
The simplified expression is $-x^2 + 8x + 1$