Question

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 quadratic with a degree of 2

Explanation:

Step1: Expand \((x + 3)(x + 2)\)

Using FOIL method: \((x+3)(x + 2)=x^{2}+2x+3x + 6=x^{2}+5x+6\)

Step2: Remove parentheses in \((3x^{2}-x - 7)-(5x^{2}-4x - 2)\)

\(3x^{2}-x - 7-5x^{2}+4x + 2=(3x^{2}-5x^{2})+(-x + 4x)+(-7 + 2)=-2x^{2}+3x-5\)

Step3: Combine with the expanded \((x + 3)(x + 2)\)

\(-2x^{2}+3x-5+x^{2}+5x+6=(-2x^{2}+x^{2})+(3x + 5x)+(-5 + 6)=-x^{2}+8x + 1\)

Answer:

The polynomial simplifies to \(-x^{2}+8x + 1\) which is a quadratic trinomial with a degree of 2.