Question

which polynomial represents the difference below?\\((7x^2 + 8) - (4x^2 + x + 6)\\)\\(\bigcirc\\) a. \\(11x^2 + x + 14\\)\\(\bigcirc\\) b. \\(3x^2 - x + 2\\)\\(\bigcirc\\) c. \\(3x^2 + x + 14\\)\\(\bigcirc\\) d. \\(11x^2 - x + 2\\)

Explanation:

Step1: Distribute the subtraction

To subtract the second polynomial from the first, we distribute the negative sign to each term in the second polynomial:
$(7x^2 + 8) - (4x^2 + x + 6) = 7x^2 + 8 - 4x^2 - x - 6$

Step2: Combine like terms

• For the $x^2$ terms: $7x^2 - 4x^2 = 3x^2$
• For the $x$ terms: $-x$ (since there is no $x$ term in the first polynomial, we just have $-x$)
• For the constant terms: $8 - 6 = 2$

Putting it all together, we get $3x^2 - x + 2$.

Answer:

B. $3x^2 - x + 2$