Which polynomial represents the difference below?

(7x^2 + 8) - (4x^2 + x + 6)

A. 11x^2 - x + 2
B. 11x^2 + x + 14
C. 3x^2 - x + 2
D. 3x^2 + x + 14



Answer :

To find the difference between the polynomials [tex]\(7x^2 + 8\)[/tex] and [tex]\(4x^2 + x + 6\)[/tex], let's subtract the coefficients from each other step-by-step.

1. Identify the corresponding terms:

- The [tex]\(x^2\)[/tex] terms are [tex]\(7x^2\)[/tex] and [tex]\(4x^2\)[/tex].
- The [tex]\(x\)[/tex] term is [tex]\(0x\)[/tex] (for [tex]\(7x^2 + 8\)[/tex]) and [tex]\(x\)[/tex] (for [tex]\(4x^2 + x + 6\)[/tex]).
- The constant terms are [tex]\(8\)[/tex] and [tex]\(6\)[/tex].

2. Subtract the [tex]\(x^2\)[/tex] terms:

[tex]\[ 7x^2 - 4x^2 = (7 - 4)x^2 = 3x^2 \][/tex]

3. Subtract the [tex]\(x\)[/tex] terms:

[tex]\[ 0x - 1x = -1x = -x \][/tex]

4. Subtract the constant terms:

[tex]\[ 8 - 6 = 2 \][/tex]

Putting it all together, the difference between the two polynomials is:

[tex]\[ 3x^2 - x + 2 \][/tex]

Therefore, the polynomial that represents the difference is:

C. [tex]\(3x^2 - x + 2\)[/tex]