Question

1. which of the polynomials has the largest degree? a ((x - 4)(x - 3) - x^2 + 4) b ((x + 3)^2 - 9 + x) c ((x + 4)(x - 4) - x(x - 1)^2) d ((2x - 1)^2 - 4x(x - 1))

Explanation:

Step1: Simplify Option A

Expand and combine like terms:

$$\begin{align*} (x-4)(x-3)-x^2+4&=x^2-7x+12-x^2+4\\ &=-7x+16 \end{align*}$$

Degree = 1

Step2: Simplify Option B

Expand and combine like terms:

$$\begin{align*} (x+3)^2-9+x&=x^2+6x+9-9+x\\ &=x^2+7x \end{align*}$$

Degree = 2

Step3: Simplify Option C

Expand and combine like terms:

$$\begin{align*} (x+4)(x-4)-x(x-1)^2&=x^2-16-x(x^2-2x+1)\\ &=x^2-16-x^3+2x^2-x\\ &=-x^3+3x^2-x-16 \end{align*}$$

Degree = 3

Step4: Simplify Option D

Expand and combine like terms:

$$\begin{align*} (2x-1)^2-4x(x-1)&=4x^2-4x+1-4x^2+4x\\ &=1 \end{align*}$$

Degree = 0

Answer:

C. $(x + 4)(x - 4) - x(x - 1)^2$