The polynomial (x - 2) is a factor of the polynomial 5x2 - 6x + 4.A.TrueB.FalseSUBMITarrow_backPREVIOUS

To determine whether $(x - 2)$ is a factor of the polynomial $5x^2 - 6x + 4$, we can use the Factor Theorem, which states that $(x - c)$ is a factor of a polynomial $f(x)$ if and only if $f(c) = 0$.

Step 1: Define the polynomial

Let $f(x) = 5x^2 - 6x + 4$.

Step 2: Substitute $x = 2$

We need to calculate $f(2)$: $f(2) = 5(2)^2 - 6(2) + 4$

Step 3: Perform the calculation

Calculating step-by-step:

1. Calculate $(2)^2 = 4$, then $5(4) = 20$
2. Calculate $-6(2) = -12$
3. Now adding up: $f(2) = 20 - 12 + 4 = 12$

Step 4: Verify and summarize

Since $f(2) = 12$, which is not equal to 0, it follows that $(x - 2)$ is not a factor of the polynomial $5x^2 - 6x + 4$.

Final Answer

B. False