which three statements are true when solving $x^{2}-8x + 16 = 0$? a $x=pm4$ b factor to solve. c $x = 4$ is…

which three statements are true when solving $x^{2}-8x + 16 = 0$? a $x=pm4$ b factor to solve. c $x = 4$ is a double root. d complete the square to solve. e the equation is a perfect square trinomial.

which three statements are true when solving $x^{2}-8x + 16 = 0$? a $x=pm4$ b factor to solve. c $x = 4$ is a double root. d complete the square to solve. e the equation is a perfect square trinomial.

Answer

Explanation:

Step1: Identify the type of trinomial

The equation $x^{2}-8x + 16=0$ is of the form $a^{2}-2ab + b^{2}$ where $a = x$ and $b = 4$ ($2ab=2\times x\times4 = 8x$), so it is a perfect - square trinomial.

Step2: Factor the trinomial

Using the formula $a^{2}-2ab + b^{2}=(a - b)^{2}$, we have $x^{2}-8x + 16=(x - 4)^{2}=0$.

Step3: Solve for x

If $(x - 4)^{2}=0$, then $x-4 = 0$, which gives $x = 4$ as a double root. We can also solve it by factoring or completing the square.

Answer:

B. Factor to solve., C. $x = 4$ is a double root., E. The equation is a perfect square trinomial.