Question

A student is deriving the quadratic formula. Her first two steps are shown.

Answer 1

Please consider the complete question.

A student is deriving the quadratic formula. Her first two steps are shown. Step 1: $-c = ax^2 + bx$

Step 2: $-c = a[x^2+\frac{b}{a}x]$

Which best explains or justifies Step 2?

A. division property of equality

B. factoring the binomial

C. completing the square

D. subtraction property of equality

We can see that in step 2 student has factored the right side of equation.

The student factored our a from the right side of equation. To factor our a from right side, student has divide the bx term by a.

We can multiply and divide by same quantity in an equation.

$-c = ax^2+a\cdot \frac{b}{a}x$

Now we can factor out a as:

$-c = a(x^2+\frac{b}{a}x)$

Therefore, the 2nd step is known as factoring of binomial and option B is the correct choice.