Question

Is y^2 - 6y + 5 = (y - 5)(y - 1) completely factored? Why?

a) Yes, it is completely factored because it equals the product of two binomials.
b) No, it is not completely factored because it can be simplified further.
c) Yes, it is completely factored because it cannot be factored any more.
d) No, it is not completely factored because it contains irreducible factors.

Answer 1

The quadratic expression y^2 - 6y + 5 is correctly factored into (y - 5)(y - 1), and it cannot be factored further, so it is considered completely factored.

Step-by-step explanation:

The expression y^2 - 6y + 5 is factored into the product of two binomials (y - 5)(y - 1). To verify if it is completely factored, we can use the FOIL method (First, Outer, Inner, Last) to expand the product of the two binomials:

• First: y * y = y^2
• Outer: y * (-1) = -y
• Inner: (-5) * y = -5y
• Last: (-5) * (-1) = +5

Adding together the 'Outer' and 'Inner' terms:

-y - 5y = -6y

So, the expanded form is:

y^2 - 6y + 5

Since this expansion matches our original expression, it confirms that the two binomials (y - 5) and (y - 1) are, in fact, the correct factors of the quadratic expression. Therefore, the correct answer is:

c. Yes, it is completely factored because it cannot be factored any more.