Question

Factor completely, then place the factors in the proper location on the grid.

4x²+ 8xy - 60y²
A) Factor the expression and place the factors on the grid.
B) Factor the expression only.
C) Place the factors on the grid only.
D) There is no need to factor the expression; place the original expression on the grid.

Answer 1

To factor the expression 4x² + 8xy - 60y² completely, first factor out the GCF of 4, and then factor the trinomial to get 4(x + 5y)(x - 3y). Place each factor in its own space on the grid provided.

Step-by-step explanation:

To factor completely the quadratic expression 4x² + 8xy - 60y², we first look for a greatest common factor (GCF) that can be factored out. In this case, the GCF is 4. Factoring out the GCF gives us:

4(x² + 2xy - 15y²)

Now we need to factor the trinomial x² + 2xy - 15y². We are looking for two numbers that multiply to give -15 (the product of the coefficient of x² and the constant term) and add to give 2 (the coefficient of xy). Those numbers are 5 and -3. Thus, the trinomial can be factored as:

(x + 5y)(x - 3y)

So the completely factored form of the expression is:

4(x + 5y)(x - 3y)

To place the factors on the grid, you would set each factor in its own cell or a designated space on the grid provided in your assignment.