Question

Think about the expression (x-8)(x + 4).

(a) For what values of x will this expression be equal to zero? Show how you arrived at your answer.
(b) Write this product as an equivalent trinomial.
(c) Show that this trinomial is also equal to zero at the larger value of x from part (a).

Answer 1

The expression (x-8)(x + 4) will be equal to zero when x is either 8 or -4. It can be written as the trinomial x² - 4x - 32. Substituting x = 8 into the trinomial gives a value of zero.

Step-by-step explanation:

The correct answer is option (a) For the expression (x-8)(x + 4) to be equal to zero, one or both of the factors must be equal to zero. This means we have the following equations:

x - 8 = 0 and x + 4 = 0

Solving these equations, we find that:

x = 8 and x = -4

Therefore, the expression will be equal to zero when x is either 8 or -4.

(b) To write the product as an equivalent trinomial, we can use the distributive property to expand the expression:

(x - 8)(x + 4) = x(x) + x(4) - 8(x) - 8(4)

Simplifying this, we get:

x² + 4x - 8x - 32

Combining like terms, we have:

x² - 4x - 32

(c) To show that the trinomial is also equal to zero at the larger value of x from part (a), we substitute x = 8 into the trinomial:

8² - 4(8) - 32

64 - 32 - 32

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