Question

the product two consecutive even integers is 288. find the integers.
a. 12,24 and -12,-24
b. 14,16 and -14,-16
c. 16,18 and -16,-18
d. 20,22 and -20,-22

Explanation:

Step1: Define the integers

Let the first even integer be $x$. The next consecutive even integer is $x+2$.

Step2: Set up the equation

The product equals 288, so:
$$x(x+2)=288$$

Step3: Rearrange to quadratic form

$$x^2 + 2x - 288 = 0$$

Step4: Solve the quadratic equation

Use factoring: find two numbers that multiply to $-288$ and add to $2$. These numbers are $18$ and $-16$.
$$(x+18)(x-16)=0$$
Set each factor to 0:
$x+18=0 \implies x=-18$, so the pair is $-18, -16$
$x-16=0 \implies x=16$, so the pair is $16, 18$

Step5: Verify options

Match the pairs to the given choices.

Answer:

C. 16,18 and $-16,-18$