Maths-

General

Easy

Question

# Make and test a conjecture about the sign of the cube of negative integers.

Hint:

### Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.

Deductive reasoning is the process by which a person makes conclusions based on previously known facts.

## The correct answer is: Hence, we conclude that the cube of negative integers is also an negative integer and we have proved this conjecture by deductive reasoning

### Let’s create a conjecture for the negative integers -2, -7 and -9. We are asked to make a conjecture about the sign of cube of negative integers.

So first, do the cube of the assumed negative integers. We got

(-2)^{3} = -8

(-7)^{3} = -343

(-9)^{3} = -729

So, we conclude that the cube of negative integers will also be an negative integer and this is the conjecture.

Now, let’s see if the conjecture is true or not by deductive reasoning. Let’s say the negative is -x.

Taking the cube of -x

(-x)^{2} = -x × (-x) × (-x)

= -x^{3}

We can see that the cube of negative integers is also an negative integer.

Final Answer:

Hence, we conclude that the cube of negative integers is also an negative integer and we have proved this conjecture by deductive reasoning

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