Step by step
The question
Question: find the value of 2x³ − x when x = −1.
2x3 − x
x = −1
1 Put the numbers in
We put −1 in place of x.
2x³ means 2 times x³.
So we write a times sign.
A negative number goes in brackets, so its minus stays with it.
= 2 × (−1)3 − (−1)
2x³ = 2 × x³
2 Powers
Powers come before times and minus.
Order: ( ) → x² √ → × ÷ → + −
(−1)³ means −1 times −1 times −1.
An odd number of minuses gives minus.
(−1)3 = (−1) × (−1) × (−1) = −1
That is −1.
= 2 × (−1) − (−1)
3 Times and divide
Times comes before minus.
+ × − = −
Plus times minus is minus.
2 times 1 is 2.
So we get −2.
= −2 − (−1)
4 Plus and minus
Taking away a negative is the same as adding.
− (−) = +
So −2 − (−1) becomes −2 + 1.
= −2 + 1
Start at −2.
Go up 1.
We land on −1.
= −1
So 2x³ − x is −1 when x = −1.
Let's look back.
First: put the numbers in.
Then: powers.
Then: times and divide.
Last: plus and minus.
Answer
= −1