← Back to the game

Three-part batteries · Quadratic Grand Prix

Batteries with three parts

These batteries have three separate things to work out before you add them all together. Nothing new here — just more steps. Take it one part at a time and you will be fine.

Work out each part separately

A battery like x² + 3x − 4 has three parts:

Part 1

x²

x times x

Part 2

3x

3 times x

Part 3

−4

just a number — nothing to work out

Work out parts 1 and 2 first. Then add them all together at the end.

x² + 3x − 4, with x = 5

x² + 3x − 4 = 36
Your car: x = 5
  1. Swap x for 5 everywhere
    5² + 3 × 5 − 4
  2. Do the ² first — (5) × (5) = 25
    25 + 3 × 5 − 4
  3. Multiply — 3 × 5 = 15
    25 + 15 − 4
  4. Add and take away left to right
    40 − 4 = 36 ✓

x² + 3x − 4, with x = −2

This one has more to watch. Go one part at a time.

x² + 3x − 4 = −6
Your car: x = −2
  1. Part 1 — (−2) × (−2) = 4
    Part 1 = 4
  2. Part 2 — 3 × (−2) = −6
    Part 2 = −6
  3. Part 3 — just a number
    Part 3 = −4
  4. Put them together
    4 + (−6) + (−4) = 4 − 6 − 4
    = −6 ✓

Key point

The answer came out negative. That is fine. A negative answer is not a sign something went wrong. It is just the correct answer.

x² + 2x ≤ 0, with x = −2

x² + 2x ≤ 0
Your car: x = −2
  1. Part 1 — (−2) × (−2) = 4
    Part 1 = 4
  2. Part 2 — 2 × (−2) = −4
    Part 2 = −4
  3. Put them together — 4 + (−4) = 0
    0
  4. Is 0 ≤ 0?
    Yes — 0 equals 0, and ≤ includes an exact match. ✓

Write each part out before you add

With x = −2 and battery x² + 3x − 4, write it like this:

  1. Part 1
    (−2)² = 4
  2. Part 2
    3 × (−2) = −6
  3. Part 3
    −4
  4. Add them up
    4 + (−6) + (−4) = −6

Writing it out separately stops you losing your place. It takes a few extra seconds. It saves a lot of mistakes.

Three easy mistakes

Mistake 1

Getting the sign wrong on the middle part

x² + 3x − 4 with x = −2. Some people work out 3x as 3 × 2 = 6. They forgot the negative.

x is −2. So 3x = 3 × (−2) = −6.

Mistake 2

Thinking (−2)² is negative

(−2)² = (−2) × (−2) = 4. Positive. Two negatives multiplied together always give a positive.

(−2)² = 4. Not −4.

Mistake 3

Worrying when the answer is negative

Some players see −6 and think they must have gone wrong. They have not. Batteries with negative x often give negative answers.

Check your working. If each step looks right, the answer is right.

Try one yourself

Your car:

Work out each part separately, then add them up

    Ready for more?

    Next topic

    Cubic expressions

    Add a fourth part to the battery — and a cube instead of a square. Same idea, one step more.

    ← Powers and negative numbers
    → Cubic expressions Back to the game