Quadratic Equations | Algebraic Expression | Middle Term Splitting | Shortcut Trick | Class 9 & 10, by SAM Education Academy on YouTube. 3 min.
- Video length
- 3 min
- Time to do it
- 10 minutes
- Difficulty
- Easy
- Steps
- 10
What you need
Steps
Rewrite the equation so everything sits on one side and equals zero. Move terms across the equals sign and change their signs, so you have the form ax² + bx + c = 0.
Write down a, b and c with their signs. For 6x² + 11x + 4 = 0, a is 6, b is 11 and c is 4.
Multiply a by c. Here 6 times 4 gives 24. This product is the number you will split.
List factor pairs of that product and pick the pair that adds up to b. For 24 you check 1 and 24, 2 and 12, 3 and 8, 4 and 6. Only 3 and 8 add to 11.
Replace the middle term with those two numbers. Write 6x² + 3x + 8x + 4 = 0 instead of 6x² + 11x + 4 = 0. Keep the signs correct if b is negative.
Group the four terms into two pairs and take out the common factor from each pair. From 6x² + 3x take 3x, and from 8x + 4 take 4.
Check that both brackets are now the same. You should get 3x(2x + 1) + 4(2x + 1), so the shared bracket is (2x + 1).
Factor out the common bracket to get (2x + 1)(3x + 4) = 0. If the brackets do not match, go back and recheck your factor pair.
Set each bracket to zero and solve for x. 2x + 1 = 0 gives x = -1/2, and 3x + 4 = 0 gives x = -4/3.
Substitute each answer back into the original equation to confirm it gives zero. Both values should work before you write the final answer.
Tips and common mistakes
Always rearrange to ax² + bx + c = 0 first, because the method fails if the equation is not equal to zero.
If no factor pair of ac adds to b, the quadratic may not factor neatly and you may need the formula instead.
Watch the signs: when c is negative, one factor is positive and one is negative, and their difference must equal b.
Do the grouping step slowly, since a small sign slip there is the most common reason the brackets do not match.
Questions
What if a is 1?
Then ac is just c, so you look for two numbers that multiply to c and add to b. For x² + 5x + 6, the pair is 2 and 3, giving (x + 2)(x + 3).
How do I know which factor pair to pick?
Test each pair of factors of ac by adding them. Pick the pair whose sum equals b exactly, signs included.
Can I use this when the equation does not factor?
No. Splitting the middle term only works when the quadratic has neat factor pairs, so if none fit, use the quadratic formula.
This guide was drafted from the video's details and general task knowledge. It has not been checked against the full video. Check the video and relevant product instructions before following a procedure. Report a correction.
