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Question
Factorise the following expressions
4x2 – 8x + 3
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Solution
4x2 – 8x + 3
This is of the form ax2 + bx + c with a = 4, b = – 8, c = 3
Product ac = 4 × 3 = 12
sum b = – 8
| Product = 12 | Sum = – 8 |
| (–1) × (–12) = 12 | (–1) + (–12) = – 13 |
| (– 2) × (– 6) = 12 | (– 2) + (– 6) = – 8 |
The middle term can be written as – 8x = – 2x – 6x
4x2 – 8x + 3 = 4x2 – 2x – 6x + 3
= 2x(2x – 1) – 3(2x – 1)
= (2x – 1)(2x – 3)
4x2 – 8x + 3 = (2x – 1)(2x – 3)
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