Factorise Quadratic Db5407

1. **State the problem:** Fully factorise the quadratic expression $$2x^2 - 13x + 15$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Calculate the product and sum:** Here, $$a = 2$$, $$b = -13$$, and $$c = 15$$. Calculate $$a \times c = 2 \times 15 = 30$$. We need two numbers that multiply to $$30$$ and add to $$-13$$. 4. **Find the pair:** The numbers are $$-10$$ and $$-3$$ because $$-10 \times -3 = 30$$ and $$-10 + (-3) = -13$$. 5. **Rewrite the middle term:** $$2x^2 - 10x - 3x + 15$$ 6. **Group terms:** $$(2x^2 - 10x) + (-3x + 15)$$ 7. **Factor each group:** $$2x(x - 5) - 3(x - 5)$$ 8. **Factor out the common binomial:** $$(2x - 3)(x - 5)$$ 9. **Final answer:** The fully factorised form of $$2x^2 - 13x + 15$$ is $$\boxed{(2x - 3)(x - 5)}$$.