Factor Quadratic 058599

1. **State the problem:** Fully factorise the quadratic expression $$5x^2 + 22x + 8$$. 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 product and sum:** Here, $$a = 5$$, $$b = 22$$, and $$c = 8$$. Calculate $$a \times c = 5 \times 8 = 40$$. We need two numbers that multiply to $$40$$ and add to $$22$$. 4. **Find the pair:** The numbers $$20$$ and $$2$$ satisfy this because $$20 \times 2 = 40$$ and $$20 + 2 = 22$$. 5. **Rewrite the middle term:** Rewrite $$22x$$ as $$20x + 2x$$: $$5x^2 + 20x + 2x + 8$$ 6. **Group terms:** Group the terms in pairs: $$(5x^2 + 20x) + (2x + 8)$$ 7. **Factor each group:** Factor out $$5x$$ from the first group: $$5x(x + 4)$$ Factor out $$2$$ from the second group: $$2(x + 4)$$ 8. **Factor out the common binomial:** $$ (5x + 2)(x + 4) $$ **Final answer:** $$5x^2 + 22x + 8 = (5x + 2)(x + 4)$$.