Factor Quadratic 153Feb

1. **State the problem:** We need to factor the quadratic expression $$x^2 - 7x + 10$$ into the product of two binomials. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, if $a=1$, we look for two numbers that multiply to $c$ and add to $b$. 3. **Identify $a$, $b$, and $c$:** Here, $a=1$, $b=-7$, and $c=10$. 4. **Find two numbers that multiply to $10$ and add to $-7$:** The pairs of factors of $10$ are $(1, 10)$ and $(2, 5)$. Since the sum must be $-7$, and the product positive, both numbers must be negative: $-2$ and $-5$. 5. **Write the factored form:** Using these numbers, the factorization is $$(x - 2)(x - 5)$$. 6. **Verify by expansion:** $$ (x - 2)(x - 5) = x^2 - 5x - 2x + 10 = x^2 - 7x + 10 $$ This matches the original expression. **Final answer:** $$(x - 2)(x - 5)$$