Factoring Trinomials
When you see a trinomial like x² + 14x + 40, you can break it down into two binomials multiplied together. Think of it like finding two simpler expressions that, when multiplied, give you back your original trinomial.
To factor this trinomial, we need to find two numbers that multiply to give 40 (the last term) and add up to 14 (the middle term's coefficient). Let's try some possibilities! After checking a few number pairs, we find that 4 and 10 work perfectly because 4 × 10 = 40 and 4 + 10 = 14.
Once we've found our magic numbers (4 and 10), we can write our factored form: x + 4$$x + 10. You can check this is correct by multiplying these factors using the box method shown in the diagram.
Quick Tip: When factoring trinomials in the form x² + bx + c, always look for two numbers that multiply to give c and add up to b. This approach works every time!