Question

can someone please help me:
what is x^2 + 14x + 48 factored???!

Answer 1

To factor \(x^2+14x+48\) we'll need to find two binomials to multiply together so that
\[(x+a)(x+b) = x^2 + 14x + 48\]
Let's expand \((x+a)(x+b)\) to get\[(x+a)(x+b) = x^2 + ax + bx + ab = x^2 + (a+b)x + ab\]

Look at that for a minute. That means if we can think of two numbers, \(a, b\), such that \(a+b = 14\) and \(a * b = 48\) we can just plug them in and be done!

What are all the pairs of numbers that multiply together to give you 48?