Factor completely: 𝑦^2 + 14 𝑦 + 48

Answer 1

To factor the expression 𝑦^2 + 14𝑦 + 48, we look for two numbers that multiply to 48 and add up to 14.

The two numbers are 6 and 8 because 6*8 = 48 and 6 + 8 = 14.

Now, we rewrite the expression using these numbers:

𝑦^2 + 6𝑦 + 8𝑦 + 48

Next, we factor by grouping:

𝑦(𝑦 + 6) + 8(𝑦 + 6)

Finally, we factor out the common binomial factor:

(𝑦 + 6)(𝑦 + 8)

Therefore, the expression 𝑦^2 + 14𝑦 + 48 fully factors to (𝑦 + 6)(𝑦 + 8).