Question

factor the given polynomial.

\\y^2 + 4yt + 3t^2 = \\

if the expression cannot be factored then answer with prime.

Explanation:

Identify the trinomial structure

We are given the quadratic trinomial in two variables:

$$ y^2 + 4yt + 3t^2 $$

Find factors of the constant and middle terms

We need two terms that multiply to \(3t^2\) and add up to \(4yt\).
The factors of \(3t^2\) are \(1t\) and \(3t\).
Checking their sum:

$$ 1t + 3t = 4t $$

Thus, the factors are \(y + t\) and \(y + 3t\).

Verify the factorization

Multiply the binomials to confirm:

$$ (y + t)(y + 3t) = y^2 + 3yt + yt + 3t^2 = y^2 + 4yt + 3t^2 $$

Answer:

Factor the given polynomial.
\(y^2 + 4yt + 3t^2 =\) <blank>\((y+t)(y+3t)\)</blank>