Factorising y³-2y²-29y-52 using Factor Theorem


Factor Theorem Overview:
The factor theorem states that if a polynomial f(x) has a factor (x - a), then f(a) = 0. This theorem allows us to factorise polynomials by finding the roots of the polynomial.


Given Polynomial:
y³-2y²-29y-52


Step 1: Finding a Factor:
To factorise the given polynomial, we need to find a factor by using the factor theorem. We can start by guessing potential roots or factors of the polynomial.


Step 2: Testing Potential Roots:
We can test different values of y to find a root that makes the polynomial equal to zero. By using trial and error, we can find that y = 4 is a root of the polynomial.


Step 3: Applying Factor Theorem:
Once we have found a root (y = 4), we can use the factor theorem to divide the polynomial by (y - 4) to obtain the other factor.


Step 4: Division and Factorisation:
By dividing y³-2y²-29y-52 by (y - 4), we get (y²+2y+13). Therefore, the factorised form of the polynomial is (y - 4)(y²+2y+13).


Final Factorised Form:
Therefore, the factorised form of y³-2y²-29y-52 is (y - 4)(y²+2y+13).