Question

factorise -
z cube - 3z square -9z -5 .​

Answer 1

Answer:

First, convert the polynomial into the standard form.

z³-3z²-9z-5

Now, we find out zeros in the polynomials.

Factors of the last term, 5, are ±5, ±1.

We substitute the possible factors in the variable and using trial and error, check whether the value is equal to 0.

After some recalculation, I found out that +5 is a possible factor.

Now, we synthesis the coefficients with the factor.

5 l 1 , -3 , -9 , -5

  l      5    10   5      

    1    2     1    0

Thus, using the above values, we can tell that:

a = 1, b = 2, c = 1.

New equation = az²+bz+c

1z²+2z+1.

Then, we already know that z=5 ⇒ z-5=0

Multiply z-5 and 1z²+2z+1.

=(1z²+2z+1)(z-5)

Now factorise 1z²+2z+1

=(1z²+1z+1z+1)(z-5)

=(z+1)(z+1)(z−5)

It was quite a lenghty sum!

HOPE THIS HELPS :D