For the polynomial below, 2 is a zero. express f(x) as a product of linear factors .

Step-by-step explanation:

since this is a cubic polynomial (highest power of  x is 3), we know that there are 3 possible values of x for which the f(x) is equal to zero (or there are values of x which satisfy f(x) = 0 ). In other words, there are 3 linear factors of this f(x) as the highest power of x is 3.

hence x = 2, is one of the values that satisfy f(x) = 0, we can write this out in linear factors as (x-2) (think of this as taking 2 from the right hand side of the equation x = 2 to the left making x - 2 = 0)

for this we first need to reduce this cubic (3rd power) polynomial f(x) into a quadratic (2nd power) polynomial. We can do this by "comparison method"

since we already know that one of the linear factors of f(x) is (x-2) we can write

here, '==' is simply implying that the two expressions are the same. All we need to find now is the values of a,b and c. First simplify the right hand side of the equation by multiplying with . this will yield

here is when the comparison takes place. compare all the x^3 terms on both sides, similarly the x^2 terms, the x terms, and finally the terms without any x. By comparing you can easily find the values of a b and c

you can see that all the x's cancel out. and the values can be found

from the 2nd equation

from the last equation

now you have your quadratic equation

now you can solve this equation using the quadratic formula

solving and simplifying will yield

convert them to linear factors

hope this helps :)

1,8,15,22,29,36,43,50

step-by-step explanation: