Express the polynomial as a product of linear factors f(x)=x3-5x2-18x+72

 The given polynomial can be expressed as  (x-3)(x+4)(x-6).

Step-by-step explanation:  We are given to express the following cubic polynomial as a product of linear factors :

We have the factor theorem that states as follows :

FACTOR THEOREM :  If x = a is a zero of the polynomial p(x), then (x - a) is a factor of the polynomial p(x).

If x = 1, then

If x = 2, then

If x = 3, then

So, x = 3 is a zero of f(x), implies that (x - 3) is a factor of f(x).

Therefore, we have

Thus, the given polynomial can be expressed as  (x-3)(x+4)(x-6).

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions