Use the factor theorem to determine whether the first polynomial is a factor of the second polynomial.
x - 5; 3x2 + 7x + 40

The polynomial (x -5) is not a factor of second polynomial

Step-by-step explanation:

Factor theorem states that if you divide a polynomial p(x) by a factor x -a of that polynomial, then you will get a zero remainder.

i.,e   which means that if x - a is a factor of p(x), then the remainder, when we do synthetic division by  x= a, will be zero.

Determine whether the first polynomial is a factor of the second polynomial.

Given the polynomial:  

For   to be a factor of , the factor theorems implies that x = 5 must be a zero of f(x).

Now, to test whether  is a factor;

Set x -5 = 0

⇒x = 5

Then,

we will use synthetic division method to divide f(x) by x =5

you can see the figure as shown below in the attachment.

Since, the remainder is 150 which is not equal to zero, then Factor theorem says that (x-5) is not a  factor of

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2