Factor f(x) = 4x2 + 11x? - 104x + 105 into linear factors given that – 7 is a zero of f(x). f(x) = 4x + 11x2 - 104x + 105 = |
(Factor completely.)

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5)

Step-by-step explanation:

f(x) = 4x^3 + 11x2 - 104x + 105

has the coefficients {4, 11 -104, 105}.  We perform synthetic division using the given -7 as divisor:

-7   /   4      11     -104     105

                -28     119     -105

          4      -17      15         0

Since the remainder is zero (0), we have shown that -7 is a zero of f(x).  The coefficients of the quotient (above) are {4, -17, 15}.  Let's try factoring the corresponding polynomial again using synthetic division.  Start out by using 5 as divisor and determining whether or not the remaindeer is zero:

5    /     4     -17      15

                    20     15

             4        3     30           No, the remainder is 30 and so 5 is not a

                                               root of this quadratic.  Try the divisor 3 instead:

3     /     4      -17      15

                      12      -15

             4       -5        0        Yes, the remainder is 0 and so 3 is a root.

Thus, the given f(x) = 4x + 11x2 - 104x + 105 factors as follows:

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5).  Notice that the coefficients of the last factor come from those we found above when using 3 as a divisor in synthetic division.  

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !