Use the remainder theorem to verify this statement. (x + 5) is a factor of the function f(x) = x3 + 3x2 – 25x– 75

1.) Find the (blank) of f(x) =x^3 + 3x^2 - 25x - 75

2.) The (Blank) of this operation is 0

3.) Therefore, (x+5) is (Blank) of function F.

4.) So f(-(Blank)-) = 0

Options for 1.)
Difference
Product
Quotient
Sum

Options for 2.)
Discriminant
Remainder
Sum
Quotient

Options for 3.)
The simplified form
The opposite
A factor
Not a factor

Options for 4.)
-5
75
-75
5

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

i'm sure goog can you get that answer

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.