Is (x+1) a factor of the function f(x) = 7x^4 – 5x^3 – 10x² + 2x, and why?

Mathematics

1 answer:

Schach [20]2 years ago

7 0

Answer:

first option

Step-by-step explanation:

If ( x + h) is a factor of f(x) then f(- h) = 0 , then

If (x + 1) is a factor of f(x) then f(- 1) = 0

f(- 1) = 7 $(-1)^{4}$ - 5(- 1)³ - 10(- 1)² + 2(- 1)

= 7(1) - 5(- 1) - 10(1) - 2

= 7 + 5 - 10 - 2

= 12 - 12

= 0

Since f(- 1) = 0 then (x + 1) is a factor of f(x)

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Gretchen has eight socks, two of each color: magenta, cyan, black, and white. she randomly draws four socks. what is the probabi

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Begin by computing the number of all the possibilities:
It is given by the following formula: $C_8^4=\frac{8!}{4!(8-4)!}= \frac{8\times7\times6\times5}{4\times3\times2}=70$
Computing the number of favorable cases:
Exactly one pair of socks with the same color means either one magenta pair,
or one cyan pair, or one black pair or one white pair:
Number of possibilities with one magenta pair means"a magenta pair plus two socks with different colors from three possibilities" means 3 possibilities.
Same computation for the other colors.
Adding we get: $3+3+3+3=12\text{ possibilities }$
By definition, the probability of an event is the number of favorable cases over the number of possible cases:
$\frac{12}{70}= \frac{6}{35}$

The probability is $\frac{6}{35}$