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VARVARA [1.3K]
3 years ago
12

See screenshot below​

Mathematics
2 answers:
Varvara68 [4.7K]3 years ago
4 0

Answer:

B only

Step-by-step explanation:

well to solve this question we can consider <u>factor</u><u> </u><u>theorem</u><u> </u>which states that if a Polynomial f(x) is divided by a monomial x-a then x-a is a factor of f(x) if and only if f(a)=0

and to figure "a " we can consider the following equation:

\displaystyle x - a = 0

substitute the given value of a:

\displaystyle x - 2= 0

therefore,

\displaystyle x = 2

<h3>option-1:</h3>

plugin the value of x to the function A(x):

\displaystyle A(2)  = {2}^{3}  +  {2}^{2}  + 4

simplify which yields:

\displaystyle A(2)  = 16

since A(2)≠0 x-2 is <u>not </u>a factor of A(x)

<h3>option-2:</h3>

similarly substitute the value of x to the function B(x) which yields:

\displaystyle B(2)  = {2}^{3}   - {2}^{}   - 6

simplify:

\displaystyle B(2)  =0

so, B(2)=0 Hence x-2 is a factor of x³-x-6

<h3>option-3:</h3>

substitute the value of x to the function C(x)

\displaystyle C(2)  = {2}^{4}  +  3.{2}^{}   -  10

simplify:

\displaystyle C(2)  =12

as C(2)≠0 x-2 is not a factor of C(x)

<h3>option-4:</h3>

likewise plugin the value of x to the function D(x):

\displaystyle D(2)  = {2}^{4}   -  2.{2}^{3}   -  2

simplify and that yields:

\displaystyle D(2)  =    -  2

therefore,D(2)≠0 hence,x-2 isn't a factor of D(-2)

Dafna1 [17]3 years ago
3 0

\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}

The factor

  • x-2=0
  • x=2

we have find the value of x .

Now,

we have to select all the polynomial which has x-2 As a factor.

<u>According</u><u> </u><u>to</u><u> </u><u>the question</u><u>, </u>

<h3>option A:-</h3>

A(x)=x^3+x^2+4\\\\A(2)=(2)^3+(2)^2+4\\\\=8+4+4\\\\16≠0

  • so it is not a factor.

<h3>Option B:-</h3>

B(x)=x^3-x-6\\\\=B(2)=(2)^2-2-6\\\\0=0

  • so it is a factor

<h3>Option C:-</h3>

C(x)=x^4+3x-10\\\\=C(2)=(2)^4+3(2)-10\\\\=16+6-10\\\\12≠0

  • so it is not a factor

<h3>option D:-</h3>

D(x)=x^4-2x^3-2\\\\D(2)=(2)^4-2(2)^3-2\\\\=16-16-2\\\\-2≠0

  • so it is not a factor

<h2><u>therefore</u><u>:</u><u>-</u></h2>

The option B is correct.

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