Question

please solve this fast .very urgent whoever gives the correct first will be marked as brainliest and I will follow them.
question: show that.......... Refer the above pic ​

Answer 1

Answer:

x-2=0

×=2

Step-by-step explanation:

p(x) = x³- 6x²+ 11x - 6

p(2)=(2)³-6(2)³+11(2)-6

= 8-48+22-6

= 8-26-6

=8-32

= -24

since -24 is not equal to 0

therefore x-2 is not a factor of p(x)=x³-6x²+11x-6

I hope i'm able to help you by this

Answer 2

GIVEN :-

• DIVISOR : x - 2

• p (x) = x³ - 6x² + 11x - 6

TO FIND :-

• that ( x - 2 ) is a factor of x³ - 6x² + 11x - 6

SOLUTION :-

NOW WE HAVE TO PROVE THAT ( x - 2 ) is a factor of x³ - 6x² + 11x - 6

so if values of x of divisor brings result 0 after putting in p(x) : x³ - 6x² + 11x - 6 so it will be a factor

x - 2 = 0

x = 2

now put the value of x in dividend

$\implies \rm{ x³ - 6x² + 11x - 6 }$

$\implies \rm{ (2)³ - 6(2)² + 11(2)- 6 }$

$\implies \rm{ 8 - 24 + 22- 6 }$

$\implies \rm{ 30 - 30 = 0 }$

$\implies \boxed {\boxed{ \rm{ so \:(x - 2) \:is \: a \: factor \: of \: x³ - 6x² + 11x - 6 }}}$

OTHER INFORMATION :-

NOTES FOR POLYNOMIAL

• A term is either a variable or a single number or it can be a combination of variable and numbers.

• The degree of the polynomial is the highest power of the variable in a polynomial.

• A polynomial of degree 1 is called as a linear polynomial.

• A polynomial of degree 2 is called a quadratic polynomial.

• A polynomial of degree 3 is called a cubic polynomial.

• A polynomial of 1 term is called a monomial.

• A polynomial of 2 terms is called binomial.

• A polynomial of 3 terms is called a trinomial.

• A real number ‘a’ is a zero of a polynomial p(x) if p(a) = 0, where a is also known as root of the equation p(x) = 0.

• A linear polynomial in one variable has a unique zero, a polynomial of a non-zero constant has no zero, and each real number is a zero of the zero polynomial.

Remainder Theorem:

• If p(x) is any polynomial having degree greater than or equal to 1 and if it is divided by the linear polynomial x – a, then the remainder is p(a).

Factor Theorem :

• x – c is a factor of the polynomial p(x), if p(c) = 0. Also, if x – c is a factor of p(x), then p(c) = 0.
• The degree of the zero polynomial is not defined.

other identities :

• (x + y + z)² = x² + y² + z²+ 2xy + 2yz + 2zx

• (x + y)³ = x³ + y³ + 3xy(x + y)

• (x – y)³ = x³– y³– 3xy(x – y)

• x³ + y³+ z³ – 3xyz = (x + y + z) (x² + y² + z²– xy – yz – zx)