Question

p(x) =69+11x-x²+x³,g(x) =x+3​

Answer 1

Given:-

•g(x)= x + 3

•p(x) = 69 +11x - ${x}^{2}$+${x}^{3}$

To Find:-

• The value of p(x)

Solution:-

Firstly, find the value of x in g(x)

$\: \: \sf \: g(x) = x + 3 = 0 \\ \\ \: \: \sf \: g(x) = x = - 3$

After getting the value of x now we will put the value of x in p(x) and find the p(x)

$\: \: \sf \: p(x) = 69 + 11x - {x}^{2} + {x}^{3} \\ \\ \: \: \sf \: p(x) = 69 + 11 \times ( - 3) - {( - 3)}^{2} + {( - 3)}^{3} \\ \\ \: \: \sf \: p(x) = 69 + ( - 33) - 9 + ( - 27) \\ \\ \: \: \sf \: p(x) = 69 - 33 - 9 - 27 \\ \\ \: \: \sf \: p(x) = 69 - 33 - 36 \\ \\ \: \: \sf \: p(x) = 69 - 69 \\ \\ \: \: \sf \: p(x) = 0$

Hence,the value of p(x) is 0.

__________________________

Additional Information:

Remainder Theorem: It says that if you divide a polynomial,f(x),by a linear expression,x-A,the remainder will be same as f(A).

Example:- The remainder when x^2-4x+2 is divided by x-3 is (3)^2-4(3)+2 or -1.

Polynomials: Polynomials are algebraic expressions that consist of variables and coefficents.

Polynomial Equation: The equation formed with variables, exponents and coefficents are called a polynomials equation.

Answer 2

: Required Answer

$\implies$ p(x) =69+11x-x²+x³,g(x) =x+3

$\implies$x + 3 = 0

$\implies$x = - 3

$\implies$ $69 - 11( - 3) - ( - 3) {}^{2} + ( - 3) {}^{3}$

$\implies$$69 - 33 - 9 - 27$

$\implies$ $69 - 42 - 27$

$\implies$ $69 - 69$

$= 0$

$\huge \sf \pink{ \: hence,it is \: factors}$