Question

x^2 - 2 divided by x^3 - 3x^2 + 5x - 3

Answer 1

Answer:

Similarly, quadratic polynomials and cubic polynomials have a degree of 2 and 3 respectively. A polynomial with only one term is known as a monomial. A monomial containing only a constant term is said to be a polynomial of zero degrees. A polynomial can account to null value even if the values of the constants are greater than zero.

Step-by-step explanation:

Your answer divya :)

Answer 2

Concept :

• Polynomials = Poly (means many) + nomials (means terms).

• Thus, a polynomial contains many terms.

• Thus, a type of algebraic expression with many terms having variables and coefficients is called polynomial.

Let's Start :

$\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: {x }^{2} - 2\overline{) \cancel{{x}^{3}} - 3 {x}^{2} + 5x - 3 (} {x - 3}\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\underline{ \cancel{ {x}^{3}} \:\: \downarrow } \: \: - 2x\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \cancel{- 3 {x}^{2} } + 7x - 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \cancel{- 3 {x }^{2}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + 6} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\: \: \: \: \: \ \: \: \: 7x - 9}\end{gathered}$

Step 1 :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf{ \purple{ \cancel\frac{ {x}^{3} }{ {x}^{2} } = x}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf{ \purple{x( {x}^{2} - 2) }}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf{ \purple{ {x}^{3} - 2x }}}}$

Step 2 :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf{ \red{ \cancel \frac{ - 3 {x}^{2} }{ {x}^{2} } = - 3 }}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf{ \red{ - 3( {x}^{2} - 2) }}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \sf{ \red{ - 3 {x}^{2} + 6 }}}}$

So your answer is completed :)