Question

Q20. Divide: 8x^3 – 12x² + 16x by 2x​

Answer 1

Answer :-

4x² – 6x + 8.

Solution :-

$\begin{array}{c|c|c}\sf 2x&\sf 8x^3-12x^2 + 16x&\sf 4x^2-6x+8\\&\sf -8x^3 \quad\quad \: \: \qquad\qquad&\\&\dfrac{\qquad \: \: \: \: \:\:\quad\qquad\:\:\:}{\sf \qquad\qquad\qquad -12x^2+16x}\qquad\qquad\quad&\\&\sf \qquad+12x^2 \: \: \: \: \: \: \: \: \:\: \: \: \: \:&\\&\sf {\dfrac{\qquad\qquad \:\:\:\:\:\: }{\qquad\qquad}}\end{array}\put(-146,-40){ \sf+16x }\put(-146,-60){ \dfrac{\sf -16x}{0} }$

Refer to the attachment for the solution if you are not able to see the code.

Extra Information :-

• Polynomials are the algebraic expressions that contains variables and coefficients.

• Types of Polynomial :-

On the basis of degrees,

1. Linear Polynomial.
2. Quadratic Polynomial.
3. Cubic Polynomial.
4. Biquadratic Polynomial.

On the basis of Terms,

1. Monomial.
2. Binomial.
3. Trinomial.

Answer 2

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \frac{8 {x}^{3} - 12 {x}^{2} + 16x }{2x} }$

FORMULA TO BE IMPLEMENTED

$\displaystyle \sf{ 1. \: \: \frac{a + b}{c} = \frac{a}{c} + \frac{b}{c} }$

2. We are aware of the law of indices

$\displaystyle \sf{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

EVALUATION

Here the given expression

$\displaystyle \sf{ \frac{8 {x}^{3} - 12 {x}^{2} + 16x }{2x} }$

We now simplify it

$\displaystyle \sf{ \frac{8 {x}^{3} - 12 {x}^{2} + 16x }{2x} }$

$\displaystyle \sf{ = \frac{8 {x}^{3} }{2x} - \frac{12 {x}^{2} }{2x} + \frac{16x}{2x} } \: \: (using \: formula \: 1)$

$\displaystyle \sf{ =4. {x}^{3 - 1} - 6 {x}^{2 - 1} + 8 {x}^{1 - 1} } \: (\: using \: formula \: 2)$

$\displaystyle \sf{ =4. {x}^{2} -6 {x}^{1} + 8 {x}^{0} }$

$\displaystyle \sf{ =4{x}^{2} -6 x+ 8 \: \: ( \because \: \: {x}^{0} = 1) }$

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