Question

(9) Divide polynomial 3x3-8x2 + x + 7 by x-3
Find quotient and remainder.
9th Std
Subject : Algebra
chapter No. 3 polynomials
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Answer 1

Answer:

$\huge \: x - 3 = 0$

$\huge \red{ \boxed{x \: = \: 3}}$

$\huge \underline{let \: us \: substute}$

$\huge \underline \blue{x \: = \: 3}$

${(3x)}^{3} - {(8x)}^{2} + x + 7 = 0$

${(3 (3))}^{3} - {(8(3))}^{2} + 3 + 7 = 0$

$= {(9)}^{3} - {(24)}^{2} + 10 = 0$

$= > (729) - (576) + (10) = 0$

$= > (739) - (576) = 163$

$\blue{\boxed{163 \: not \: equal \: to \: zero}}$

$\sf{so \: that \: (x - 3) \: is \: not \: a \: factor \: of}$

$\sf{{(3x)}^{3} - {(8x)}^{2} + 3 + 7 = 0}$

_____________________

Extra related to this:-

Factor therom:-

In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if.

. x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number.

Remainder therom:-

It says that if you divide a polynomial, f(x), by a linear expression, x-A, the remainder will be the same as f(A). For example, the remainder when x^2 - 4x + 2 is divided by x-3 is (3)^2 - 4(3) + 2 or -1.

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Answer 2

X - 3 = 0

X = 0

Let us substute

X = 3

${3x}^{3} - {8x}^{2} + x + 7 = 0$

${3(3)}^{3} - ({8(3)})^{2} + 3 + 7 = 0$

${9}^{3} - {24}^{2} + 10 = 0$

$(729) -( 576 )+ 10 = 0$

$(739) + (576) = 163$

163 is not equal to zero.

( X- 3 ) is not factor of

${3x}^{3} - {8x}^{2} + 3 + 7 = 0$

More⬇

Theorem. Factor Theorem. x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number.

Hope this will help you...