Answer:
2. remainder = 6x
3. no 7 + 3x is not the factory of the polynomial
hope it helps you
[tex] = > \red{(x - a)}[/tex]
✎ Acc. to remainder theorem:-
Put divisor equal to zero-
[tex](x - a )= 0 \\ \green{\boxed{x = a}}[/tex]
Put value of 'x'. as 'a' in the polynomial:-
[tex]✎ \bf \blue{p(x) = {x}^{3} - a {x}^{2} + 6x - a}[/tex]
[tex] \orange{ = >} p(a) = {a}^{3} - a( {a}^{2} ) + 6a - a[/tex]
[tex] = \not {a}^{3} - \not {a}^{3} + 6a - a \\ \color{cyan} = > \boxed{5a}[/tex]
So,
For the first question, the remainder would be '5a'
If ( 7+3x) is a factor of this:-
Then, reamainder must be zero:-
[tex]7 + 3x = 0 \\ \color{plum}\boxed{ x = \frac{ - 7}{3} }[/tex]
Put this value of 'x' in the polynomial--
[tex] = 3 {x}^{3} + 7x \\ = 3 \times (\frac{ - 7}{3} ) {}^{3} + 7 \times \frac{ - 7}{3} [/tex]
[tex] = \frac{ - 343}{9} \frac{ - 49}{3} \\ \\ = = > \overbrace{ \underbrace \frac{ - 490}{9} }[/tex]
As remainder is not 0, So it is not its factor
[tex] \maltese \: plz \: thanks \maltese[/tex]
Hope this may help!
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Answers & Comments
Answer:
2. remainder = 6x
3. no 7 + 3x is not the factory of the polynomial
hope it helps you
Verified answer
Divisor:-
[tex] = > \red{(x - a)}[/tex]
✎ Acc. to remainder theorem:-
Put divisor equal to zero-
[tex](x - a )= 0 \\ \green{\boxed{x = a}}[/tex]
Put value of 'x'. as 'a' in the polynomial:-
[tex]✎ \bf \blue{p(x) = {x}^{3} - a {x}^{2} + 6x - a}[/tex]
[tex] \orange{ = >} p(a) = {a}^{3} - a( {a}^{2} ) + 6a - a[/tex]
[tex] = \not {a}^{3} - \not {a}^{3} + 6a - a \\ \color{cyan} = > \boxed{5a}[/tex]
So,
For the first question, the remainder would be '5a'
Now ,
If ( 7+3x) is a factor of this:-
Then, reamainder must be zero:-
[tex]7 + 3x = 0 \\ \color{plum}\boxed{ x = \frac{ - 7}{3} }[/tex]
Put this value of 'x' in the polynomial--
[tex] = 3 {x}^{3} + 7x \\ = 3 \times (\frac{ - 7}{3} ) {}^{3} + 7 \times \frac{ - 7}{3} [/tex]
[tex] = \frac{ - 343}{9} \frac{ - 49}{3} \\ \\ = = > \overbrace{ \underbrace \frac{ - 490}{9} }[/tex]
As remainder is not 0, So it is not its factor
[tex] \maltese \: plz \: thanks \maltese[/tex]
Hope this may help!