Question

3. f
7 + 3x is a factor of 3x3 + 7x.​

Answer 1

Answer:

• REQUIRED ANSWER :)

Finding reminder when $3x {}^{3} + 7x$is divided by 7 + 3x

Step 1 :-

Put divisor = 0

$7 + 3x = 0 \\ 3x = - 7 \\ \times = \frac{ - 7}{3}$

Step 2:-

Let,

$p(x) = 3x {}^{3} + 7x \\ putting \: x = \frac{ - 7}{3} \\ \\ p( \frac{ - 7}{3} ) = 3( \frac{ - 7}{3} ) {}^{3} + 7( \frac{ - 7}{3} ) \\ \\ = - 3( \frac{7 {}^{3} }{3 {}^{3} } ) - \frac{49}{3} \\ \\ = \frac{ - 343}{9} - \frac{49}{3} \\ \\ = \frac{ - 343 - 49(3)}{9} \\ \\ = \frac{ - 343 - 147}{9} \\ \\ = \frac{ - 590}{9}$

Thus, reminder = $p( \frac{ - 7}{3} ) = \frac{ - 590}{9}$

Since, reminder is not 0

Thus 7 + 3x is not a factor of $3x {}^{3} + 7x$