Question

Check whether 7+3x is a factor of 3x³+7x​

Answer 1

Answer: 7+3x = 0

3x = -7

x = -7/3

P(x) = 3x³ + 7x

= 3(-7/3)³ + 7(-7/3)

= 3(-343/27) + (-49/3)

= -343/9 - 49/3

= (-343-147)/9

= -490/9

As the remainder is not 0, therefore, 7+3x is not a factor of 3x³+7x

Answer 2

Answer:

(7 + 3x) is not a factor of (3x³ + 7x).

Step-by-step explanation:

Let f(x) = 3x³ + 7x……….(1)

Zero of 7 + 3 x is  x = - 7/3

Now to check whether (7 + 3x) the polynomial is a factor of 3x³ + 7x, we prove that, f(–7/3) = 0, by using remainder theorem ,  

On putting x = - 7/3 in eq 1,  

f(–7/3) = 3(–7/3)³ + 7 (–7/3)

f(–7/3) = 3(-343/27) – (49/3)

f(–7/3) = (-343/9) – (49/3)

f(–7/3) = (-343 × 3  – 49 × 9)/27

f(–7/3) = (- 1029 - 441)/27

f(–7/3) = - 1470 /27

f(–7/3) = - 490/9

Hence, (7 + 3x) is not a factor of (3x³ + 7x).