Question

3. Check whether 7 + 3x is a factor of 3r+ 7x.​

Answer 1

(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).