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

Solution:

When a polynomial p(x) is divided by x - a then by factor theorem if p(a) = 0, we can say that x - a is a factor of p(x).

For 7 + 3x to be a factor, it is very important for the remainder to be equal to 0.

Let us proceed step by step.

Let p(x) = 3x³ + 7x

The root of 7 + 3x = 0 is -7 / 3.

p(-7/3) = 3(-7 / 3)³ + 7 (-7 / 3)

= 3 × (-343) / 27 + (-49 / 3)

= [(-343) - 147] / 9

= -490 / 9 ≠ 0

Since the remainder of p(-7/3) ≠ 0, 7 + 3x is not a factor of 3x³ + 7x.

☛ Check: NCERT Solutions Class 9 Maths Chapter 2 Polynomials

Video Solution:

Check whether 7 + 3x is a factor of p(x) = 3x³ + 7x.

NCERT Solutions Class 9 Maths Chapter 2 Exercise 2.3 Question 3

Summary:

7 + 3x is not a factor of p(x) = 3x³ + 7x since, the remainder of p(-7/3) is not equal to 0.

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