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# Check whether 7 + 3x is a factor of 3x^{3} + 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) = 3x^{3} + 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 3x^{3} + 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) = 3x^{3} + 7x since, the remainder of p(-7/3) is not equal to 0.

**☛ Related Questions:**

- Find the zero of the polynomials in each of the following cases:(i) p(x) = x + 5(ii) p(x) = x - 5(iii) p(x) = 2x + 5(iv) p(x) = 3x - 2(v) p(x) = 3x(vi) p(x) = ax, a ≠ 0(vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.
- Find the remainder when x3 + 3x2 + 3x + 1 is divided byi) x + 1ii) x - (1/2)iii) xiv) x + πv) 5 + 2x
- Find the remainder when x3 - ax2 + 6x - a is divided by x - a

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