Show that : x + 3 is a factor of 69 + 11x - x² + x³.

Solution:

Let the given polynomial be p(x) = 69 + 11x - x² + x³.

Let the given factor be g(x) = x + 3.

We have to check if x + 3 is a factor of 69 + 11x - x² + x³.

Let g(x) = 0

x + 3 = 0

x = -3

Substitute x = -3 in p(x),

p(-3) = 69 + 11(-3) - (-3)² + (-3)³

= 69 - 33 - 9 - 27

= 36 - 9 - 27

= 9 - 9

= 0

Since p(x) = 0 when x = -3, x + 3 is the factor of p(x)

Therefore, x + 3 is the factor of 69 + 11x - x² + x³.

✦ Try This: If both (x + 1) and (x - 1) are factors of ax³ + x² - 2x + b , find a and b.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 16(i)

Show that : x + 3 is a factor of 69 + 11x - x² + x³

Summary:

A factor of a number in math is a number that divides the given number. It is shown that x + 3 is a factor of 69 + 11x - x² + x³ as p(x) = 0 when x = -3

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