Show that : 2x - 3 is a factor of x + 2x³ - 9x² + 12
Solution:
Let the given polynomial be p(x) = x + 2x³ - 9x² + 12
Let the given factor be g(x) = 2x - 3.
We have to check if x + 3 is a factor of x + 2x³ - 9x² + 12
Let g(x) = 0
2x - 3 = 0
2x = 3
x = 3/2
Substitute x = 3/2 in p(x),
p(3/2) = (3/2) + 2(3/2)³ - 9(3/2)² + 12
= 3/2 + 2(27/8) - 9(9/4) + 12
= 3/2 + 27/4 - 81/4 + 12
= (3(2) + 27 - 81 + 12(4))/4
= (6 + 27 - 81 + 48)/4
= (33 + 48 - 81)/4
= (81 - 81)/4
= 0/4
= 0
Since p(x) = 0 when x = 3/2, 2x - 3 is the factor of p(x)
Therefore, 2x-3 is the factor of x + 2x³ - 9x² + 12.
✦ Try This: Find the values of x for which the functions f(x) = 3x2 -1 and g(x) = 3+ x are equal.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 16(ii)
Show that : 2x - 3 is a factor of x + 2x³ - 9x² + 12
Summary:
A factor is a number that divides the given number without any remainder. It is shown that 2x - 3 is a factor of x + 2x³ - 9x² + 12 as p(x) = 0 when x = 3/2
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