One of the factors of (25x² - 1) + (1 + 5x)² is
a. 5 + x
b. 5 - x
c. 5x - 1
d. 10x
Solution:
It is given that
(25x² - 1) + (1 + 5x)²
Using the algebraic identity (a + b)² = a² + b² + 2ab
= 25x² - 1 + 1 + 25x² + 10x
By further calculation
= 50x² + 10x
Taking out the common term
= 10x (5x + 1)
Therefore, one of the factors is 10x.
✦ Try This: One of the factors of (16x² - 1) + (1 + 4x)² is a.4x - 1, b. 4 - x, c. 4 + x, d. 8x
It is given that
(16x² - 1) + (1 + 4x)²
Using the algebraic identity (a + b)² = a² + b² + 2ab
= 16x² - 1 + 1 + 16x² + 8x
By further calculation
= 32x² + 8x
Taking out the common term
= 8x (4x + 1)
Therefore, one of the factors is 8x.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 14
One of the factors of (25x² - 1) + (1 + 5x)² is a. 5 + x, b. 5 - x, c. 5x - 1, d. 10x
Summary:
Factoring Polynomials means decomposing the given polynomial into a product of two or more polynomials using prime factorization. One of the factors of (25x² - 1) + (1 + 5x)² is 10x
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