Extra Questions For Class 9 Maths Polynomials | Q2

Question 2: Factorize the given expression: 27x³ - 63x² + 49x - \\frac{343}{27})

Video Explanation

Explanatory Answer | Chapter 2 Extra Question 2

The given polynomial is a cubic polynomial.
Let us compare it with the standard algebraic identity (a - b)³ because the polynomial has both positive and negative terms.

Compare the given expression to the standard cubic algebraic identity to factorise

(a - b)³ = a³ - 3a²b + 3ab² - b³

Compare 27x³ - 63x² + 49x - \\frac{343}{27}) to a³ - 3a²b + 3ab² - b³
We can deduce that 27x³ = a³ or (3x)³ = a³
∴ a = 3x

And \\frac{343}{27}) = b³ or \\left[\frac{7}{3}\right]^3) = b³
∴ b = \\frac{7}{3})

So, 27x³ - 63x² + 49x - \\frac{343}{27}) = (3x)³ - 3(3x)² \\frac{7}{3}) + 3(3x)\\left[\frac{7}{3}\right]^2) - \\left[\frac{7}{3}\right]^3)
= \\left[3x - \frac{7}{3}\right]^3)

Hence, 27x³ - 63x² + 49x - \\frac{343}{27}) factorizes as \\left[3x - \frac{7}{3}\right]\left[3x - \frac{7}{3}\right]\left[3x - \frac{7}{3}\right])