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Factorize the quadratic expression: f(x)=3x^(3)-21x^(2)-54 x

Factorize the quadratic expression: $f(x)=3x^{3}-21x^{2}-54x$

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Operations with rational exponents

Full solution

Q. Factorize the quadratic expression:

f(x)=3x^{3}-21x^{2}-54x

Identify Common Factor: Identify the common factor in the terms of $f(x)$ . $f(x) = 3x^3 - 21x^2 - 54x$ Common factor = $3x$
Factor Out Common Factor: Factor out the common factor from each term. $\newline$ $f(x) = 3x(x^2 - 7x - 18)$
Factorize Quadratic Expression: Factorize the quadratic expression inside the parentheses. $\newline$ $x^2 - 7x - 18$ $\newline$ Factors of $-18$ that add up to $-7$ are $-9$ and $+2$ . $\newline$ $(x - 9)(x + 2)$
Write Fully Factored Form: Write the fully factored form of $f(x)$ . $f(x) = 3x(x - 9)(x + 2)$

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