Using a given zero to write a polynom For the polynomial below, 3 is a zero. f(x) =x 2. 9x + 25x - 21 - Express f (x) as a product of linear factors. f(2) = [ = %3D

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Using a Given Zero to Write a Polynomial**

For the polynomial below, 3 is a zero.

\[ f(x) = x^3 - 9x^2 + 25x - 21 \]

**Task:** Express \( f(x) \) as a product of linear factors.

**Hint:** Knowing that 3 is a zero implies \( f(3) = 0 \). Use this information to help factor the polynomial, starting with \((x - 3)\) as one of the factors. Consider using synthetic or long division to find the other factors.
Transcribed Image Text:**Using a Given Zero to Write a Polynomial** For the polynomial below, 3 is a zero. \[ f(x) = x^3 - 9x^2 + 25x - 21 \] **Task:** Express \( f(x) \) as a product of linear factors. **Hint:** Knowing that 3 is a zero implies \( f(3) = 0 \). Use this information to help factor the polynomial, starting with \((x - 3)\) as one of the factors. Consider using synthetic or long division to find the other factors.
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