Below are practice questions on factoring polynomials into products of linear factors. Complete answers are provided at the end of the page.
For additional practice, see: Polynomial Questions and Problems .
Write the polynomial \( P \) as a product of linear factors:
\[ P(x) = x^2 - 4 \]Write the polynomial \( P \) as a product of linear factors:
\[ P(x) = 9x^3 - 19x - 10 \]Write the polynomial \( P \) as a product of linear factors:
\[ P(x) = 5x^3 - 2x^2 + 5x - 2 \]Write the polynomial \( P \) as a product of linear factors:
\[ P(x) = -x^3 - 2x^2 + 5x + 6 \]Write the polynomial \( P \) as a product of linear factors:
\[ P(x) = (x + 2)(20x^2 + 41x + 20) \]Show that \( 1 \) and \( -3 \) are zeros of the polynomial
\[ P(x) = x^4 + 4x^3 + 6x^2 + 4x - 15 \]Then express \( P(x) \) as a product of linear factors.
Show that \( -1 \) and \( -5 \) are zeros of the polynomial
\[ P(x) = x^4 + 12x^3 + 54x^2 + 108x + 65 \]Then express \( P(x) \) as a product of linear factors.
Show that \( -2 \), \( -3 \), and \( 2 \) are zeros of the polynomial
\[ P(x) = x^5 + x^4 + 26x^2 - 16x - 120 \]Then write \( P(x) \) as a product of linear factors.
1.
\[ P(x) = (x - 2)(x + 2) \]2.
\[ P(x) = (x + 1)(3x + 2)(3x - 5) \]3.
\[ P(x) = (x + i)(x - i)(5x - 2) \]4.
\[ P(x) = (x + 1)(2 - x)(x + 3) \]5.
\[ P(x) = 20(x + 2)\left(x + \frac{5}{4}\right)\left(x + \frac{4}{5}\right) \]6.
\[ P(1) = 0 \quad \text{and} \quad P(-3) = 0 \] \[ P(x) = (x - 1)(x + 3)(x + 1 + 2i)(x + 1 - 2i) \]7.
\[ P(-1) = 0 \quad \text{and} \quad P(-5) = 0 \] \[ P(x) = (x + 1)(x + 5)(x + 3 + 2i)(x + 3 - 2i) \]8.
\[ P(-2) = 0,\quad P(-3) = 0,\quad P(2) = 0 \] \[ P(x) = (x + 2)(x + 3)(x - 2)(x - 1 + 3i)(x - 1 - 3i) \]