Vertical multiplication of trinomials:
[tex]\begin{gathered} \text{ }4x^2-5x+3 \\ \times\text{ }5x^2+3x+2 \\ \text{ ------------} \end{gathered}[/tex]Step 1: Multiply the top trinomial by the last term in the bottom trinomial.
[tex]\begin{gathered} \text{ }4x^2-5x+3 \\ \times\text{ }5x^2+3x+2 \\ \text{ ----------} \\ \text{ }8x^2-10x+6 \end{gathered}[/tex]Step 2: Multiply the top trinomial by the next term:
[tex]\begin{gathered} \text{ }4x^2-5x+3 \\ \times5x^2+3x+2 \\ \text{ -----------} \\ \text{ }8x^2-10x+6 \\ 12x^3-15x^2+9x \end{gathered}[/tex]Step 3: Multiply the top trinomial by the first term:
[tex]\begin{gathered} \text{ }4x^2-5x+3 \\ \times\text{ }5x^2+3x+2 \\ _{\text{ ----------------}} \\ \text{ }8x^2-10x+6 \\ 12x^{3}-15x^{2}+9x \\ 20x^4-25x^3+15x^2 \end{gathered}[/tex]Step 4: Algebraically add the three polynomials:
8x² - 10x + 6
12x³ - 15x² + 9x
20x⁴ - 25x³ + 15x²
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ANSWER
20x⁴ - 13x³ + 8x² - x + 6
