Question

Use the vertical method to multiply two trinomials. Step 1: Multiply the top trinomial by the last term in the bottom trinomial. Place each result in the blank spaces provided.

Answer 1

Vertical multiplication of trinomials:

`\begin{gathered} \text{ }4x^2-5x+3 \\ *\text{ }5x^2+3x+2 \\ \text{ ------------} \end{gathered}`

Step 1: Multiply the top trinomial by the last term in the bottom trinomial.

`\begin{gathered} \text{ }4x^2-5x+3 \\ *\text{ }5x^2+3x+2 \\ \text{ ----------} \\ \text{ }8x^2-10x+6 \end{gathered}`

Step 2: Multiply the top trinomial by the next term:

`\begin{gathered} \text{ }4x^2-5x+3 \\ *5x^2+3x+2 \\ \text{ -----------} \\ \text{ }8x^2-10x+6 \\ 12x^3-15x^2+9x \end{gathered}`

Step 3: Multiply the top trinomial by the first term:

`\begin{gathered} \text{ }4x^2-5x+3 \\ *\text{ }5x^2+3x+2 \\ _{\text{ ----------------}} \\ \text{ }8x^2-10x+6 \\ 12x^(3)-15x^(2)+9x \\ 20x^4-25x^3+15x^2 \end{gathered}`

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