Problem 18 - College Algebra

Question

Find each product. $$(2 x-1)\left(x^{2}-4 x+3\right)$$

Step-by-Step Solution

Answer

The product of \((2x-1)\) and \(\left(x^{2}-4 x+3\right)\) is \(2x^3 -9x^2 + 4x -3\).

Step 1: Apply the FOIL Method

Use the FOIL method (First, Outer, Inner, Last) to multiply these two expressions. For the First elements: \(2x * x^2 = 2x^3\). For the Outer elements: \(2x * -4x = -8x^2\). For the Inner elements: \(-1 * x^2 = -x^2\). For the Last elements: \(-1 * -4x = 4x\) and \(-1 * 3 = -3\)

Step 2: Combine like terms

Now, combine like terms to simplify the resulting expression. The terms -8x^2 and -x^2 combine to -9x^2, and the singular terms 4x and -3 can also be combined.

Step 3: Write the final expression

Write the final simplified expression. From the previous steps, the simplified expression is: \(2x^3 -9x^2 + 4x -3\).