Questions: Calculate [ (x^2-4 x+2)(3 x-5) ]

Calculate [ (x^2-4 x+2)(3 x-5) ]
Transcript text: Calculate \[ \left(x^{2}-4 x+2\right)(3 x-5) \]
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Solution

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Solution Steps

To solve the given expression \((x^2 - 4x + 2)(3x - 5)\), we need to use the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms.

Step 1: Expand the Expression

We start with the expression \((x^2 - 4x + 2)(3x - 5)\). Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial.

Step 2: Combine Like Terms

After performing the multiplication, we obtain the following expression: \[ 3x^3 - 17x^2 + 26x - 10 \] This is achieved by combining like terms from the expansion.

Final Answer

The expanded form of the expression is \[ \boxed{3x^3 - 17x^2 + 26x - 10} \]

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