Questions: Factor. 14x^3-7x^2+10x-5

Transcript text: Factor. \[ 14 x^{3}-7 x^{2}+10 x-5 \]

Solution

Solution Steps

To factor the polynomial \(14x^3 - 7x^2 + 10x - 5\), we can use the method of grouping. We will group the terms in pairs and factor out the common factors from each pair. Then, we will check if the resulting expression can be factored further.

Step 1: Identify the Polynomial

We start with the polynomial: \[ 14x^3 - 7x^2 + 10x - 5 \]

Step 2: Factor by Grouping

We can factor the polynomial by grouping the terms. We group the first two terms and the last two terms: \[ (14x^3 - 7x^2) + (10x - 5) \] Factoring out the common factors from each group gives us: \[ 7x^2(2x - 1) + 5(2x - 1) \]

Step 3: Factor Out the Common Binomial

Now, we can factor out the common binomial \((2x - 1)\): \[ (2x - 1)(7x^2 + 5) \]