Problem 125 - Algebra and Trigonometry

Question

Explain how to factor \(3 x^{2}+10 x+8\)

Step-by-Step Solution

Answer

The factored form of \(3x^{2}+10x+8\) is \((3x+4)(x+2)\).

Step 1: Find factors of 24

First, find two numbers that multiply to \(3 * 8 = 24\) and add up to 10. The numbers are 6 and 4.

Step 2: Rewrite middle term

Re-write the original quadratic by splitting the middle term using the numbers found in Step 1. This becomes \(3x^{2} + 6x + 4x + 8\). Note that you haven't modified the equation, just expressed it differently.

Step 3: Group terms and factor

Then break the four-term polynomial into two groups and factor out the Greatest Common Factor (GCF) of each group:\((3x^{2} + 6x) + (4x + 8)\) becomes \(3x(x + 2) + 4(x + 2)\). 'x+2' is a common factor.

Step 4: Complete factoring

Finally, you write the answer as \((x + 2)\) times \((3x + 4)\). So, the factored form of the quadratic equation \(3x^{2}+10x+8\) is \((3x+4)(x+2)\).