The expression 5x² + 18x + 8 can be factored using a systematic approach. To factor a quadratic expression of the form ax² + bx + c, we look for two numbers that multiply to give ac (the product of a and c) and that add up to b.
In this case, we have:
- a = 5
- b = 18
- c = 8
- ac = 5 * 8 = 40
Next, we need to find two numbers that multiply to 40 and add up to 18. Those numbers are 10 and 4, as:
- 10 * 4 = 40
- 10 + 4 = 14
Now we can rewrite the middle term of the expression using 10 and 4:
- 5x² + 10x + 8x + 8
Next, we can group the terms:
- (5x² + 10x) + (8x + 8)
Factoring out the common terms in each group gives us:
- 5x(x + 2) + 4(x + 2)
We can then factor out the common factor (x + 2):
- (x + 2)(5x + 4)
Therefore, the factored form of the expression 5x² + 18x + 8 is:
(x + 2)(5x + 4)
To summarize, 5x² + 18x + 8 can be expressed in its factored form as (x + 2)(5x + 4).