To factor the trinomial \( 5x^2 + 26x + 5 \), we can use the method of factoring by grouping or simply look for two numbers that multiply to the product of the leading coefficient (5) and the constant term (5), which is \( 5 \times 5 = 25 \), and add up to the middle coefficient (26).
-
First, let's find the product and the sum we need:
- Product: \( 25 \)
- Sum: \( 26 \)
-
The two numbers that multiply to \( 25 \) and add to \( 26 \) are \( 25 \) and \( 1 \).
-
Rewrite the middle term \( 26x \) using these two numbers: \[ 5x^2 + 25x + 1x + 5 \]
-
Now, group the terms: \[ (5x^2 + 25x) + (1x + 5) \]
-
Factor out the common factors in each group: \[ 5x(x + 5) + 1(x + 5) \]
-
Now, factor out the common binomial factor \((x + 5)\): \[ (5x + 1)(x + 5) \]
So the factored form of the trinomial \( 5x^2 + 26x + 5 \) is: \[ (5x + 1)(x + 5) \]
1 answer