Factor the trinomial:
5, x, squared, plus, 21, x, plus, 4
5x
2
+21x+4
The factored form of the trinomial 5x^2 + 21x + 4 is (5x + 1)(x + 4).
To factor the trinomial 5x^2 + 21x + 4, you can use the factoring method.
Step 1: Look for pairs of numbers that multiply to give you 5 * 4 = 20 and add up to 21, which is the coefficient of the middle term (21x). In this case, the numbers are 20 and 1.
Step 2: Rewrite the middle term (21x) using these two numbers.
5x^2 + 20x + x + 4
Step 3: Group the terms into two pairs and factor out the greatest common factor from each pair.
(5x^2 + 20x) + (x + 4)
Step 4: Factor out the greatest common factor from each pair separately.
5x(x + 4) + 1(x + 4)
Step 5: Notice that both terms have a common binomial factor, which is (x + 4).
(x + 4)(5x + 1)
So the factored form of the trinomial 5x^2 + 21x + 4 is (x + 4)(5x + 1).
To factor the trinomial 5x^2 + 21x + 4, follow these steps:
Step 1: Find the product of the coefficients of the first and last terms.
In this case, the product of 5 (coefficient of x^2) and 4 (constant term) is 20.
Step 2: Look for two numbers whose product is equal to the product found in step 1 and whose sum is equal to the coefficient of the middle term (21x). In this case, the numbers are 1 and 20.
Step 3: Rewrite the middle term (21x) using the two numbers found in step 2. Replace 21x with 1x + 20x, maintaining the sign of the middle term. The trinomial becomes:
5x^2 + 1x + 20x + 4.
Step 4: Group the terms in pairs and factor them separately. The trinomial can be rewritten as:
(5x^2 + 1x) + (20x + 4).
Step 5: Factor out the greatest common factor (GCF) from each group. For the first group, the GCF is x, and for the second group, the GCF is 4. Factoring out the GCF, we get:
x(5x + 1) + 4(5x + 1).
Step 6: Notice that both groups now have a common factor, (5x + 1). Factor out this common binomial:
(5x + 1)(x + 4).
Therefore, the factored form of the trinomial 5x^2 + 21x + 4 is (5x + 1)(x + 4).