Factor the trinomial:
2, x, squared, plus, 11, x, plus, 14
2x
2
+11x+14
The factored form of the trinomial is:
(2x + 7)(x + 2)
To factor the trinomial 2x^2 + 11x + 14, we need to find two binomials that when multiplied together, give us the given trinomial. To do this, we'll look for two numbers that multiply to give 2 * 14 = 28 and add up to 11 (the coefficient of the middle term).
The pair of numbers that satisfy these conditions is 4 and 7, as 4 * 7 = 28 and 4 + 7 = 11.
Now we can write the trinomial as the sum of two binomials:
2x^2 + 11x + 14 = (2x + 4)(x + 7).
Therefore, the factored form of the trinomial 2x^2 + 11x + 14 is (2x + 4)(x + 7).
To factor the trinomial 2x^2 + 11x + 14, we need to find two binomials that, when multiplied, equal the trinomial.
To do this, we need to find two numbers, let's call them a and b, such that:
- The product of a and b is equal to the product of the coefficient of the x^2 term (which is 2) and the constant term (which is 14). In other words, a*b = 2*14 = 28.
- The sum of a and b is equal to the coefficient of the x term (which is 11). In other words, a + b = 11.
We can now determine the two numbers a and b that satisfy these conditions. By trial and error or by using factoring techniques, we can find that 7 and 4 are the numbers that satisfy these conditions. (7*4 = 28 and 7+4 = 11).
Now we can express the middle term of the trinomial (11x) using these two numbers (7 and 4). We rewrite 11x as 7x + 4x, and the trinomial becomes:
2x^2 + 7x + 4x + 14
Next, we group the terms:
(2x^2 + 7x) + (4x + 14)
Now, we factor out the greatest common factor from each group:
x(2x + 7) + 2(2x + 7)
Notice that we have a common binomial factor of (2x + 7). Now we can factor it out:
(2x + 7)(x + 2)
Therefore, the factored form of the trinomial 2x^2 + 11x + 14 is (2x + 7)(x + 2).