Factor the polynomial:
2x^2+18x+14
How do you do it?
can SOMEONE HELP ME!!
2x^2+18x+14
2(x^2+9x+7)
This does not factor. There are no factors of 7 that add to 9.
Use the Quadratic Theorem if you want to find the roots, but is does not factor using integers.
Since the roots are (-9±√53)/2 It factors as
2(x-(-9-√53)/2)(x-(-9+√53)/2)
To factor the given polynomial 2x^2 + 18x + 14, you need to follow these steps:
Step 1: Look for a common factor, if any
The given polynomial does not have a common factor greater than 1.
Step 2: Check if it can be factored using grouping
You can try grouping the terms, but it won't work in this case.
Step 3: Use the factoring pattern for quadratic trinomials
Since the coefficient of the x^2 term is 2, you need to factor it using the "ac" method. Multiply the coefficient of the x^2 term (2) by the constant term (14): 2 * 14 = 28.
Step 4: Find two numbers whose product is 28 and whose sum is the coefficient of the x term (18). In this case, the numbers are 4 and 7, since 4 * 7 = 28 and 4 + 7 = 11.
Step 5: Write the quadratic trinomial as the sum of the two numbers from step 4, replacing the middle term:
2x^2 + 4x + 7x + 14
Step 6: Group the terms and factor them separately:
(2x^2 + 4x) + (7x + 14)
2x(x + 2) + 7(x + 2)
Step 7: Factor out the common binomial term:
(x + 2)(2x + 7)
Therefore, the factored form of the polynomial 2x^2 + 18x + 14 is (x + 2)(2x + 7).