Please help with this question:
Rewrite the middle term as the sum of two terms and then factor completely.
10x2 + 19x + 6
it is for a test...thanks
You forgot to include the algebraic expression that is supposed to be factored
oops forgot sorry, but i have figured this out, however i have another question posted can you or anyone help.?
To rewrite the middle term as the sum of two terms, we need to find two numbers that multiply to the product of the coefficient of the quadratic term (10) and the constant term (6) and add up to the coefficient of the linear term (19).
The product of 10 and 6 is 60. Now, we need to find two numbers that multiply to 60 and add up to 19. By trial and error, we can determine that the numbers 10 and 6 fulfill this condition since 10 * 6 = 60 and 10 + 6 = 16.
Now we can rewrite the middle term, 19x, as the sum of two terms using these numbers:
19x = 10x + 9x
So now our quadratic expression becomes:
10x^2 + 10x + 9x + 6
Next, we can group the terms and factor them by grouping:
(10x^2 + 10x) + (9x + 6)
Now, we can factor out the greatest common factor from each group:
10x(x + 1) + 3(3x + 2)
Finally, we have factored the quadratic expression completely as:
(10x + 3)(x + 1)