Rewrite the middle term as the sum of two terms and then factor completely.
25x^2+35x+12
Is the following true or false?
x^2+2x-3=(x+1)(x-3)
Can you show me how to do these two problems?
Thank you for any help you can give me.
If the middle is the sume of 20 x and 15 x ...
25x^2+35x+12
25x^2+20x + 15x+12
5x(5x + 4) + 3(5x+4)
(5x+3)(5x+4)...
does -3 and 1 add to +2?
If the middle is the sume of 20 x and 15 x ...
25x^2+35x+12
25x^2+20x + 15x+12
5x(5x + 4) + 3(5x+4)
(5x+3)(5x+4)...
does -3 and 1 add to +2?
To rewrite the middle term as the sum of two terms and then factor completely:
Consider the quadratic polynomial: 25x^2+35x+12.
Step 1: Find two numbers that multiply to give the product of the coefficient of the squared term (25) and the constant term (12), which is 25*12=300. The numbers that satisfy this criteria are 20 and 15.
Step 2: Rewrite the middle term (35x) as the sum of these two numbers. Replace 35x with 20x+15x.
The polynomial now becomes: 25x^2+20x+15x+12.
Step 3: Group the terms and factor by grouping. Group the first two terms together and the last two terms together:
(25x^2+20x) + (15x+12).
Now factor out the greatest common factor from each group:
5x(5x+4) + 3(5x+4).
Step 4: Notice that both groups have a common factor, which is (5x+4). Factor out this common factor:
(5x+4)(5x+3).
Therefore, the factored form of 25x^2+35x+12 is (5x+4)(5x+3).
To determine if the statement x^2+2x-3=(x+1)(x-3) is true or false:
Let's expand the right side of the equation to see if it matches the left side:
(x+1)(x-3) = x(x) + x(-3) + 1(x) + 1(-3) = x^2 - 3x + x - 3 = x^2 - 2x - 3.
Comparing the expanded right side (x^2 - 2x - 3) with the left side (x^2 + 2x - 3), we can see that they are not equivalent. Therefore, the statement is false.
To summarize the steps:
1. Multiply the factors to expand the right side of the equation.
2. Compare the expanded right side with the left side of the equation.
3. If they are equal, the statement is true. If they are not equal, the statement is false.
Hope this helps! Let me know if you have any further questions.