SOLUTION: I am having trouble factoring trinomials. Can you help me with the following problems:1. 2a^2-a-15;2.30c^2+19c-63:3.20c^2-13c-15;5c^2+18c-35. I have been working on them for two da

Algebra ->  Equations -> SOLUTION: I am having trouble factoring trinomials. Can you help me with the following problems:1. 2a^2-a-15;2.30c^2+19c-63:3.20c^2-13c-15;5c^2+18c-35. I have been working on them for two da      Log On


   

Question 317455: I am having trouble factoring trinomials. Can you help me with the following problems:1. 2a^2-a-15;2.30c^2+19c-63:3.20c^2-13c-15;5c^2+18c-35. I have been working on them for two days and can not get them factored out completely, I get so far and still get the wrong answers.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
2a^2-a-15
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aa%5E2%2Bba%2Bc=0 (in our case 2a%5E2%2B-1a%2B-15+=+0) has the following solutons:

a%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A2%2A-15=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+121+%29%29%2F2%5Ca.

a%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+121+%29%29%2F2%5C2+=+3
a%5B2%5D+=+%28-%28-1%29-sqrt%28+121+%29%29%2F2%5C2+=+-2.5

Quadratic expression 2a%5E2%2B-1a%2B-15 can be factored:
2a%5E2%2B-1a%2B-15+=+2%28a-3%29%2A%28a--2.5%29
Again, the answer is: 3, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-15+%29

2.30c^2+19c-63
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ac%5E2%2Bbc%2Bc=0 (in our case 2.3c%5E2%2B19c%2B-63+=+0) has the following solutons:

c%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2819%29%5E2-4%2A2.3%2A-63=940.6.

Discriminant d=940.6 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-19%2B-sqrt%28+940.6+%29%29%2F2%5Ca.

c%5B1%5D+=+%28-%2819%29%2Bsqrt%28+940.6+%29%29%2F2%5C2.3+=+2.53678321601785
c%5B2%5D+=+%28-%2819%29-sqrt%28+940.6+%29%29%2F2%5C2.3+=+-10.7976527812352

Quadratic expression 2.3c%5E2%2B19c%2B-63 can be factored:
2.3c%5E2%2B19c%2B-63+=+2.3%28c-2.53678321601785%29%2A%28c--10.7976527812352%29
Again, the answer is: 2.53678321601785, -10.7976527812352. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2.3%2Ax%5E2%2B19%2Ax%2B-63+%29

3.20c^2-13c-15
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ac%5E2%2Bbc%2Bc=0 (in our case 3.2c%5E2%2B-13c%2B-15+=+0) has the following solutons:

c%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-13%29%5E2-4%2A3.2%2A-15=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+361+%29%29%2F2%5Ca.

c%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+361+%29%29%2F2%5C3.2+=+5
c%5B2%5D+=+%28-%28-13%29-sqrt%28+361+%29%29%2F2%5C3.2+=+-0.9375

Quadratic expression 3.2c%5E2%2B-13c%2B-15 can be factored:
3.2c%5E2%2B-13c%2B-15+=+3.2%28c-5%29%2A%28c--0.9375%29
Again, the answer is: 5, -0.9375. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3.2%2Ax%5E2%2B-13%2Ax%2B-15+%29

5c^2+18c-35
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ac%5E2%2Bbc%2Bc=0 (in our case 5c%5E2%2B18c%2B-35+=+0) has the following solutons:

c%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2818%29%5E2-4%2A5%2A-35=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+1024+%29%29%2F2%5Ca.

c%5B1%5D+=+%28-%2818%29%2Bsqrt%28+1024+%29%29%2F2%5C5+=+1.4
c%5B2%5D+=+%28-%2818%29-sqrt%28+1024+%29%29%2F2%5C5+=+-5

Quadratic expression 5c%5E2%2B18c%2B-35 can be factored:
5c%5E2%2B18c%2B-35+=+5%28c-1.4%29%2A%28c--5%29
Again, the answer is: 1.4, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B18%2Ax%2B-35+%29