Answer:
a. (x+5)(x-5)
b. 3(x+1)(x-5)
c. (x^2+3)(x+2)
Step-by-step explanation:
a. x^2-25
The given expression can be factorized using the formula:
b. 3x^2-12x-15
We can see that 3 is common in all terms
=3(x^2-4x-5)
In order to make factors, the constant will be multiplied by the co-efficient of highest degree variable
So,
![3[x^{2} -4x-5]\\=3[x^{2}-5x+x-5]\\=3[x(x-5)+1(x-5)]\\=3(x+1)(x-5)](https://tex.z-dn.net/?f=3%5Bx%5E%7B2%7D%20-4x-5%5D%5C%5C%3D3%5Bx%5E%7B2%7D-5x%2Bx-5%5D%5C%5C%3D3%5Bx%28x-5%29%2B1%28x-5%29%5D%5C%5C%3D3%28x%2B1%29%28x-5%29)
c. x^3+2x^2+3x+6
Combining the first and second pair of terms
![x^{3}+2x^{2}+3x+6 \\=[x^{3}+2x^{2}]+[3x+6]\\Taking\ x^{2}\ common\ from\ first\ two\ terms\\=x^{2} (x+2)+3(x+2)\\=(x^{2}+3)(x+2)](https://tex.z-dn.net/?f=x%5E%7B3%7D%2B2x%5E%7B2%7D%2B3x%2B6%20%5C%5C%3D%5Bx%5E%7B3%7D%2B2x%5E%7B2%7D%5D%2B%5B3x%2B6%5D%5C%5CTaking%5C%20x%5E%7B2%7D%5C%20common%5C%20from%5C%20first%5C%20two%5C%20terms%5C%5C%3Dx%5E%7B2%7D%20%28x%2B2%29%2B3%28x%2B2%29%5C%5C%3D%28x%5E%7B2%7D%2B3%29%28x%2B2%29)
Answer:
I really don't know this one but I have a feeling it os option c
Here is some pro tips, I take algebra 1, and I’m in middle school too.
x * x = x^2
If you see anything like (x + 5)(x - 5), solve using FOIL, (front, outer, inner, last), it’s basically the distributive property for four numbers and x’es.
Distributive property is a must know.
And also, if you are feeling nervous, remember, even if you fail the leap test, it doesn’t make you less of a intelligent, kind, and caring person.
