Question 698324
Completely factor the polynomial 3x*3+12x*2+3x+12
Factor out a 3
Use ^, Shift 6, for exponents.  * is used for multiply.  
The other tutor saw * as multiply.
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= 3*(x^3 + 4x^2 + x + 4)
Try the factors of 4, = 1, 2 & 4.  Note that all terms are positive, so no negative factors.
f(x) = x^3 + 4x^2 + x + 4
Try x+1.  If it's a factor, then f(-1) will be zero.
f(-1) = -1 + 4 - 1 + 4 <> 0
x+1 doesn't work.
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Try x+2
f(-2) = -8 + 16 - 2 + 4 also <> 0
Try x+4
f(-4) = -64 + 64 - 4 + 4 which is zero.
Divide the polynomial by (x+4)
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= 3(x+4)(x^2+1)
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Factor the trinomial completely x*2+15x+29
That can't be factored.
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Factor the trinomial completely x*2-12x+35
Find 2 factors of 35, both negative, that add to -12.
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Factor the trinomial. X*2-4x-5
Easy one.
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Factor the trinomial completely. Y*3-15y*2+35y
Factor out a y, then look for 2 factors of 35 (both -) that add to -15.
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Factor the trinomial. 4b*2-4b-15
This one has more possibilities, both end terms have more than 1 pair of factors.
It could be (b + p)*(4b + q) or (2b + p)*(2b + q), and the signs of p & q are opposite.
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Factor the trinomial completely. 4x*3+10*2-50x
Step 1, factor out 2x.
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Factor x*3-512
A difference of 2 cubes.
{{{a^3 - b^3 = (a-b)*(a^2 + ab + b^2)}}}
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Solve the equation (x-3)(2x+1)=0
If the product is zero, either
x-3 = 0
or
2x+1 = 0
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Solve and check. 2x*2-7=0
{{{2x^2 = 7}}}
{{{x^2 = 7/2}}}
{{{x = sqrt(7/2) = sqrt(14)/2}}}
Plus and minus.