Mister Exam
Factor polynomial y^2-x*y-5*y+x+4
The solution
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2 y - x*y - 5*y + x + 4
$$\left(x + \left(- 5 y + \left(- x y + y^{2}\right)\right)\right) + 4$$
y^2 - x*y - 5*y + x + 4
Factorization
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(x + 4 - y)*(y - 1)
$$\left(x + \left(4 - y\right)\right) \left(y - 1\right)$$
(x + 4 - y)*(y - 1)
General simplification
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2 4 + x + y - 5*y - x*y
$$- x y + x + y^{2} - 5 y + 4$$
4 + x + y^2 - 5*y - x*y
Combining rational expressions
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4 + x + y*(-5 + y - x)
$$x + y \left(- x + y - 5\right) + 4$$
4 + x + y*(-5 + y - x)
Common denominator
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2 4 + x + y - 5*y - x*y
$$- x y + x + y^{2} - 5 y + 4$$
4 + x + y^2 - 5*y - x*y
Combinatorics
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-(-1 + y)*(4 + x - y)
$$- \left(y - 1\right) \left(x - y + 4\right)$$
-(-1 + y)*(4 + x - y)
Rational denominator
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2 4 + x + y - 5*y - x*y
$$- x y + x + y^{2} - 5 y + 4$$
4 + x + y^2 - 5*y - x*y
Assemble expression
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2 4 + x + y - 5*y - x*y
$$- x y + x + y^{2} - 5 y + 4$$
2 4 + x + y + y*(-5 - x)
$$x + y^{2} + y \left(- x - 5\right) + 4$$
2 4 + y - 5*y + x*(1 - y)
$$x \left(1 - y\right) + y^{2} - 5 y + 4$$
4 + y^2 - 5*y + x*(1 - y)
Trigonometric part
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2 4 + x + y - 5*y - x*y
$$- x y + x + y^{2} - 5 y + 4$$
4 + x + y^2 - 5*y - x*y