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The general expression for a quadratic polynomial is: ax2 + bx + c
Comparing x2 - 4x - 45 with general expression we get
a = 1, b = -4 and c = -45
Multiplying a and c: ac = -45
Now break down b in two numbers in such a way that sum of the numbers is -4 and product is equal to -45, product of a and c.
The two numbers are -9 and 5. Since sum of -9 and 5 is -4 and the product is -45.
So in place of -4x we can write -9x + 5x.
The expression now becomes: x2 - 9x + 5x - 45
x(x - 9) + 5(x - 9)
(x + 5)(x - 9)
So factors are (x + 5) and (x - 9).
Note: The middle term is split into two terms so that there are in total four terms in the expression and the product of extreme terms is equal to product of middle terms.
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