To know how to factor quadratic expressions,
Example 1 :
Factor :
x2 + 13x + 30
Solution :
In the given quadratic expression, the coefficient of x2 is 1.
Decompose the constant term +30 into two factors such that the product of the two factors is equal to +30 and the addition of two factors is equal to the coefficient of x, that is +13.
Then, the two factors of +30 are
+3 and +10
Factor the given quadratic expression using +3 and +10.
x2 + 13x +30 = (x + 3)(x + 10)
Therefore, the factors of the given quadratic expression are
(x + 3) and (x + 10)
Example 2 :
Factor :
x2 + 22x + 21
Solution :
In the given quadratic expression, the coefficient of x2 is 1.
Decompose the constant term +21 into two factors such that the product of the two factors is equal to +21 and the addition of two factors is equal to the coefficient of x, that is 22.
Then, the two factors of -21 are
+1 and +21
Factor the given quadratic expression using +1 and +21.
x2 + 22x + 21 = (x + 1)(x + 21)
Therefore, the factors of the given quadratic expression are
(x + 1) and (x + 21)
Example 3 :
Factor :
x2 + 3x – 28
Solution :
In the given quadratic expression, the coefficient of x2 is 1.
Decompose the constant term -28 into two factors such that the product of the two factors is equal to -28 and the addition of two factors is equal to the coefficient of x, that is +3.
Then, the two factors of -28 are
-4 and +7
Factor the given quadratic expression using -4 and +7.
x2 + 3x – 28 = (x - 4)(x + 7)
Therefore, the factors of the given quadratic expression are
(x - 4) and (x + 7)
Example 4 :
Factor :
x2 – x – 30
Solution :
In the given quadratic expression, the coefficient of x2 is 1.
Decompose the constant term -30 into two factors such that the product of the two factors is equal to -30 and the addition of two factors is equal to the coefficient of x, that is -1.
Then, the two factors of -30 are
-6 and +5
Factor the given quadratic expression using -6 and +5.
x2 – x – 30 = (x - 6)(x + 5)
Therefore, the factors of the given quadratic expression are
(x - 6) and (x + 5)
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