Factoring
Factoring Rules of Quadratic Expressions (No.2)
• Always factor out the common factor first.
ma+mb=m(a+b)…(A)
Examples
(1)2x2+6x+4=2(x2+3x+2)
(2)x2+6x=x(x+6)
(3)3x2−75=3(x2−25)
• Difference of squares
a2−b2=(a+b)(a−b)…(B)
Examples
(1)x2−12=(x+1)(x−1)
(2)x2−4=x2−22=(x+2)(x−2)
(3)x2−9=x2−32=(x+3)(x−3)
Note that this type of polynomial has no x-term.
• Perfect square trinomials
a2+2ab+b2=(a+b)2…(C)
a2−2ab+b2=(a−b)2…(D)
 Examples
(1)x2+2x+1=x2+2·1·x+12=(x+1)2
(2)x2+6x+9=x2+2·3·x+32=(x+3)2
(3)x2−4x+4=x2−2·2·x+22=(x−2)2

(*)x2+3x+9=x2+3·x+32
→The middle term is not written in the form 2ab.
→The polynomial cannot be factored.
• Product and Sum
x2+(a+b)x+ab=(x+a)(x+b)…(E)
[Step 1]
Find all factor pairs whose products are the last term (constant term).
[Step 2]
From the pairs, find the pair whose sum is the coefficient of the middle term (x-term).

[Step 1] → The last term of the trinomial = Product
[Step 2] → The middle term of the trinomial = Sum
 Examples
(1)x2+5x+6
Product 6 6 6 6
Pairs 1 2 -1 -2
6 3 -6 -3
Sum 7 5 -7 -5
Out of the factor pairs whose products are 6, only the sum of 2 and 3 is 5.
2×3=6
2+3=5
The answer is (x+2)(x+3)

(2)x2−3x−10
Product −10 −10 −10 −10
Pairs 1 2 5 10
−10 −5 −2 −1
Sum −9 −3 3 9
Out of the factor pairs whose products are −10, only the sum of 2 and −5 is −3.
2×(−5)=−10
2+(−5)=−3
The answer is (x+2)(x−5)
QuestionFactor the following polynomials.
(Choose a correct answer from the right column.)
[1 / 10]BackNext
Answer
Top menu

JPN Menu→JPN Version