Factor each trinomial by splitting the middle term.
Example 1 :
(p - q)2 - 6(p - q) - 16
Solution :
= (p - q)2 - 6(p - q) - 16
Let t = p - q
= t2 - 6t - 16
= t2 - 8t + 2t - 16
= t(t - 8) + 2(t - 8)
= (t + 2)(t - 8)
= (p - q + 2)(p - q - 8)
The factors are (p - q + 2) and (p - q - 8).
Example 2 :
m2 + 2mn - 24n2
Solution :
= m2 + 2mn - 24n2
= m2 + 6mn - 4mn - 24n2
= m(m + 6n) - 4n (m + 6n)
= (m - 4n)(m + 6n)
The factors are (m - 4n) and (m + 6n).
Example 3 :
√5 a2 + 2a - 3√5
Solution :
= √5 a2 + 2a - 3√5
√5(3√5) = 15
= √5 a2 + 5a - 3a - 3√5
= √5 a(a + √5) - 3(a + √5)
= (√5a - 3)(a + √5)
The factors are (√5a - 3) and (a + √5).
Example 4 :
a4 - 3a2 + 2
Solution :
= a4 - 3a2 + 2
= (a2)2 - 3a2 + 2
Let t = a2
= t2 - 3t + 2
= t2 - 2t - t + 2
= t(t - 2) - 1(t - 2)
= (t - 1)(t - 2)
Substitute a2 for t.
= (a2 - 1)(a2 - 2)
= (a + 1)(a - 1)(a2 - 2)
The factors are (a + 1), (a - 1) and (a2 - 2).
Example 5 :
8m3 - 2m2n - 15mn2.
Solution :
= 8m3 - 2m2n - 15mn2
= m(8m2 - 2mn - 15n2)
= m(8m2 - 12mn + 10mn - 15n2)
= m[4m(2m - 3n) + 5n(2m - 3n)]
= m(4m + 5n)(2m - 3n)
The factors are m, (4m + 5n) and (2m - 3n).
Example 6 :
(1/x2) + (1/y2) + (2/xy)
Solution :
= (1/x2) + (1/y2) + (2/xy)
= (1/x)2 + (1/y)2 + 2(1/x) (1/y)
= [(1/x) + (1/y)]2
= (1/x + 1/y)(1/x + 1/y)
The factors are (1/x + 1/y) and (1/x + 1/y).
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Jul 27, 24 04:58 AM
Jul 27, 24 04:44 AM
Jul 27, 24 04:15 AM