Factoring Trinomials Formula
Polynomial expression in the form of
\(\begin{array}{l}ax^{2}+bx+c\end{array} \)
is known as a Trinomial.
\(\begin{array}{l}\large a^{2} + 2ab + b^{2} = (a+b)^{2}\end{array} \)
\(\begin{array}{l}\large a^{2} – 2ab + b^{2} = (a-b)^{2}\end{array} \)
\(\begin{array}{l}\large a^{2} – b^{2} = (a+b)(a-b)\end{array} \)
\(\begin{array}{l}\large a ^{3} + b ^{3} = (a + b) (a ^{2} – a b + b ^{2})\end{array} \)
\(\begin{array}{l}\large a ^{3} – b ^{3} = (a – b) (a ^{2} + a b + b ^{2})\end{array} \)
Solved Examples
Question 1: FactorÂ
\(\begin{array}{l}2 x ^{2} – 5 x – 12\end{array} \)
.
Solution:
\(\begin{array}{l}2 x ^{2} – 5 x – 12\end{array} \)
=
\(\begin{array}{l}2 x^{2} + 3x – 8x – 12\end{array} \)
=
\(\begin{array}{l}x (2x + 3) – 4 (2x + 3)\end{array} \)
=
\(\begin{array}{l}(2x + 3) (x – 4)\end{array} \)
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