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Question
Factorize each of the following algebraic expression:
a2 + 2a − 3
Sum
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Solution
\[\text{ To factorise }a^2 + 2a - 3,\text{ we will find two numbers p and q such that }p + q = 2\text{ and }pq = - 3 . \]
Now,
\[3 + ( - 1) = 2 \]
and
\[3 \times ( - 1) = - 3\]
\[\text{ Splitting the middle term 2a in the given quadratic as }- a + 3a,\text{ we get: }\]
\[ a^2 + 2a - 3 = a^2 - a + 3a - 3\]
\[ = ( a^2 - a) + (3a - 3)\]
\[ = a(a - 1) + 3(a - 1)\]
\[ = (a + 3)(a - 1)\]
Now,
\[3 + ( - 1) = 2 \]
and
\[3 \times ( - 1) = - 3\]
\[\text{ Splitting the middle term 2a in the given quadratic as }- a + 3a,\text{ we get: }\]
\[ a^2 + 2a - 3 = a^2 - a + 3a - 3\]
\[ = ( a^2 - a) + (3a - 3)\]
\[ = a(a - 1) + 3(a - 1)\]
\[ = (a + 3)(a - 1)\]
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