Advertisements
Advertisements
Question
Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 − 14a − 51
Sum
Advertisements
Solution
\[a^2 - 14a - 51\]
\[ = a^2 - 14a + \left( \frac{14}{2} \right)^2 - \left( \frac{14}{2} \right)^2 - 51 [\text{ Adding and subtracting }\left( \frac{14}{2} \right)^2 ,\text{ that is }, 7^2 ]\]
\[ = a^2 - 14a + 7^2 - 7^2 - 51\]
\[ = (a - 7 )^2 - 100 [\text{ Completing the square }]\]
\[ = (a - 7 )^2 - {10}^2 \]
\[ = [(a - 7) - 10][(a - 7) + 10]\]
\[ = (a - 7 - 10)(a - 7 + 10)\]
\[ = (a - 17)(a + 3)\]
\[ = a^2 - 14a + \left( \frac{14}{2} \right)^2 - \left( \frac{14}{2} \right)^2 - 51 [\text{ Adding and subtracting }\left( \frac{14}{2} \right)^2 ,\text{ that is }, 7^2 ]\]
\[ = a^2 - 14a + 7^2 - 7^2 - 51\]
\[ = (a - 7 )^2 - 100 [\text{ Completing the square }]\]
\[ = (a - 7 )^2 - {10}^2 \]
\[ = [(a - 7) - 10][(a - 7) + 10]\]
\[ = (a - 7 - 10)(a - 7 + 10)\]
\[ = (a - 17)(a + 3)\]
shaalaa.com
Is there an error in this question or solution?
RELATED QUESTIONS
Factorize each of the following expression:
(x + 2y)2 − 4(2x − y)2
Factorize each of the following expression:
3a5 − 48a3
Factorize each of the following expression:
(x - 4y)2 − 625
Factorize each of the following expression:
75a3b2 - 108ab4
Factorize each of the following expression:
x − y − x2 + y2
Factorize each of the following expression:
16(2x − 1)2 − 25y2
Factorize each of the following expression:
18a2x2 − 32
Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 + 2a − 3
Factorize each of the following quadratic polynomials by using the method of completing the square:
4x2 − 12x + 5
Find the factors of y2 – 7y + 12.
