Advertisements
Advertisements
Question
Factorize each of the following algebraic expression:
x2 + 14x + 45
Advertisements
Solution
\[\text{ To factorise }x^2 + 14x + 45,\text{ we will find two numbers p and q such that }p + q = 14 \text{ and }pq = 45 . \]
Now,
\[9 + 5 = 14 \]
and
\[9 \times 5 = 45\]
\[\text{ Splitting the middle term }14x\text{ in the given quadratic as }9x + 5x,\text{ we get: }\]
\[ x^2 + 14x + 45 = x^2 + 9x + 5x + 45\]
\[ = ( x^2 + 9x) + (5x + 45)\]
\[ = x(x + 9) + 5(x + 9)\]
\[ = (x + 5)(x + 9)\]
RELATED QUESTIONS
Find the greatest common factor of the terms in each of the following expression:
5a4 + 10a3 − 15a2
Find the greatest common factor of the terms in each of the following expression:
3a2b2 + 4b2c2 + 12a2b2c2
Factorize each of the following algebraic expressions:
a(x − y) + 2b(y − x) + c(x − y)2
Factorize each of the following expressions:
qr − pr + qs − ps
Factorize each of the following algebraic expression:
96 − 4x − x2
Factorize each of the following algebraic expression:
a2 + 4b2 − 4ab − 4c2
Factorize each of the following algebraic expression:
a2 + 3a − 88
Factorize each of the following algebraic expression:
x2 − 4x − 21
Factorize each of the following algebraic expression:
y2 + 5y − 36
Match the following :
| Column A | Column B |
| (a) `x/2` = 10 | (i) x = 4 |
| (b) 20 = 6x − 4 | (ii) x = 1 |
| (c) 2x − 5 = 3 − x | (iii) x = 20 |
| (d) 7x − 4 − 8x = 20 | (iv) x = `8/3` |
| (e) `4/11 - x = (-7)/11` | (v) x = −24 |
