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
Factorize each of the following algebraic expressions:
9a(6a − 5b) −12a2(6a − 5b)
Factorize each of the following algebraic expressions:
16(2l − 3m)2 −12(3m − 2l)
Factorize each of the following algebraic expression:
16 − a6 + 4a3b3 − 4b6
Factorize each of the following algebraic expression:
96 − 4x − x2
Factorize each of the following algebraic expression:
4x4 + y4
Factorize each of the following algebraic expression:
25x2 − 10x + 1 − 36y2
Factorize each of the following algebraic expression:
49 − x2 − y2 + 2xy
Factorize each of the following algebraic expression:
x2 + 12x − 45
Factorise the following expression and write in the product form.
24a2b2
Factorise the following expression.
p2 − q2
