Factorise
1)x² - 11x + 30
2) x² + x - 12
Answers
Since the product is positive , therefore , either both the numbers will be positive or negative .
But the sum is negative , hence , both the numbers will also be negative .
Required factors of 30 are ( - 6 ) and ( - 5 ) .
x² - 11x + 30 = x² + [( - 6 ) + ( - 5 )] x + 30
= x² - 6x - 5x + 30
= x ( x - 6 ) - 5 ( x - 6 )
= ( x - 6 ) ( x - 5 )
2) To find two numbers whose product is ( - 12 ) and sum is '1' .
Since the product is negative , one number will be positive and the other number will be negative .
Since the product is positive , the numerically greater of the two numbers will be positive .
So the required factors are 4 and ( - 3 ) .
x² + x - 12 = x² + [( 4 + ( - 3 )] x - 12
= x² + 4x - 3x - 12
= x ( x + 4 ) - 3 ( x + 4 )
= ( x + 4) ( x - 3 )
Answer:
1) Let us first find two numbers whose product is 30 and sum is ( - 11 ) .
Since the product is positive , therefore , either both the numbers will be positive or negative .
But the sum is negative , hence , both the numbers will also be negative .
Required factors of 30 are ( - 6 ) and ( - 5 ) .
x² - 11x + 30 = x² + [( - 6 ) + ( - 5 )] x + 30
= x² - 6x - 5x + 30
= x ( x - 6 ) - 5 ( x - 6 )
= ( x - 6 ) ( x - 5 )
2) To find two numbers whose product is ( - 12 ) and sum is '1' .
Since the product is negative , one number will be positive and the other number will be negative .
Since the product is positive , the numerically greater of the two numbers will be positive .
So the required factors are 4 and ( - 3 ).
x² + x - 12 = x² + [( 4 + ( - 3 )] x - 12
= x² + 4x - 3x - 12
= x ( x + 4 ) - 3 ( x + 4 )
= ( x + 4) ( x - 3 )