Divide the following also write the quotient and the remainder:
x² + 7x + 12 by x – 3
Answers
Answer: x+4 is the remainder
Given,
x² + 7x + 12
(x+ 3)(x+ 4)=0
By factorizing numerator, we get the solution (x+3)(x+4)
divide (x+3)(x+4)/(x+3)=x+4
x+4 is the remainder
Step-by-step explanation:
Let us first factorize the numerator of the given
x^2+7x+12
1) Make the skeleton(x )(x )=0
2) Add the signs
(i)if all the terms are positive:(x+ )(x+ )=0
(ii)if the center term is negative:(x- )(x- )=0
(iii)if the last term is negative(x+ )(x- )=0
(iv)if both the middle term and last term is negative(x+ )(x- )=0
3)Find the factors for last term should equal the middle term
4)Check work with FOIL method
As mentioned above step:
1)Make a skelton
(x )(x )=0
2)(i)if all the terms are positive:
(x+ )(x+ )=0
3)Now, Find the factors for last term should equal the middle term
12 factors are=1 x 12 and 3 x 4
So,(x+ 3)(x+ 4)=0
(x+3)(x+4)=0
x^2+4x+3x+12=0
x^2+7x+12=0
By factorizing we get the solution (x+3)(x+4)
Now, we will divide (x+3)(x+4)/(x+3)=x+4
x+4 is the remainder