Question

factorize the following algebraic expressions. x²+10x+21​

Answer 1

$\huge\mathfrak\pink{Answér}$

x²+10x +21

Using splitting the middle term,

= x²+7x +3x +21

= x(x+7) +3(x+7)

= (x+3) (x+7)

Hence the two factors are: x+3 and x+7..

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Answer 2

Answer: (x+ 3)(x+ 7)  is the solution

(x+ 3)(x+ 7) = x²+10x+21​

Step-by-step explanation:

1) Make the skelton(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

Solution:

As mentioned above step:

1)Make a skeleton

(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

21 factors are=1 x 21  and 3 x 7

So,(x+ 3)(x+7)=0

(x+ 3)(x+ 7)

Hence we factorize the x²+10x+21​ and get solution (x+ 3)(x+ 7)