Question

${x }^{2} + 16x + 28$
by middle term splitting​

Answer 1

Answer:

Step-by-step explanation:

The first term is, x2 its coefficient is 1 .

The middle term is, -16x its coefficient is -16 .

The last term, "the constant", is +28

: Multiply the coefficient of the first term by the constant 1 • 28 = 28

Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is -16 .

-28 + -1 = -29

-14 + -2 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and -2

x2 - 14x - 2x - 28

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-14)

Add up the last 2 terms, pulling out common factors :

2 • (x-14)

Step-5 : Add up the four terms of step 4 :

(x-2) • (x-14)

Which is the desired factorization

Than x=2,14

Answer 2

To factorize : $x^{2} + 16x + 28$

Solution :

• According to question we are asked to split the given expression by splitting the middle term.

• We spilt the middle term such that product of the numbers is last term and sum or difference of those numbers is middle term.

• Here, $16$ is the middle term and $28$ is the last term.
• $x^{2} + 16x + 28$

       $=x^{2} + 14x + 2x + 28 \\= x(x+ 14) + 2 ( x + 14 ) \\= ( x + 2 )(x + 14 )$

• Therefore , $x = -2$ or $x = -14$

Hence, on splitting the middle term of $x^{2} + 16x + 28$ we get value of $x$ as $x = -2$ or $x = -14$ .