Math, asked by harrisraj10d, 7 months ago

factries the 4-48+53-636​

Answers

Answered by ayushyadav26112004
2

Answer:

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Answered by jasleen202kaur202
0

Answer:

I surfed and this is all I got

n= -13.250

n= 12

step by step solution:-

STEP

1

:

Equation at the end of step 1

(22n2 + 5n) - 636 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 4n2+5n-636

The first term is, 4n2 its coefficient is 4 .

The middle term is, +5n its coefficient is 5 .

The last term, "the constant", is -636

Step-1 : Multiply the coefficient of the first term by the constant 4 • -636 = -2544

Step-2 : Find two factors of -2544 whose sum equals the coefficient of the middle term, which is 5 .

-2544 + 1 = -2543

-1272 + 2 = -1270

-848 + 3 = -845

-636 + 4 = -632

-424 + 6 = -418

-318 + 8 = -310

-212 + 12 = -200

-159 + 16 = -143

-106 + 24 = -82

-53 + 48 = -5

-48 + 53 = 5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -48 and 53

4n2 - 48n + 53n - 636

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

4n • (n-12)

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

53 • (n-12)

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

(4n+53) • (n-12)

Which is the desired factorization

Equation at the end of step

2

:

(n - 12) • (4n + 53) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : n-12 = 0

Add 12 to both sides of the equation :

n = 12

Solving a Single Variable Equation:

3.3 Solve : 4n+53 = 0

Subtract 53 from both sides of the equation :

4n = -53

Divide both sides of the equation by 4:

n = -53/4 = -13.250

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