Math, asked by vershasingh8b, 5 months ago

Square root of trinomial Q 64-176x+121x^2

Answers

Answered by raizajeansilvosa2098
0

Answer:

(11x - 8)2

Step-by-step explanation:

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

(64 - 176x) + 112x2

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 121x2-176x+64

The first term is, 121x2 its coefficient is 121 .

The middle term is, -176x its coefficient is -176 .

The last term, "the constant", is +64

Step-1 : Multiply the coefficient of the first term by the constant 121 • 64 = 7744

Step-2 : Find two factors of 7744 whose sum equals the coefficient of the middle term, which is -176 .

-7744 + -1 = -7745

-3872 + -2 = -3874

-1936 + -4 = -1940

-968 + -8 = -976

-704 + -11 = -715

-484 + -16 = -500

-352 + -22 = -374

-242 + -32 = -274

-176 + -44 = -220

-121 + -64 = -185

-88 + -88 = -176 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -88 and -88

121x2 - 88x - 88x - 64

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

11x • (11x-8)

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

8 • (11x-8)

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

(11x-8) • (11x-8)

Which is the desired factorization

Multiplying Exponential Expressions:

2.2 Multiply (11x-8) by (11x-8)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (11x-8) and the exponents are :

1 , as (11x-8) is the same number as (11x-8)1

and 1 , as (11x-8) is the same number as (11x-8)1

The product is therefore, (11x-8)(1+1) = (11x-8)2

Final result :

(11x - 8)2

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