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