One root of f(x)=x^3-4x^2-20x+48 is x = 6. What are all the factors of the function? Use the Remainder Theorem.

Mathematics

2 answers:

Shalnov [3]4 years ago

8 0

the correct answer is C

kkurt [141]4 years ago

4 0

If one root is x = 6, then this polynomial is divisible by: x - 6.
( x³ - 4 x² - 20 x + 48 ) : ( x - 6 ) = x² + 2 x - 8
- x³ + 6x²
---------------
   2 x² - 20 x
      -2x² + 12 x
   -----------------
   - 8 x + 48
   8 x - 48
   --------------------
After that : x²+ 2 x - 8 = x² + 4 x - 2 x - 8 = x * ( x + 4 ) - 2 * ( x + 4 ) =
= ( x + 4 ) ( x - 2 )
Answer: C ) ( x - 2 ) ( x + 4 ) ( x - 6 )

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You just need to put the given value of x-input in function f(x)=2x²+6x-8 to get y-output

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What is the product? (2 x minus 1)(x 4) 2 x squared minus 4 2 x squared 4 2 x squared 7 x minus 4 2 x squared minus 7 x minus 4

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<h3>What is a quadratic equation?</h3>

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The given expression is

$(2x - 1)(x +4)$