x + 2 is not a factor of the polynomial and - 2 is not a root of the function.
The synthetic subdivision of the polynomial is calculated as follows;
if -2 is a root, then x + 2 is a factor of the polynomial.
-3x³ + 6x² - 10x + 17
--------------------------------------
x + 2 √-3x⁴ + 2x² - 3x + 4
- (-3x⁴ - 6x³)
-----------------------------
6x³ + 2x² - 3x + 4
- (6x³ + 12x²)
-----------------------------
-10x² - 3x + 4
- (-10x² - 20x)
----------------------------
17x + 4
- (17x + 34)
-----------------------
-30
The remainder is not equal to zero, thus, x + 2 is not a factor of the polynomial and - 2 is not a root of the function.
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x + 2 is not a factor of the polynomial and - 2 is not a root of the function.
A simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions.
The synthetic subdivision of the polynomial is calculated as follows;
if -2 is a root, then x + 2 is a factor of the polynomial.
-3x³ + 6x² - 10x + 17
--------------------------------------
x + 2 ÷ -3x⁴ + 2x² - 3x + 4
- (-3x⁴ - 6x³)
-----------------------------
6x³ + 2x² - 3x + 4
- (6x³ + 12x²)
-----------------------------
-10x² - 3x + 4
- (-10x² - 20x)
----------------------------
17x + 4
- (17x + 34)
-----------------------
-30
Thus, the remainder is not equal to zero, thus, x + 2 is not a factor of the polynomial and - 2 is not a root of the function.
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