Solve Polynomialrootcalculator 3x^3-2x^2-15x-10 Tiger Algebra ...

Trang chủ » G X 3x 3 2x 2 15x 10 » Solve Polynomialrootcalculator 3x^3-2x^2-15x-10 Tiger Algebra ...

Có thể bạn quan tâm

Step 1 :

Equation at the end of step 1 :

(((3 • (x3)) - 2x2) - 15x) - 10

Step 2 :

Equation at the end of step 2 :

((3x3 - 2x2) - 15x) - 10

Step 3 :

Checking for a perfect cube :

3.1 3x3-2x2-15x-10 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 3x3-2x2-15x-10 Thoughtfully split the expression at hand into groups, each group having two terms :Group 1: -15x-10 Group 2: 3x3-2x2 Pull out from each group separately :Group 1: (3x+2) • (-5)Group 2: (3x-2) • (x2)Bad news !! Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(x) = 3x3-2x2-15x-10Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 3 and the Trailing Constant is -10. The factor(s) are: of the Leading Coefficient : 1,3 of the Trailing Constant : 1 ,2 ,5 ,10 Let us test ....

PQP/QF(P/Q)Divisor
-1 1 -1.00 0.00 x+1
-1 3 -0.33 -5.33
-2 1 -2.00 -12.00
-2 3 -0.67 -1.78
-5 1 -5.00 -360.00
-5 3 -1.67 -4.44
-10 1 -10.00 -3060.00
-10 3 -3.33 -93.33
1 1 1.00 -24.00
1 3 0.33 -15.11
2 1 2.00 -24.00
2 3 0.67 -20.00
5 1 5.00 240.00
5 3 1.67 -26.67
10 1 10.00 2640.00
10 3 3.33 28.89

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms In our case this means that 3x3-2x2-15x-10 can be divided with x+1

Polynomial Long Division :

3.4 Polynomial Long Division Dividing : 3x3-2x2-15x-10 ("Dividend") By : x+1 ("Divisor")

dividend 3x3 - 2x2 - 15x - 10
- divisor * 3x2 3x3 + 3x2
remainder- 5x2 - 15x - 10
- divisor * -5x1 - 5x2 - 5x
remainder- 10x - 10
- divisor * -10x0 - 10x - 10
remainder0

Quotient : 3x2-5x-10 Remainder: 0

Trying to factor by splitting the middle term

3.5 Factoring 3x2-5x-10 The first term is, 3x2 its coefficient is 3 .The middle term is, -5x its coefficient is -5 .The last term, "the constant", is -10 Step-1 : Multiply the coefficient of the first term by the constant 3 • -10 = -30 Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -5 .

-30 + 1 = -29
-15 + 2 = -13
-10 + 3 = -7
-6 + 5 = -1
-5 + 6 = 1
-3 + 10 = 7
-2 + 15 = 13
-1 + 30 = 29

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Final result :

(3x2 - 5x - 10) • (x + 1)

Từ khóa » G X 3x 3 2x 2 15x 10