SOLUTION: find the factors of poly nomial equation of degree greater than 2 A.Give the factored form of the polynomial equations 1.X^3+2x^2-23x-60=0 B.x^5-5x^4-3x^3+15x^2-4x+20=0, given t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the factors of poly nomial equation of degree greater than 2 A.Give the factored form of the polynomial equations 1.X^3+2x^2-23x-60=0 B.x^5-5x^4-3x^3+15x^2-4x+20=0, given t      Log On


   

Question 1170428: find the factors of poly nomial equation of degree greater than 2
A.Give the factored form of the polynomial equations
1.X^3+2x^2-23x-60=0
B.x^5-5x^4-3x^3+15x^2-4x+20=0, given that one root is 2
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A.Give the factored form of the polynomial equations
x%5E3%2B2x%5E2-23x-60=0
x%5E3+%2B+7x%5E2%2B+12x-5x%5E2-35x-60+=+0
%28+x%5E3-5x%5E2%29+%2B+%287x%5E2-35x%29%2B+%2812x-60%29+=+0
x%5E2%28+x-5%29+%2B+7x%28x-5%29%2B+12%28x-5%29+=+0
+%28x+-+5%29+%28x%5E2+%2B+7x%2B+12%29+=+0
%28x+-+5%29+%28x%5E2+%2B+4x+%2B3x%2B+12%29+=+0
%28x+-+5%29+%28%28x%5E2+%2B+4x%29+%2B%283x%2B+12%29%29+=+0
%28x+-+5%29+%28x%28x+%2B+4%29+%2B3%28x%2B+4%29%29+=+0
%28x+-+5%29+%28x+%2B+3%29+%28x+%2B+4%29+=+0


B. x%5E5-5x%5E4-3x%5E3%2B15x%5E2-4x%2B20=0, given that one root is 2; since given root, first group to factor out x-2

x%5E5-5x%5E4-3x%5E3%2B15x%5E2-4x%2B20=0
x%5E5-3x%5E4++-9x%5E3++-+3x%5E2-10x++-+2x%5E4%2B6x%5E3%2B18x%5E2%2B6x+%2B20++=0

x%5E4%28x+-+2%29++-3x%5E3%28x++-2%29-9x%5E2%28x+-2%29+-3x+%28x-2%29+-10%28x-2%29++++++=0
%28x+-+2%29+%28x%5E4+-+3x%5E3+-+9x%5E2+-+3x+-+10%29+=+0
%28x+-+2%29+%28x%5E4+%2B2x%5E3-+5x%5E3%2Bx%5E2+-+10x%5E2%2B2x+-+5x+-+10%29+=+0

%28x+-+2%29+%28x%5E3%28x+-+5%29%2B2x%5E2%28x+-+5%29%2Bx%28x+-+5%29%2B2%28x+-+5%29%29+=+0
%28x+-+2%29+%28x+-+5%29%28x%5E3+%2B+2+x%5E2+%2B+x+%2B+2%29+=+0
%28x+-+2%29+%28x+-+5%29%28%28x%5E3+%2B+2+x%5E2%29+%2B+%28x+%2B+2%29%29+=+0
%28x+-+2%29+%28x+-+5%29%28x%5E2%28x+%2B+2+%29+%2B+%28x+%2B+2%29%29+=+0
%28x+-+2%29+%28x+-+5%29%28x+%2B+2%29+%28x%5E2+%2B+1%29+=+0

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

find the factors of poly nomial equation of degree greater than 2
A.Give the factored form of the polynomial equations
1.X^3+2x^2-23x-60=0
B.x^5-5x^4-3x^3+15x^2-4x+20=0, given that one root is 2
Use the RATIONAL ROOT THEOREM, and you'll find that - 3 is a zero, and so, x + 3 is a factor. From there, you can continue with the RATIOANL ROOT THEOREM, 
and you'll find that the other zeroes are - 4 and 5, thus making the factors, x + 4 and x - 5. This gives you the factors: (x + 3)(x + 4)(x - 5).

OR

Finding the first zero (- 3), you can then use SYNTHETIC DIVISION, over and over, to find the other factors!

OR

Finding the first zero (- 3), you can then use POLYNOMIAL LONG DIVISION, over and over, to find the other factors!