SOLUTION: For the polynomial below, -1 is a zero. f(x)=x^3 +5x^2 +17x +13 Express f(x) as a product of linear factors. f(x)= ?

Algebra ->  Real-numbers -> SOLUTION: For the polynomial below, -1 is a zero. f(x)=x^3 +5x^2 +17x +13 Express f(x) as a product of linear factors. f(x)= ?      Log On


   

Question 697214: For the polynomial below, -1 is a zero.
f(x)=x^3 +5x^2 +17x +13
Express f(x) as a product of linear factors.
f(x)= ?
Answer by mouk(232) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29=x%5E3+%2B5x%5E2+%2B17x+%2B13+

If x=-1 is a root then +%28x%2B1%29+ is a factor so
+f%28x%29=%28x%2B1%29%28ax%5E2+%2B+bx+%2Bc%29+
By observation we can see the coefficient of +x%5E3+ is 1 so +a+=+1+ so:
+f%28x%29=%28x%2B1%29%28x%5E2+%2B+bx+%2Bc%29+
+f%28x%29=%28x%5E3+%2B+bx%5E2+%2Bcx%29+%2B+%28x%5E2+%2B+bx+%2Bc%29+
+f%28x%29=x%5E3+%2B+%28b%2B1%29x%5E2+%2B+%28c%2Bb%29x+%2B+c+

Comparing coefficients of +x%5E0+ : +c=13+
Comparing coefficients of +x%5E2+ : +b%2B1=5+ so +b=4+
Comparing coefficients of +x%5E1+ : +c%2Bb=17+ and is consistent with above


Hence,
+f%28x%29=%28x%2B1%29%28x%5E2+%2B+4x+%2B+13%29+

This does not factorize further