what is the factorization of v(x)=x^3-5x^2+6x

Question

lucaz · Answer

first factor out x:
x(x^2-5x+6), then from Ax^2+Bx+C you need two numbers the product=C and the sum=B

lucaz · Answer

sorry, the product must be equal to A*C

lucaz · Answer

in this case AC=1*6=6, try -3 and -2
-2*-3=6 and -2+(-3)=-5

anonymous · Answer

$$v(x)=x3−5x2+6x$$

Factor out the GCF of x from each term in the polynomial. 

$$v(x)=x(x^2)+x(−5x)+x(6)$$

Factor out the GCF of x from x^3−5x^2+6x.

$$v(x)=x(x^2−5x+6)$$

Rewrite the middle term as a sum of two terms whose product is 1⋅6=6 and whose sum is −5.

$$v(x)=x(x^2−3x−2x+6)$$

Factor the greatest common facto from each group. 

$$v(x)=x(x(x−3)−2(x−3))$$

Factor the polynomial by grouping the first two terms together and finding the greatest common factor. Next, group the second two terms together and find the GCF. Since both groups contain the factor (x−3), they can be combined. 

$$v(x)=x(x−2)(x−3)$$