Question

using factor thorem, factorize each of the following ploynomials


(1) x cube -6xsquare + 3x +10
(2) 2Y cube -5y square - 19y + 42​

Answer 1

Answer:

x³-6x²+3x+10

Let f(x) = x³ - 6x²+3x+10

Puting x = 2, f(2) = 2³ - 6×2²+3×2+10 = 8-24+6+10 = 0

So, (x-2) is a factor. Comparing (x-2) with (x-a), a=2

Using synthetic division,

2     x³    x²      x      x°

      1       -6     3      10

      0      2       -8     -10

       1       -4      -5     0 = Remainder

      x²       x        x°

So, f(x) = (x-2)(x²-4x-5) = (x-2)(x² - 5x +x-5) =(x-2)[x(x-5)+1(x-5)] =(x-2)(x-5)(x+1)

Step-by-step explanation:

Do 2 no. in same process

Answer 2

X3 - 6x2 + 3x + 10

2 is the zero of polynomial

Therefore X-2 is the factor of polynomial

divide polynomial by X-2

we get X2 - 4X - 5

X2 - 5X + X - 5

X(X-5)+1(X-5)

(X+1)(X-5)

X3 - 6X2 + 3X + 10 = (X+1)(X-5)(X-2)