Question

factorize x^4+10x^3+35x^2+50x+24

Answer 1

u have to just go on factorising nothing else

Answer 2

Answer:

Factors of p(x) are ( x - 1 ) ( x - 2 )( x - 3 )( x - 4 )

Step-by-step explanation:

Given Expression: $x^4+10x^3+35x^2+50x+24$

let p(x) = $x^4+10x^3+35x^2+50x+24$

If a polynomial function has integer coefficients, then every rational zero will have the form  

$\frac{p}{q}$   where  p  is a factor of the constant and  q  is a factor of the leading coefficient.

p  =  ±1  ,  ±2 , ±3 , ±4 , ±6 , ±8  , ±12 , ±24

q  = ±1

Find every combination of  $\pm\frac{p}{q}$.

These are the possible roots of the polynomial function.

±1 , ±2 , ±3 , ±4 , ±6 , ±8 , ±12  , ±24

So, by hint and trail,

for x = 4  we get p(4) = 0

So ( x - 4 ) is factor of p(x).

Now by dividing p(x) by (x - 4) we get

Quotient, q(x)= x³  −  6x²  +  11x  −  6

Again by hint and trial

for q = 3 we get q(3) = 0

Thus, Another factor is ( x - 3 )

Again diving q(x) with x - 3  we get

Quotient = x²  −  3x  +  2

Factorizing x²  −  3x  +  2 by middle term split we get,

x²  −  3x  +  2 = x² - 2x - x + 2 = x ( x - 2 ) - ( x - 2 )

= ( x -2 ) ( x - 1 )

Therefore, Factors of p(x) are ( x - 1 ) ( x - 2 )( x - 3 )( x - 4 )