Question

Using the factor theorem, factorise x^4-10x^3+35x^2-50x+24
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Answer 1

hola mate....

step-by-step explanation:

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

4

+10x

3

+35x

2

+50x+24

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

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}

q

p

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}±

q

p

.

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 )

hope it helpful for u