Use the expression 3x4 x3 29x2 x 24 to a List all of the

Use the expression 3x^4 - x^3 - 29x^2 + x - 24 to a. List all of the possible zeros of the polynomial b. Write the polynomial as the product of a linear Write the expression in standard form.

Solution

5. given expession 3x⁴-x³-29x²+x-24

a)using rational zeros theorem:

factors of leading coefficient 3 are ±(1,3)

factors of constant -24 are ±(1,2,3,4,6,8,12)

possible zeroes are ±(1,2,3,4,6,8,12)_/±(1,3)

possible zeroes are ±(1,2,3,4,6,8,12 ,1_/3,2_/3,3_/3,4_/3,6_/3,8_/3,12_/3)

possible zeroes are ±(1,2,3,4,6,8,12 ,1_/3,2_/3,4_/3,8_/3)

possible zeroes are ±(1_/3,2_/3,1,4_/3,2,8_/3,3,4,6,8,12 )

(b)

but for any of the above possible zeroes,3x⁴-x³-29x²+x-24 never equals to zero.so there are no rational zeroes for the given expression

so we cannot write expression using linear factors.

by calculator only 2 real zeroes are x=-3.0948,3.3757 , other 2 zeroes are imaginary