Question

it -4 is a zero of polynomial(rest in figure)​

Answer 1

P(x) = x³ - x² - 14 x + 24

factors of 24 are possible rational roots of P(x), if at all rational roots exist.

so roots are possibly : + 1, 2, 3, 4, 6,8, 12, 24  or -1, -2, -3, -4, -6, -8, -12, -24

check with 1, -1, 2 ..  x = 2 => P(2) = 0

let,   P(x) = (x - 2) [ x² - a x + (24/-2)  ]

then compare coefficients of x² term or x term, then

       

          -a x² - 2 x²  = - 1 x²      =>  a = -1

          2 a x -12 x = - 14 x    =>  a = -1

P(x) =  ( x -2 ) ( x² +x-12) =

       

find factors of -12 that have difference of  -1.  

so  -4 and 3 are roots of x² +x -12

      P(x) = (x - 2 ) ( x + 4 ) ( x - 3)

ZERO OF POLYNOMIAL ARE  +2, -4 AND +3

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Answer 2

(-4) is the zero of the given p(x).

so, (x+4) is the zero of the given p(x) too.

Now,

By dividing p(x) by (x+4)

we get,

$x {}^{2} - 5x + 6 = 0 \\ x {}^{2} - 2x - 3x + 6 = 0 \\ x(x - 2) - 3(x - 2) = 0 \\ (x - 3)(x - 2) = 0 \\ x = 3 \: or \: 2$

so, other zeroes of given p(x) are 3 and 2.

Hope it helps you!!!