Question

20 POINTS PLEASE HELP MEEEE

Answer 1

its actually 10 points

x^4 + 9x^3 + 15x^2 + 9x + 14

 

Split  15x^2  into  14x^2  +  x^2

 

x^4 + 9x^3 + 14x^2 + x^2 + 9x + 14     factor as

 

x^2  [x^2 + 9x + 14 ]  +  1 [ x^2 + 9x + 14 ]   take out GCF

 

[ x^2 + 1 ] [ x^2 + 9x + 14 ]

 

[ x^2 + 1 ] [  x + 7 ] [ x + 2 ]

mark brainliest

Answer 2

Answer:

$(x+i)(x-i)(x+2)(x+7)$

Step-by-step explanation:

We are given a polynomial in the question.

$f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14$

We have to factor the given polynomial to find its root.

The factorization takes place in the following manner:

$f(x) = x^4 + 9x^3 + 15x^2 + 9x + 14\\= x^4 + 9x^3 + 14x^2+x^2 + 9x + 14=0\\\text{Taking out the common factor}\\= x^2(x^2+9x+14)+1(x^2+9x+14)=0\\=(x^2+1)(x^2+9x+14)=0\\=(x^2-(i^2)(x^2+9x+14)=0\\=(x^2-(i^2)(x^2+7x+2x+14)=0\\\text{Using the technique of splitting the middle term}\\=((x^2-(i^2))(x(x+7)+2(x+7))=0\\=(x+i)(x-i)(x+2)(x+7) = 0\\x = i, x = -i, x =-2, x = -7$