kloseyq
2021-12-15
Answered

Find an equation of a degree 3 polynomial(in factor form) with the given zeros of f(x): -5,2,3. Assume the leading coefficient is 1.

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lalilulelo2k3eq

Answered 2021-12-16
Author has **38** answers

Step 1

given, A degree 3 polynomial with the given zeros of f(x) :−5,2,3 leading coefficient is 1.

Step 2

Now,

So, zeros of f(x): -5,2,3

$\therefore x=-5$

(x+5) is a factor.

$\therefore x=2$

(x-2) is a factor.

$\therefore x=3$

(x-3) is a factor.

Step 3

$\therefore$ The polynomial f(x) becomes

f(x)=(x+5)(x-2)(x-3)

$=(x+5)({x}^{2}-5x+6)$

$=x({x}^{2}-5x+6)+5({x}^{2}-5x+6)$

$={x}^{3}-5{x}^{2}+6x+5{x}^{2}-25x+30$

$={x}^{3}-19x+30$

$\therefore f\left(x\right)={x}^{3}-19x+30$

with leading coefficient of 1.

given, A degree 3 polynomial with the given zeros of f(x) :−5,2,3 leading coefficient is 1.

Step 2

Now,

So, zeros of f(x): -5,2,3

(x+5) is a factor.

(x-2) is a factor.

(x-3) is a factor.

Step 3

f(x)=(x+5)(x-2)(x-3)

with leading coefficient of 1.

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