Write a polynomial function ff of least degree

Ella Smith

Ella Smith

Answered question

2022-03-16

Write a polynomial function ff of least degree that has a leading coefficient of 1 and the given zeros. Write the function in standard form.

−4,−2,5


 

Answer & Explanation

alenahelenash

alenahelenash

Expert2022-04-29Added 556 answers

f(x)=(x+4)(x+2)(x-5)

Expand (x+4)(x+2) using the FOIL Method.

Apply the distributive property.

f(x)=(x(x+2)+4(x+2))(x-5)

Apply the distributive property.

f(x)=(xx+x2+4(x+2))(x-5)

Apply the distributive property.

f(x)=(xx+x2+4x+42)(x-5)

Simplify and combine like terms.

f(x)=(x2+6x+8)(x-5)

Expand (x2+6x+8)(x-5) by multiplying each term in the first expression by each term in the second expression.

f(x)=x2x+x2-5+6xx+6x-5+8x+8-5

Simplify each term.

Multiply x2 by x by adding the exponents.

f(x)=x3+x2-5+6xx+6x-5+8x+8-5

Move -5 to the left of x2.

f(x)=x3-5x2+6xx+6x-5+8x+8-5

Multiply x by x by adding the exponents.

f(x)=x3-5x2+6x2+6x-5+8x+8-5

Multiply -5 by 6.

f(x)=x3-5x2+6x2-30x+8x+8-5

Multiply 8 by -5.

f(x)=x3-5x2+6x2-30x+8x-40

Simplify by adding terms.

Add -5x2 and 6x2.

f(x)=x3+x2-30x+8x-40

Add -30x and 8x.

f(x)=x3+x222x40

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