A polynomial p has zeros when x=5,x=-1, and x=-(1)/(4). What could be the equation of p ? Choose 1 answer: (A) p(x)=(x+5)(x+1)(4x+1) (B) p(x)=(x-5)(x+1)(4x+1) (C) p(x)=(x+5)(x-1)(4x-1) (D) p(x)=(5x)(-1x)(-(1)/(4)x)

Identify Zeros: Zeros of the polynomial are given as x=5, x=-1, and x=-(1)/(4). To form a polynomial, we use the fact that if x=a is a zero, then (x-a) is a factor of the polynomial.Form Polynomial Factors: The factors corresponding to the zeros are (x-5), (x+1), and (x+(1)/(4)). We multiply these factors to get the polynomial equation.Correct Last Factor: p(x) = (x-5)(x+1)(x+(1)/(4)). However, we need to correct the last factor to have an integer coefficient. The correct factor for x=-(1)/(4) is (4x+1), not (x+(1)/(4)).

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A polynomial
p has zeros when
x=5,x=-1, and
x=-(1)/(4).
What could be the equation of
p ?
Choose 1 answer:
(A)
p(x)=(x+5)(x+1)(4x+1)
(B)
p(x)=(x-5)(x+1)(4x+1)
(C)
p(x)=(x+5)(x-1)(4x-1)
(D)
p(x)=(5x)(-1x)(-(1)/(4)x)

A polynomial $p$ has zeros when $x=5, x=-1$ , and $x=-\frac{1}{4}$ . $\newline$ What could be the equation of $p$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $p(x)=(x+5)(x+1)(4 x+1)$ $\newline$ (B) $p(x)=(x-5)(x+1)(4 x+1)$ $\newline$ (C) $p(x)=(x+5)(x-1)(4 x-1)$ $\newline$ (D) $p(x)=(5 x)(-1 x)\left(-\frac{1}{4} x\right)$

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Math Problems

Algebra 2

Write a quadratic function from its x-intercepts and another point

Full solution

Q. A polynomial

p

has zeros when

x=5, x=-1

, and

x=-\frac{1}{4}

\newline

What could be the equation of

p

\newline

Choose

1

answer:

\newline

(A)

p(x)=(x+5)(x+1)(4 x+1)

\newline

(B)

p(x)=(x-5)(x+1)(4 x+1)

\newline

(C)

p(x)=(x+5)(x-1)(4 x-1)

\newline

(D)

p(x)=(5 x)(-1 x)\left(-\frac{1}{4} x\right)

Identify Zeros: Zeros of the polynomial are given as $x=5$ , $x=-1$ , and $x=-\frac{1}{4}$ . To form a polynomial, we use the fact that if $x=a$ is a zero, then $(x-a)$ is a factor of the polynomial.
Form Polynomial Factors: The factors corresponding to the zeros are $(x-5)$ , $(x+1)$ , and $\left(x+\frac{1}{4}\right)$ . We multiply these factors to get the polynomial equation.
Correct Last Factor: $p(x) = (x-5)(x+1)(x+\frac{1}{4})$ . However, we need to correct the last factor to have an integer coefficient. The correct factor for $x=-\frac{1}{4}$ is $(4x+1)$ , not $(x+\frac{1}{4})$ .