A polynomial p has zeros when x=(1)/(5),x=-4, and x=2. What could be the equation of p ? Choose 1 answer: (A) p(x)=((1)/(5)x)(-4x)(2x) (B) p(x)=(-(1)/(5)x)(4x)(-2x) (C) p(x)=(5x+1)(x-4)(x+2) (D) p(x)=(5x-1)(x+4)(x-2)

Given zero implies factor: If x=(1)/(5) is a zero, then (x - (1)/(5)) is a factor of p.Zero implies factor: If x=-4 is a zero, then (x - (-4)) or (x + 4) is a factor of p.Another zero implies factor: If x=2 is a zero, then (x - 2) is a factor of p.Find equation by multiplying factors: To find the equation of p, we multiply these factors together: (x - (1)/(5))(x + 4)(x - 2).Convert fraction to factor: First, convert (1)/(5) to 5 in the denominator to a factor with x: (5x - 1).Multiply all factors: Now multiply the factors: (5x - 1)(x + 4)(x - 2).Match with given options: This multiplication will give us the equation of p, but we don't need to actually multiply it out since we're just matching it to one of the given options.Comparing the factors we have with the options, we see that option (D) matches: p(x)=(5x-1)(x+4)(x-2).

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A polynomial
p has zeros when
x=(1)/(5),x=-4, and
x=2.
What could be the equation of
p ?
Choose 1 answer:
(A)
p(x)=((1)/(5)x)(-4x)(2x)
(B)
p(x)=(-(1)/(5)x)(4x)(-2x)
(C)
p(x)=(5x+1)(x-4)(x+2)
(D)
p(x)=(5x-1)(x+4)(x-2)

A polynomial $p$ has zeros when $x=\frac{1}{5}, x=-4$ , and $x=2$ . $\newline$ What could be the equation of $p$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $p(x)=\left(\frac{1}{5} x\right)(-4 x)(2 x)$ $\newline$ (B) $p(x)=\left(-\frac{1}{5} x\right)(4 x)(-2 x)$ $\newline$ (C) $p(x)=(5 x+1)(x-4)(x+2)$ $\newline$ (D) $p(x)=(5 x-1)(x+4)(x-2)$

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Math Problems

Algebra 2

Fundamental Theorem of Algebra

Full solution

Q. A polynomial

p

has zeros when

x=\frac{1}{5}, x=-4

, and

x=2

\newline

What could be the equation of

p

\newline

Choose

1

answer:

\newline

(A)

p(x)=\left(\frac{1}{5} x\right)(-4 x)(2 x)

\newline

(B)

p(x)=\left(-\frac{1}{5} x\right)(4 x)(-2 x)

\newline

(C)

p(x)=(5 x+1)(x-4)(x+2)

\newline

(D)

p(x)=(5 x-1)(x+4)(x-2)

Given zero implies factor: If $x=\frac{1}{5}$ is a zero, then $(x - \frac{1}{5})$ is a factor of $p$ .
Zero implies factor: If $x=-4$ is a zero, then $(x - (-4))$ or $(x + 4)$ is a factor of $p$ .
Another zero implies factor: If $x=2$ is a zero, then $(x - 2)$ is a factor of $p$ .
Find equation by multiplying factors: To find the equation of $p$ , we multiply these factors together: $(x - \frac{1}{5})(x + 4)(x - 2)$ .
Convert fraction to factor: First, convert $(\frac{1}{5})$ to $5$ in the denominator to a factor with $x$ : $(5x - 1)$ .
Multiply all factors: Now multiply the factors: $(5x - 1)(x + 4)(x - 2)$ .
Match with given options: This multiplication will give us the equation of $p$ , but we don't need to actually multiply it out since we're just matching it to one of the given options.
Match with given options: This multiplication will give us the equation of $p$ , but we don't need to actually multiply it out since we're just matching it to one of the given options.Comparing the factors we have with the options, we see that option (D) matches: $p(x)=(5x-1)(x+4)(x-2)$ .