A polynomial p has zeros when x=0,x=-(1)/(6), and x=-3. What could be the equation of p ? Choose 1 answer: (A) p(x)=x(6x+1)(x+3) (B) p(x)=x(6x-1)(x-3) (C) p(x)=x((1)/(6)x)(x+3) (D) p(x)=x(-(1)/(6)x)(x-3)

Identify Zeros: Zeros of the polynomial are given as x=0, x=-(1)/(6), and x=-3. The factors of the polynomial will be (x-0), (x-(-(1)/(6))), and (x-(-3)).Simplify Factors: Simplify the factors to get x, (x+(1)/(6)), and (x+3).Multiply Factors: Multiply the factors to form the polynomial equation p(x) = x * (x+(1)/(6)) * (x+3).Eliminate Fraction: To get rid of the fraction in the second factor, multiply (x+(1)/(6)) by 6 to get 6x+1. The polynomial equation becomes p(x) = x * (6x+1) * (x+3).Final Polynomial Equation: The equation p(x) = x * (6x+1) * (x+3) matches with option (A) p(x)=x(6x+1)(x+3).

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A polynomial
p has zeros when
x=0,x=-(1)/(6), and
x=-3.
What could be the equation of
p ?
Choose 1 answer:
(A)
p(x)=x(6x+1)(x+3)
(B)
p(x)=x(6x-1)(x-3)
(C)
p(x)=x((1)/(6)x)(x+3)
(D)
p(x)=x(-(1)/(6)x)(x-3)

A polynomial $p$ has zeros when $x=0, x=-\frac{1}{6}$ , and $x=-3$ . $\newline$ What could be the equation of $p$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $p(x)=x(6 x+1)(x+3)$ $\newline$ (B) $p(x)=x(6 x-1)(x-3)$ $\newline$ (C) $p(x)=x\left(\frac{1}{6} x\right)(x+3)$ $\newline$ (D) $p(x)=x\left(-\frac{1}{6} x\right)(x-3)$

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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=0, x=-\frac{1}{6}

, and

x=-3

\newline

What could be the equation of

p

\newline

Choose

1

answer:

\newline

(A)

p(x)=x(6 x+1)(x+3)

\newline

(B)

p(x)=x(6 x-1)(x-3)

\newline

(C)

p(x)=x\left(\frac{1}{6} x\right)(x+3)

\newline

(D)

p(x)=x\left(-\frac{1}{6} x\right)(x-3)

Identify Zeros: Zeros of the polynomial are given as $x=0$ , $x=-\frac{1}{6}$ , and $x=-3$ . The factors of the polynomial will be $(x-0)$ , $(x-\left(-\frac{1}{6}\right))$ , and $(x-(-3))$ .
Simplify Factors: Simplify the factors to get $x$ , $\left(x+\frac{1}{6}\right)$ , and $\left(x+3\right)$ .
Multiply Factors: Multiply the factors to form the polynomial equation $p(x) = x \cdot (x+\frac{1}{6}) \cdot (x+3)$ .
Eliminate Fraction: To get rid of the fraction in the second factor, multiply $x+\frac{1}{6}$ by $6$ to get $6x+1$ . The polynomial equation becomes $p(x) = x \cdot (6x+1) \cdot (x+3)$ .
Final Polynomial Equation: The equation $p(x) = x \cdot (6x+1) \cdot (x+3)$ matches with option (A) $p(x)=x(6x+1)(x+3)$ .