What could be the equation of
A. p(x) = x(x−2)(2x−7)
b. p(x)=x(2x)(72x)
C. p times x is equal to x 2 x open paren 7 halves x close paren p(x) = x(−2x)(−72x)
D. p(x) = x(−2x)(−72x) p(x) = x(x+2)(2x+7)
Let's expand each polynomial to find out its equation:
A. \( p(x) = x(x - 2)(2x - 7) \)
First, we can expand it by multiplication:
\( p(x) = x(2x^2 - 7x - 4x + 14) \)
\( p(x) = x(2x^2 - 11x + 14) \)
Now, let's distribute \( x \) into each term:
\( p(x) = 2x^3 - 11x^2 + 14x \)
So the equation of \( p(x) \) is:
\( p(x) = 2x^3 - 11x^2 + 14x \)
B. \( p(x) = x(2x)(72x) \)
This one is a bit more straightforward:
\( p(x) = 2x^2 * 72x \)
\( p(x) = 144x^3 \)
So the equation of \( p(x) \) is:
\( p(x) = 144x^3 \)
C. It seems that you've provided two expressions for C which aren't consistent with each other. According to your instruction, "p times x is equal to x 2 x open paren 7 halves x close paren p(x) = x(−2x)(−72x)," it seems like there may be a typo.
Assuming you intended "C. p(x) = x(2x)(7/2x)", let's multiply those together:
\( p(x) = 2x^2 * \frac{7}{2}x \)
\( p(x) = 7x^3 \)
So the equation of \( p(x) \) is:
\( p(x) = 7x^3 \)
D. \( p(x) = x(−2x)(−72x) \) and \( p(x) = x(x+2)(2x+7) \) are two different expressions, so let's handle them separately.
First: \( p(x) = x(-2x)(-72x) \)
\( p(x) = -2x^2 * -72x \)
\( p(x) = 144x^3 \)
So the equation of this \( p(x) \) is identical to B:
\( p(x) = 144x^3 \)
Second: \( p(x) = x(x+2)(2x+7) \)
\( p(x) = x(2x^2 + 7x + 4x + 14) \)
\( p(x) = x(2x^2 + 11x + 14) \)
Distribute \( x \):
\( p(x) = 2x^3 + 11x^2 + 14x \)
So the equation of this \( p(x) \) is:
\( p(x) = 2x^3 + 11x^2 + 14x \)