4. Polynomial Functions

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=2x⁴-4x²+4x-8; 1 and 2

Graph each polynomial function. ƒ(x)=-2x⁴+7x³-4x²-4x

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. ƒ(x)=x⁴-4x³-x+3; 0.5 and 1

For each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)²(x-5)

For each polynomial function, identify its graph from choices A–F.

$\text{ƒ}\left(x\right)=-(x-2{)}^2(x-5)$

For each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)²(x-5)²

For each polynomial function, identify its graph from choices A–F.

$\text{ƒ}\left(x\right)=(x-2)(x-5)$

Show that the real zeros of each polynomial function satisfy the given conditions. ƒ(x)=x⁴-x³+3x²-8x+8; no real zero greater than 2

Show that the real zeros of each polynomial function satisfy the given conditions. ƒ(x)=2x⁵-x⁴+2x³-2x²+4x-4; no real zero greater than 1

For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)²(x-5)²

Show that the real zeros of each polynomial function satisfy the given conditions. ƒ(x)=x⁴+x³-x²+3; no real zero less than -2

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6.

$\text{ƒ}\left(x\right)=x^5+2x^3-2x^2+5x+5$; no real zero less than -1

Show that the real zeros of each polynomial function satisfy the given conditions. ƒ(x)=3x⁴+2x³-4x²+x-1; no real zero greater than 1

Show that the real zeros of each polynomial function satisfy the given conditions. See Example 6.

$\text{ƒ}\left(x\right)=3x^4+2x^3-4x^2+x-1$; no real zero less than -2

Show that the real zeros of each polynomial function satisfy the given conditions. ƒ(x)=x⁵-3x³+x+2; no real zero greater than 2