Exercise

Draw the graph of the polynomial $p\left(x\right)=x^2-2x-8$.

Graph of polynomial $f\left(x\right)=x^3$ will intersect $x$-axis at how many points?

The graph of polynomial $p\left(x\right)$ passes through the points $\left(-5, 0\right), \left(0, -40\right), \left(8, 0\right) \text{and} \left(5, -30\right)$. Which among the following is a factor of $p\left(x\right)$?

Factorise :- $2x²-5xy-3y²+3x+19y-20$

A polynomial is divided by $\left(x-1\right).$ The quotient obtained is $3x^3-x^2-x-4$ , and the remainder is $-5.$ Which polynomial meets these conditions?

Shown below is a house of cards, a structure created by stacking playing cards on top of each other in the shape of pyramid. Each small triangle is made of $3$ cards and each layer has $1$ less triangle than the layer below it.

Ankit and his friends were having a sleepover and wanted to do something fun. One of the friends suggested they could make a house of cards.

Ankit and his friends want to use $3$ cards in the top layer and $18$ in the bottom layer.

Form an AP showing the number of cards in each layer starting from the top layer.

Shown below is a house of cards, a structure created by stacking playing cards on top of each other in the shape of pyramid. Each small triangle is made of $3$ cards and each layer has $1$ less triangle than the layer below it.

Ankit and his friends were having a sleepover and wanted to do something fun. One of the friends suggested they could make a house of cards.

Ankit is planning to make a pyramid with the top and bottom layer containing $15$ and $138$ cards respectively.

How many layers will such a pyramid have? Show your work.

Complete the following.