Introduction to Linear Polynomials

What is the zero of the linear polynomial $p(x) = 4x + 1$?

Identify the coefficient of $x$ in the expression $1 - 5x$.

What is the degree of the polynomial $f(x) = x + x + x$?

Which of these is a linear polynomial in one variable?

For a linear polynomial $p(x) = ax + b$, the sum of the coefficients $a$ and $b$ is $15$. If $x = -2$ is the zero of the polynomial, find the value of the coefficient $a$.

If $p(x)$ is a linear polynomial such that $p(2) = 7$ and $p(-1) = -2$, what is the value of $p(5)$?

In the polynomial $p(x) = \frac{x}{2} + 1$, what is the coefficient of $x$?

How many zeros can a non-zero linear polynomial have?

Is the expression $P(x) = \frac{4x+8}{2}$ a linear polynomial? If so, find its zero.

If $f(x) = mx + c$, find the value of $f(x+h) - f(x-h)$.

What is the leading coefficient of the linear polynomial $p(x) = 7 - 4x$?

What is the zero of $p(x) = 10x + 5$?

Is $p(x) = |x|$ a linear polynomial?

If $p(x) = 2x + k$ and $p(1) = 5$, what is the value of $k$?

A linear polynomial $p(x)$ satisfies the conditions $p(1) = 1$ and $p(-1) = 5$. Find the zero of $p(x)$.

Is the constant 0 considered a linear polynomial?

Find the zero of the polynomial $p(x) = \sqrt{2}x - 4$.

If $p(x) = ax+b$ and $p(1)=2, p(2)=1$, find the sum of $a$ and $b$.

If $f(x)$ is a linear polynomial, then $f(x) + f(1-x)$ is always equal to:

Find the value of $n$ such that $x^n - 2$ is a linear polynomial.

Find the zero of the polynomial $p(x) = 7x + 14$.

Which of these expressions is a linear polynomial in $z$?

In the sequence $0, 2, 4, 6, \dots$, what is the $50^{th}$ term?

What is the constant term in the polynomial $p(x) = 0.5x - 1.5$?

For what value of $a$ is the polynomial $p(x) = (a-3)x^2 + 2x + 5$ a linear polynomial?

What is the $n^{th}$ term rule for a sequence where every term is 7?

If $p(x) = 5x + 2$, what is $p(x+1) - p(x)$?

If $P(x) = ax + b$ satisfies $P(1) = 2$ and $P(P(1)) = 4$, find the value of $a + b$.

Find the value of $n$ such that the $n$-th term of the linear pattern $3, 10, 17, ...$ is the same as the $n$-th term of $100, 93, 86, ...$.

If $f(x)$ is a linear polynomial such that $f(0) = -3$ and the area between the line, the $x$-axis, and $x = 4$ is 10 square units (where $f(x) > 0$ for $x > 4$), find the slope of $f(x)$.

Find the value of $a$ if $x=1, y=1$ is a solution of $ax - 2y = 10$.

The cost of a book ($y$) is twice the cost of a pen ($x$). Which linear equation represents this?

In the linear equation $y = 4x$, if $x = -1$, find $y$.

What is the degree of a non-zero constant polynomial?

An object's weight on a certain planet ($y$) is directly proportional to its weight on Earth ($x$), expressed by the relationship $y = kx$. If a probe weighing $50$ kg on Earth weighs $20$ kg on this planet, what is the value of the constant $k$?

Calculate the area of the triangle formed by the coordinate axes and the graph of the linear equation $6x + 8y = 48$.

Find the coordinates of the point on the graph of the linear equation $5x - 3y = 21$ where the abscissa is exactly double the ordinate.

At what point does the line $3x + 2y = 12$ intersect the line $x = 2$?

If the sum of two numbers is $15$ and their difference is $3$, find the numbers using linear relationships.

A line $L$ is parallel to the y-axis and passes through the point of intersection of $x+y=5$ and $x-y=1$. What is the equation of $L$?

What is the zero of the polynomial $p(x) = x + 5$?

The linear equation $y = 3x + 5$ has:

The age of a father is twice the age of his son. If $x$ is the father's age and $y$ is the son's age, the linear equation is:

How many linear equations in $x$ and $y$ can be satisfied by $x = 1$ and $y = 2$?

On the graph of the linear equation $x - 2y = 10$, a point is moved such that its abscissa increases by $6$ units. How does its ordinate change to ensure the new point also lies on the same line?

If the point $(3, 4)$ lies on the graph of $y = ax + 1$, then find the value of $a$.

Any solution of the linear equation $2x + 0y + 9 = 0$ in two variables is of the form:

Find the coordinates of the point where the line $x - y = 5$ intersects the $y$-axis.

If $3x + y = 5$ and $x + 3y = 7$, what is the value of $x + y$?

If the line $y = (k^2 - 1)x + 3$ is parallel to the $x$-axis, find the possible values of $k$.