The expression you divide by, here (ax+b).

What is the first step of long division?

Divide the leading term of f(x) by the leading term of the divisor.

How do you divide a polynomial with a missing power?

Insert the missing power with coefficient 0.

State the remainder theorem.

The remainder when f(x) is divided by (ax+b) is f\left(-\frac{b}{a}\right).

Quotient and remainder of x^3+2x^2-5x+1 divided by (x-2)?

Quotient x^2+4x+3, remainder 7.

Quotient and remainder of 6x^3+x^2-5x+7 divided by (2x+1)?

Quotient 3x^2-x-2, remainder 9.

How can you check a long division?

Multiply the divisor by the quotient, add the remainder, and compare with f(x); or evaluate f at the root of the divisor.

What does a remainder of 0 tell you?

The divisor is a factor of f(x).

Algebraic divisionEdexcel International A Level Maths: Flashcards

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Question

In $f(x)=(ax+b)Q(x)+R$, what are $Q(x)$ and $R$?

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In $f(x)=(ax+b)Q(x)+R$ , what are $Q(x)$ and $R$ ?: $Q(x)$ is the quotient and $R$ is the remainder.
What is the divisor?: The expression you divide by, here $(ax+b)$ .
What type of expression is the remainder when dividing by $(ax+b)$ ?: A constant.
What is the first step of long division?: Divide the leading term of $f(x)$ by the leading term of the divisor.
How do you divide a polynomial with a missing power?: Insert the missing power with coefficient $0$ .
State the remainder theorem.: The remainder when $f(x)$ is divided by $(ax+b)$ is $f\left(-\frac{b}{a}\right)$ .
Remainder when $f(x)$ is divided by $(x-3)$ ?: $f(3)$
Remainder when $f(x)$ is divided by $(2x+1)$ ?: $f\left(-\frac12\right)$
Quotient and remainder of $x^3+2x^2-5x+1$ divided by $(x-2)$ ?: Quotient $x^2+4x+3$ , remainder $7$ .
Quotient and remainder of $6x^3+x^2-5x+7$ divided by $(2x+1)$ ?: Quotient $3x^2-x-2$ , remainder $9$ .
How can you check a long division?: Multiply the divisor by the quotient, add the remainder, and compare with $f(x)$ ; or evaluate $f$ at the root of the divisor.
What does a remainder of $0$ tell you?: The divisor is a factor of $f(x)$ .

Exam questions on Algebraic division

The polynomial $f(x)=x^3+2x^2-5x+1$ is divided by $(x-2)$ .
Use the remainder theorem to check your remainder.2 marks
Let $g(x)=6x^3+x^2-5x+7$ .
Find the remainder when $g(x)$ is divided by $(x+2)$ .2 marks
Let $f(x)=4x^3-8x^2+x+6$ .
Find the quotient and the remainder when $f(x)$ is divided by $(2x-1)$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).