Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 19 x^{2} + 4 x + 21\), and \(\displaystyle a=4\). Consider divisors ax−1 and (a+1)x+1.

Find the remainder for divisor ax−1.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 20 x^{2} + 5 x + 22\), and \(\displaystyle a=5\). Consider divisors ax−1 and (a+1)x+1.

Find the remainder for divisor ax−1.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 20 x^{2} + 5 x + 22\), and \(\displaystyle a=5\). Consider divisors ax−1 and (a+1)x+1.

Find the remainder for divisor (a+1)x+1.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 21 x^{2} + x + 23\), and \(\displaystyle a=2\). Consider divisors ax−1 and (a+1)x+1.

Find the remainder for divisor (a+1)x+1.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 21 x^{2} + x + 23\), and \(\displaystyle a=2\). Consider divisors ax−1 and (a+1)x+1.

Find the leading coefficient of the quotient for ax−1.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 22 x^{2} + 2 x + 24\), and \(\displaystyle a=3\). Consider divisors ax−1 and (a+1)x+1.

Find the leading coefficient of the quotient for ax−1.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 22 x^{2} + 2 x + 24\), and \(\displaystyle a=3\). Consider divisors ax−1 and (a+1)x+1.

Find P(−a).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(x^{3} + 23 x^{2} + 3 x + 25\), and \(\displaystyle a=4\). Consider divisors ax−1 and (a+1)x+1.

Find P(−a).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.