Factors and unknown coefficients · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Factor theorem and cubic equations — objective 1

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} + x^{2} + 399\). It is given that \(x - 1\) is a factor. Let \(\displaystyle u=2\).

Find k.

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

Fresh review variant

Factor theorem and cubic equations — objective 1

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} + 880\). It is given that \(x - 2\) is a factor. Let \(\displaystyle u=3\).

Find k.

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

Method

Factor theorem and cubic equations — objective 2

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} + 880\). It is given that \(x - 2\) is a factor. Let \(\displaystyle u=3\).

Find the largest real root of P.

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

Fresh review variant

Factor theorem and cubic equations — objective 2

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} - x^{2} + 1449\). It is given that \(x - 3\) is a factor. Let \(\displaystyle u=1\).

Find the largest real root of P.

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

Apply

Factor theorem and cubic equations — objective 3

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} - x^{2} + 1449\). It is given that \(x - 3\) is a factor. Let \(\displaystyle u=1\).

Find the negative real root of P.

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

Fresh review variant

Factor theorem and cubic equations — objective 3

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} - 2 x^{2} + 2112\). It is given that \(x - 4\) is a factor. Let \(\displaystyle u=2\).

Find the negative real root of P.

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

Check understanding

Factor theorem and cubic equations — objective 4

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} - 2 x^{2} + 2112\). It is given that \(x - 4\) is a factor. Let \(\displaystyle u=2\).

Find the remainder on division by x−u.

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

Fresh review variant

Factor theorem and cubic equations — objective 4

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(k x + x^{3} + x^{2} + 575\). It is given that \(x - 1\) is a factor. Let \(\displaystyle u=3\).

Find the remainder on division by x−u.

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

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