Finding a Missing Number

Part of the Polynomials & Rational Expressions section of Coddy's Algebra 2 journey. Lesson 6 of 51.

A drop of ink covers one number in ${x}^{3}+2{x}^{2}+kx-6$ . But you know that $x-1$ is a factor. So the value at x = 1 must be 0. Put x = 1 into the expression.

$1+2+k-6 = 0$

So $k-3 = 0$ , and k = 3.

Challenge

$x-2$ is a factor of $p\left(x\right) = {x}^{3}-3{x}^{2}+kx+6$ , so $p\left(2\right) = 0$ . Find k. Write each line yourself.

Try it yourself

p\cdot 2 = 0

Find k

Given $p\left(x\right) = x^{3}-3x^{2}+kx+6$

All lessons in Polynomials & Rational Expressions

1Polynomial Long Division

How Long Division Works The Remainder Theorem A Missing Term Recap: Long Division

4Polynomial Equations

Common Factor First Grouping to Solve Fourth Powers Recap: Polynomial Equations

7Adding and Subtracting

Same Bottom Different Bottoms Subtracting Factor the Bottoms First Recap: Adding Fractions

10Variation

Direct Variation Inverse Variation Work Together Recap: Variation

2Remainders and Factors

The Factor TheoremFinding a Missing NumberUsing a Known Factor Recap: Remainders and Factors

5Sign Charts

Between the Roots Outside the Roots A Negative Leading Term Reading a Sign Chart Recap: Sign Charts

8Rational Equations

Clearing Fractions x in the Bottom Cross-Multiplying A False Answer One True, One False Recap: Rational Equations

11Final Challenges

Final: Divide It Out Final: Every Root Final: One Fraction Final: Check the Answer Final: The Sign Chart

3Factoring Higher Degree

Factor by Grouping Grouping All the Way Difference of Cubes Sum of Cubes A Quadratic in Disguise Recap: Factoring

6Rational Expressions

Cancelling Factors Excluded Values Multiplying Dividing Recap: Rational Expressions

9Rational Inequalities

Signs of a Fraction Including the Edge Recap: Rational Inequalities