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A zero is an input where a polynomial's value is 0. An input is a number used in place of x. The value is the result.

This is Chapter 2, Polynomials. You already know most of its method. A polynomial is a sum of terms, like 3x² − 5x + 6. Your book writes zeroes. This track writes zeros.

What this track covers

• The zero. One substitution tests an input.
• Factors hand it over. A factor is one bracket of a product. Brackets show the zeros at once.
• The curve. A curve meets the x-axis at the zeros.
• Sum and product. Of the zeros: −b/a and c/a, in ax² + bx + c.
• Building backwards. Two zeros give back the quadratic.
• Reading the signs. S is the sum and P the product. Their signs show where the zeros are.
• Values from S and P. α² + β² and 1/α + 1/β, found without the zeros. Here α and β are the two zeros.
• The cubic. Three zeros, three relations.

Your book also shows the relations for a cubic. They come at the end of this track.

Quick catch-up

Four Class 9 lessons carry most of the weight here.

• Built from whole-number powers — what a polynomial is.
• The highest power names it — where "quadratic" comes from.
• Every pair is a point — plotting a rule's pairs.
• The pair with two jobs — splitting a quadratic into brackets.