# Write a polynomial function in factored form

You can put this solution on YOUR website! The problem tells us nothing about any zeros or factors so we will have to find them on our own. Always start factoring by factoring our the greatest common factor unless it is a 1 which we rarely bother factoring out. The GCF is a 1 so we will not factor it out. Methods for solving cubic equations appear in The Nine Chapters on the Mathematical Arta Chinese mathematical text compiled around the 2nd century BC and commented on by Liu Hui in the 3rd century.

Some others like T. Heathwho translated all Archimedes ' works, disagree, putting forward evidence that Archimedes really solved cubic equations using intersections of two conicsbut also discussed the conditions where the roots are 0, 1 or 2.

In an early paper, he discovered that a cubic equation can have more than one solution and stated that it cannot be solved using compass and straightedge constructions. He also found a geometric solution.

However, he gave one example of a cubic equation: He used what would later be known as the " Ruffini - Horner method" to numerically approximate the root of a cubic equation.

He also used the concepts of maxima and minima of curves in order to solve cubic equations which may not have positive solutions.

In fact, all cubic equations can be reduced to this form if we allow m and n to be negative, but negative numbers were not known to him at that time. Del Ferro kept his achievement secret until just before his death, when he told his student Antonio Fiore about it.

He was soon challenged by Fiore, which led to a famous contest between the two. Each contestant had to put up a certain amount of money and to propose a number of problems for his rival to solve. Whoever solved more problems within 30 days would get all the money.

Later, Tartaglia was persuaded by Gerolamo Cardano — to reveal his secret for solving cubic equations. InTartaglia did so only on the condition that Cardano would never reveal it and that if he did write a book about cubics, he would give Tartaglia time to publish.

Some years later, Cardano learned about Ferro's prior work and published Ferro's method in his book Ars Magna inmeaning Cardano gave Tartaglia six years to publish his results with credit given to Tartaglia for an independent solution.

Cardano's promise with Tartaglia stated that he not publish Tartaglia's work, and Cardano felt he was publishing del Ferro's, so as to get around the promise. Nevertheless, this led to a challenge to Cardano by Tartaglia, which Cardano denied.

The challenge was eventually accepted by Cardano's student Lodovico Ferrari — Ferrari did better than Tartaglia in the competition, and Tartaglia lost both his prestige and income. He even included a calculation with these complex numbers in Ars Magna, but he did not really understand it.

Rafael Bombelli studied this issue in detail  and is therefore often considered as the discoverer of complex numbers. Stationary point The critical points of a function are those values of x where the slope of the function is zero.Start studying Algebra II, Chapter 5. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

Write each polynomial in factored form. 2x^3+10x^2+12x. 2x(x+2)(x+3) Write each polynomial in factored form. Write a polynomial function in standard form with the given zeros. x=-1,3,4. Polynomial Graphs and Roots.

We learned that a Quadratic Function is a special type of polynomial with degree 2; these have either a cup-up or cup-down shape, depending on whether the leading term (one with the biggest exponent) is positive or negative, respectively.

Think of a polynomial graph of higher degrees (degree at least 3) as quadratic graphs, but with more twists and turns. Polynomial equations in factored form All equations are composed of polynomials. Earlier we've only shown you how to solve equations containing polynomials of the first degree, but it is of course possible to solve equations of a higher degree.

Section Factoring Polynomials.

## Footnotes:

Of all the topics covered in this chapter factoring polynomials is probably the most important topic. There are many sections in later chapters where the first step will be to factor a polynomial.

The Factor Theorem and The Remainder Theorem The graph suggests that the function has three zeros, one of which is x= 2. It’s easy to show that f(2) = 0, but the other two zeros seem to be less friendly.

This means that we no longer need to write the quotient polynomial down, nor the xin the divisor, to determine our answer.

2. Students will write zeros of a quadratic function in factored form. Discuss Factored Form of a quadratic function. Have students write each quadratic function in factored form. Ask students to explain their process for writing.

Polynomial Functions, Zeros, Factors and Intercepts