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Q: Write each factor as a polynomial in descending order x2 plus 14x plus 24?

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-79

x^2 + 10x + 9 = (x + 9)(x + 1)

If you know one linear factor, then divide the polynomial by that factor. The quotient will then be a polynomial whose order (or degree) is one fewer than that of the one that you stared with. The smaller order may make it easier to factorise.

A polynomial of order 3 (a cubic) or higher can have more than three terms. However, the the following polynomial, even though of order 7, has only 2 terms: x7 - 23.

Descartes' rule of signs (see related link) can help you determine the maximum number of real roots. If the polynomial is odd powered, then there will be at least one real root. Any even powered polynomial can be factored into a bunch of quadratics [though they may not be rational or even pretty], and any odd-powered polynomial can be factored into a bunch of quadratics and one linear (this one would have the real root). So the quadratics may have pairs of real or complex roots (having an imaginary component).To clarify, when I say complex, I'm referring to the fact that there will be an imaginary component to the root, because actually the real numbers is a subset of the set of complex numbers.The order of the polynomial will tell you how many roots it will have. If you can graph the polynomial, then you can see if it crosses the x axis. If it is a 5th order polynomial, and crosses the x axis 3 times, then there are 3 real roots (the other two roots are complex).

Related questions

Factor the polynomial x2 - 10x + 25. Enter each factor as a polynomial in descending order.

(x-2)(x-3)

2x+5x-24 7x2-24

x(x + 2)(x - 5)

Terms

-79

(3x + 7)(2x - 9)

15x^2+3x-12 3(5x^2+x-4)=Answer

7(x - 3)

(2x + 5)(6x - 5)

(x + 8)(x + 1)

(x-3)(x+7)

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