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The Factor Theorem says (x − r) is a factor of a polynomial g(x) if and only if r is a root of g(x). Since 3 is a zero, we know g(x) can be divided by (x-3)

In fact, g(x)=(x-3)(x2 +4x+8)

The (x2 +4x+8) has no real roots, (rational roots theorem tells us this) but we can still write it as a product of linear factors using complex numbers.

Since (x+2-2i)(x+2+2i)=(x2 +4x+8)

we have g(x)=(x-3)(x+2-2i)(x+2+2i) which is a product of linear factor.

Q: Given that 3 is a zero of the polynomial g of x equals x cubed plus x squared-4x-24 express g of x as a product of linear factors?

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Clouser

A factor is one of two or more numerical or algebraic components of a product. **Note : 1.To factor a counting number means to break it down into its prime number factors. 2.To factor a polynomial is to find its prime polynomial factors, a basic procedure for solving algebraic equations.

The same way that factoring a number is different from multiplying two factors. In general, it is much easier to multiply two factors together, than to find factors that give a certain product.

That property is called CLOSURE.

x2 + 15x +36

Related questions

I think something's missing, but the answer is x(6x - 13)

20x3-15x2=8,000-225=7,775

two factors is a binomial three factors is a trinomial four of more is a polynomial the product of any of these is just a polynomial

Factor

2x3x7x7

2x2x11

As a product of its prime factors: 2*3*3*5 = 90

Is sometimes possible, but not always.

express 5610 as the product of prime factors

As a product of its prime factors: 2*3*5*7 = 210

2x5x5

169 = 132