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3 years ago

10. Write (2x + 1)(x - 3)(x - 2) in standard form.

Mathematics

1 answer:

Leto [7]3 years ago

8 0

Answer:

$2x^3-9x^2+7x+6$

Step-by-step explanation:

The standard form of a polynomial is a method of writing a polynomial such that the terms are organized by degrees. In essence, the first term, or the left-most term has the highest degree or largest exponent. The right-most term or last term has the lowest degree or smallest exponent. One is given an expression in factored form. Distribute, multiply every term by another in the parenthesis, then simplify. Repeat this process until there are no more factored terms. Finally, rewrite the expression in standard form.

$(2x+1)(x-3)(x-2)$

Distribute,

$(2x+1)(x-3)(x-2)$

$((2x)(x)+(-3)(2x)+(1)(x)+(1)(-3))(x-2)$

Simplify,

$((2x)(x)+(-3)(2x)+(1)(x)+(1)(-3))(x-2)$

$(2x^2-6x+x-3)(x-2)$

$(2x^2-5x-3)(x-2)$

Distribute,

$(2x^2-5x-3)(x-2)$

$(2x^2)(x)+(-5x)(x)+(-3)(x)+(-2)(2x^2)+(-2)(-5x)+(-3)(-2)$

Simplify,

$(2x^2)(x)+(-5x)(x)+(-3)(x)+(-2)(2x^2)+(-2)(-5x)+(-3)(-2)$

$2x^3-5x^2-3x-4x^2+10x+6$

$2x^3-9x^2+7x+6$

This polynomial is already in standard form, thus there is no need to reorganize it. The leading term or the left-most term has the highest degree, three, the succeeding terms are in respective order of decreasing exponents.

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Fudgin [204]

Answer:

(-3,2)

Step-by-step explanation:

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5 0

3 years ago

A chemist working on a flu vaccine needs to mix a 20% sodium-iodine with a 60% sodium to obtain a 70-milliliter mixture.Write th

Verdich [7]

Answer:

$S(x)=-0.4x+42$

The value of S(50) is 22 in means the amount of sodium iodine in the mixture is 22 when 50 milliliters of the 20% solution used.

Step-by-step explanation:

It is given that a chemist working on a flu vaccine needs to mix a 20% sodium-iodine with a 60% sodium-iodine to obtain a 70-milliliter mixture.

Let x be the number of milliliters of the 20% sodium-iodine.

Number of milliliters of the 60% sodium-iodine = 70-x

The amount of sodium iodine in the mixture is 20% of x and 60% of (70-x).

$S(x)=0.20x+0.60(70-x)$

$S(x)=0.2x+42-0.6x$

$S(x)=-0.4x+42$

Therefore,the required function is $S(x)=-0.4x+42$ .

Substitute x=50 in the above equation.

$S(50)=-0.4(50)+42$

$S(50)=22$

The value of S(50) is 22 in means the amount of sodium iodine in the mixture is 22 when 50 milliliters of the 20% solution used.

4 0

4 years ago

Simplify xi(I-7i) ^2

topjm [15]

Note what i actually represents.
i is the very basis of a whole new level of counting. When finding discriminants, we often say that a quadratic has no real roots if the discriminant is 0. Needless to say, there are roots, they are just imaginary.

$\sqrt{-1}$ , in real terms, is non-existent. That is, there are no numbers in the real number system that when multiplied by itself produces a result of -1. This is what i unit represents.

Let's tackle this problem in smaller steps.
Let's first expand our brackets.

(i - 7i)² = (-6i)² = 36i²
Now, let's distribute the xi.

xi(i - 7i)² = xi(36i²) = 36xi³ = $-36x\sqrt{-1}$ = -36xi