Question

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

Answer 1

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.