Question

pendent practice
7)

1. find $(x - 2)(x^2 - 3x + 1)$

1. write $-8 - x^2 + 2x$ in standard form. identify the degree and leading coefficient of the polynomial. then classify the polynomial by the number of terms.

Explanation:

Step1: Distribute $x$ to each term

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

Step2: Distribute $-2$ to each term

$-2(x^2 - 3x + 1) = -2x^2 + 6x - 2$

Step3: Combine all distributed terms

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

Step4: Combine like terms

$x^3 + (-3x^2 -2x^2) + (x + 6x) - 2 = x^3 -5x^2 +7x -2$

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Step5: Rearrange polynomial to standard form

Standard form orders terms by descending degree: $-x^2 + 2x - 8$

Step6: Identify degree of polynomial

The highest exponent is 2, so degree = 2

Step7: Identify leading coefficient

Coefficient of the highest degree term: $-1$

Step8: Classify by number of terms

The polynomial has 3 terms, so it is a trinomial.

Answer:

1. $x^3 - 5x^2 + 7x - 2$
2. Standard form: $-x^2 + 2x - 8$; Degree: 2; Leading coefficient: $-1$; Classification: Trinomial