Factor completely: x3+x2−4x−$$4.x^3$$ + $$x^2 - 4x - 4.$$

Ch. 1 - Equations and Inequalities

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Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 177

Capitolo 2, Problema 177

Factor completely: $x^{3} + x^{2} - 4 x - 4.$

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Group the terms into two pairs: $ (x^3 + x^2) $ and $ (-4x - 4) $. This is called factoring by grouping.

Factor out the greatest common factor (GCF) from each pair. From $ (x^3 + x^2) $, the GCF is $ x^2 $, and from $ (-4x - 4) $, the GCF is $ -4 $. This gives $ x^2(x + 1) - 4(x + 1) $.

Notice that $ (x + 1) $ is a common factor in both terms. Factor $ (x + 1) $ out, resulting in $ (x + 1)(x^2 - 4) $.

Recognize that $ x^2 - 4 $ is a difference of squares. Use the formula $ a^2 - b^2 = (a - b)(a + b) $ to factor $ x^2 - 4 $ into $ (x - 2)(x + 2) $.

Combine all the factors to write the fully factored form: $ (x + 1)(x - 2)(x + 2) $.

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Domanda del libro di testo

Solve for x: $$\sqrt$[3]{x $\sqrt{x}$} = 9$

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Domanda del libro di testo

Exercises 177–179 will help you prepare for the material covered in the next section. If $negative 8$ is substituted for x in the equation $5 x^{\frac{2}{3}} + 11 x^{\frac{1}{3}} + 2 = 0$ , is the resulting statement true or false?