Algebra Factoring and Radicals Practice

A comprehensive set of practice flashcards covering radical simplification, greatest common factors (GCF), least common multiples (LCM), and various methods of polynomial factoring including difference of squares and trinomials.

Simplified form of $\sqrt{96}$

$4\sqrt{6}$ achieved by factoring as $\sqrt{16} \times \sqrt{6}$

Simplified form of $\sqrt{243}$

$9\sqrt{3}$ achieved by factoring as $\sqrt{81} \times \sqrt{3}$

Simplified form of $4\sqrt{108}$

$24\sqrt{3}$ calculated as $4 \times 6\sqrt{3}$

Simplified form of $-7\sqrt{320}$

$-56\sqrt{5}$ calculated as $-7 \times 8\sqrt{5}$

GCF of $12x^3y^2, 20xy^5, 30x^4y^3$

$$2xy^2$$

LCM of $12x^3y^2, 20xy^5, 30x^4y^3$

$$60x^4y^5$$

GCF of $16y^3, 24x^5y, 8x^2y^2$

$$8y$$

LCM of $16y^3, 24x^5y, 8x^2y^2$

$$48x^5y^3$$

Difference of Two Squares: $9x^2 - 4$

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

Factoring GCF: $45x^7 - 35x^6$

$$5x^6(9x - 7)$$

Factoring Completely: $3x^4 - 12x^2$

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

Factoring Completely: $x^4 - 81$

$$(x - 3)(x + 3)(x^2 + 9)$$

Factoring Trinomial: $x^2 - 10x + 24$

$$(x - 6)(x - 4)$$

Factoring Trinomial: $x^2 + 9x - 36$

$$(x + 12)(x - 3)$$

Simplified form of $\frac{3x^2 - 6x}{3x}$

$$x - 2$$

Simplified form of $\frac{x^2 - 14x + 49}{x^2 - 4x - 21}$

$$\frac{x - 7}{x + 3}$$

Factored form of $6x^2 + 18x - 324$

$$6(x + 9)(x - 6)$$

Factored form of $-x^4 + 16x^3 - 55x^2$

$$-x^2(x - 11)(x - 5)$$

Factored form of $4x^4 + 16x^3 - 48x^2$

$$4x^2(x + 6)(x - 2)$$

Factored form of $-x^2 - 2x + 3$

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