Factoring

In a common monomial factoring, what do you call the factor that consists of the GCF of the numerical coefficient and the least exponent of the component variable?

Click the types of factoring methods used in Algebra

• Sum of Two Squares

• Sum of Two Cubes

• Common Monomial Factor

• Perfect Square Trinomial

• Difference of Two Cubes

Factor this expression:  $16d^4-81$  

•  $\left(4d-9\right)\left(4d-9\right)$  

•  $\left(4d+9\right)^2$  

•  $\left(4d+9\right)\left(4d-9\right)$  

•  $\left(4d\right)\left(4d-9\right)$  

Which of the following trinomials is considered a Perfect Square Trinomial

• $x^2-7x+12$

• $4x^2-18x+25$

• $x^3-7x+5x^2$

• $9x^2-24x+16$

The factored form of the expression  $6x^4y^8-30x^{10}y^6$  is   $\left(6x^2y^4-5x^5y^3\right)\left(6x^2y^4-5x^5y^3\right)$  

• True

• False

Which of the following statements is FALSE about Perfect Square Trinomial?

• The first term and the last terms of the trinomial are perfect squares.

• The factored form of the expression $a^2-2ab+b^2$ is $\left(a+b\right)^2$

• The middle term of the perfect square trinomial is twice the product of the square roots of the first and last term

• The expression $16x^2+24x+9$ is an example of a perfect square trinomial

Which of the following is CORRECT?

• $81-9y^2=\left(81\right)\left(1-9y^2\right)$

• $100y^{12}-121m^8=\left(10y^6+11m^4\right)^2$

• $81x^{10}-100=\left(9x^5-10\right)\left(9x^5+10\right)$

• $144x^8y^2-225=\left(14x^4y-15\right)^2$

What is the factored form of the expression:  $10x-20y+30z$  

•  $10\left(x-2y+3z\right)$  

•  $1\left(10x-20y+30z\right)$  

•  $5\left(2x-4y+6z\right)$  

•  $10x\left(1-2y+3z\right)$  

What is the general form of the difference of two squares?

• $a^3-b^3$

• $a^2-b^2$

• $a^2-2ab+b^2$

• $a^2+2ab+b^2$

 $100x^2y-50x^3y^2+75xy$  

What is the GCM of the polynomial mentioned above?

•  $100xy$  

•  $50xy$  

•  $75xy$  

•  $25xy$