G10_Lesson 8-2

Lesson 8-2

Multiplying and Factoring

Objectives

• Multiplying a monomial by a polynomial

• Factor a monomial from a polynomial

 $-x^3\left(9x^4-2x^3+7\right)$  

• Use Distributive Property

•  $-x^3\left(9x^4\right)-x^3\left(-2x^3\right)-x^3\left(7\right)$  

•  $=-9x^7+2x^6-7x^3$  

Multiple Choice

What is the simpler form of

 $5n\left(3n^3-n^2+8\right)$  

•  $15n^4-5n^3+40n$  

•  $15n^3-5n^2+8n$  

•  $15n^4+5n^3+40n$  

•  $8n^4-5n^3+12n$  

Multiple Choice

What is the simpler form of

 $5x^2\left(2x-3\right)$  

•  $5x^2+2x-3$  

•  $10x^3-15x^2$  

•  $-5x^2$  

•  $7x^3-15x^2$  

Multiple Choice

There is a circular garden in the middle of a square yard. The radius of the circle is 4x . The side length of the yard is 20x. What is the area of the part of the yard that is not covered by the circle?

• 4x(5)

• $8x^2\left(5-\pi\right)$

• $16x\left(25+\pi\right)$

• $16x^2\left(25-\pi\right)$

Factoring a monomial from a polynomial

• Find GCF (Greatest Common Factor) of the terms

• Factoring out a Monomial

 $5x^3+25x^2+45x$  

•  $GCF\left(5x^3,\ 25x^2,\ 45x\right)$  

•  $5x\left(x^2+5x+9\right)$  

Multiple Choice

What is the factored form of

 $3x^4-9x^2-12x$  ?

•  $x\left(3x^3-9x-12\right)$  

•  $3\left(x^4-3x^2-4\right)$  

•  $3x\left(x^3-3x-4\right)$  

•  $3x\left(x^4-3x^2-4x\right)$  

Multiple Choice

What is the GCF of the terms of

 $8c^3+12c^2+10c$  ?

• 2

• 4

• 2c

• 4c

Multiple Choice

How can the polynomial

 $6d^4+9d^3-12d^2$  be factored?

•  $3d^2\left(2d^2+3d-4\right)$  

•  $3d^2\left(3d^2+6d-9\right)$  

•  $3d\left(d^3+3d^2-4\right)$  

•  $6d^2\left(d^2+3d^3-6\right)$