Problem 5 Multiplying a Trinomial and a Binomial

What is a simpler form of ( 3 x 2 + x − 5 ) ( 2 x − 7 ) ? open 3 , bold italic x squared , plus bold italic x minus 5 close open 2 bold italic x minus 7 close question mark

    3 x 2 + x − 5         2 x − 7   − 21 x 2 − 7 x + 35 6 x 3 + 2 x 2 − 10 x     6 x 3 − 19 x 2 − 17 x + 35     Multiply by  − 7. Multiply by  2 x . Add like terms . table with 1 row and 2 columns , row1 column 1 , table with 5 rows and 7 columns , row1 column 1 , , column 2 , column 3 3 x squared , column 4 plus , column 5 x , column 6 minus , column 7 5 , row2 column 1 , , column 2 , column 3 , column 4 , column 5 2 x , column 6 minus , column 7 7 , row3 column 1 , , column 2 minus , column 3 21 x squared , column 4 minus , column 5 7 x , column 6 plus , column 7 35 , row4 column 1 , 6 x cubed , column 2 plus , column 3 2 x squared , column 4 minus , column 5 10 x , column 6 , column 7 , row5 column 1 , 6 x cubed , column 2 minus , column 3 19 x squared , column 4 minus , column 5 17 x , column 6 plus , column 7 35 , end table , column 2 table with 5 rows and 1 column , row1 column 1 , , row2 column 1 , , row3 column 1 , cap multiplyby . minus 7. , row4 column 1 , cap multiplyby . 2 x . , row5 column 1 , cap addliketerms . . , end table , end table

The product is 6 x 3 − 19 x 2 − 17 x + 35 . 6 , x cubed , minus 19 , x squared , minus 17 x plus 35 .

✓ Got It?

5. 1. What is a simpler form of ( 2 x 2 − 3 x + 1 ) ( x − 3 ) ? open 2 , x squared , minus 3 x plus 1 close open x minus 3 close question mark
   2. Reasoning How can you use the Distributive Property to find the product of a trinomial and a binomial?

✓ Lesson Check

Do you know HOW?

Simplify each product.

1. ( x + 3 ) ( x + 6 ) open x plus 3 close open x plus 6 close
2. ( 2 x − 5 ) ( x + 3 ) open 2 x minus 5 close open x plus 3 close
3. ( x + 2 ) ( x 2 + 3 x − 4 ) open x plus 2 close open , x squared , plus 3 x minus 4 close
4. A rectangle has length x + 5 and width x − 3 . x minus 3 .  What is the area of the rectangle? Write your answer as a polynomial in standard form.

Do you UNDERSTAND?

5. Reasoning Explain how to use the FOIL method to find the product of two binomials.
6. Compare and Contrast Simplify (3x + 8)(x + 1) using a table, the Distributive Property, and the FOIL method. Which method is most efficient? Explain.
7. Writing How is the degree of the product of two polynomials p(x) and q(x) related to the degrees of p(x) and q(x)?