Problem 4 Applying Factoring Trinomials

Geometry The area of a rectangle is given by the trinomial x 2 − 2 x − 35 . bold italic x squared , minus 2 bold italic x minus 35 .  What are the possible dimensions of the rectangle? Use factoring.

To factor x 2 − 2 x − 35 , x squared , minus 2 x minus 35 comma  identify the pair of factors of − 35 negative 35  that has a sum of − 2 . negative 2 .

x 2 − 2 x − 35 = ( x + 5 ) ( x − 7 ) x squared , minus 2 x minus 35 equals open x plus 5 close open x minus 7 close

So the possible dimensions of the rectangle are x + 5 x plus 5  and x − 7 . x minus 7 .

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4. A rectangle's area is x 2 − x − 72 . x squared , minus x minus 72 .  What are possible dimensions of the rectangle? Use factoring.

Problem 5 Factoring a Trinomial With Two Variables

What is the factored form of x 2 + 6 x y − 55 y 2 ? bold italic x squared , plus 6 bold italic x bold italic y minus 55 , bold italic y squared , question mark

List the pairs of factors of − 55 . negative 55 .  Identify the pair that has a sum of 6.

x 2 + 6 x y − 55 y 2 = ( x − 5 y ) ( x + 11 y ) x squared , plus 6 x y minus 55 , y squared , equals open x minus 5 y close open x plus 11 y close

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5. What is the factored form of m 2 + 6 m n − 27 n 2 ? m squared , plus 6 m n minus 27 , n squared , question mark