Factoring Trinomials: a > 1 / Assignment

Ginny factored 6x2 - 31x - 30 as shown: ac = -180 and b = 31 36(-5) = -180 and 36 + (-5) = 31 6x2 + 36x - 5x - 30 6x(x + 6) - 5(x + 6) (x + 6)(6x - 5) Determine if Ginny factored correctly. If not, explain where she made an error. Ginny made a mistake in step 1 when she identified b = 31. It should be b = -31. Ginny was correct until step 3 when she used 36 and -5 as the coefficients of x. Ginny was correct until step 4 when she incorrectly factored the GCF from 5x - 30. Ginny factored the trinomial correctly.

Ginny made a mistake in step 1 when she identified b = 31. It should be b = -31.

Complete the factorization of 3x2 - 5x + 2. Which two factors can be multiplied together to make this trinomial? (x - 2) (x - 1) (x + 1) (3x - 2) (3x + 2)

(x - 1) / (3x - 2)

Complete the factorization of 3x2 - 10x + 8. 3x2 - 10x + 8 = (x - )( x - 4)

2 / 3

Represent the quadratic polynomial 2x2 + x - 6 using algebra tiles and determine the equivalent factored form. The number of zero pairs needed to model this polynomial is2 34 5 . The equivalent factored form is(2x - 3)(x + 2)(2x + 3)(x - 2)(2x + 2)(x - 3)(2x - 2)(x + 3) .

3 / (2x-3)(x+2)

Consider the trinomial 9x2 + 21x + 10. What value is placed on top of the X? What value is placed on the bottom of the X? What is the factored form of 9x2 + 21x + 10?

90 / 21 / (3x + 2)(3x +5)

A prime polynomial cannot be written as a product of lower-degree polynomials. Which polynomial is prime? 8x2 - 10x - 3 8x2 + 2x - 3 8x2 - 6x - 3 8x2 + 23x - 3

8x2 - 6x - 3

If you are using algebra tiles to factor a trinomial of the form ax2 + bx + c, when would you need to bring in zero pairs? Why?

If the value of c is negative, you would need zero pairs to model the factorization of the polynomial. The x-tiles on the board determine what the constants are in the factors. The product of these constants is equal to the value of c, so you would need positive tiles on one side of the x-squared tile and negative x-tiles on the other side to have opposite signs on the constants. Opposite signs on the constants will result in a negative value for c when multiplying the factors.

The trinomial 2x2 + 13x + 6 has a linear factor of x + 6. 2x2 + 13x + 6 = (x + 6)(?) What is the other linear factor? x + 3 x + 6 2x + 1 2x + 3

2x + 1

Which statement is true of a rectangle that has an area of 4x2 + 39x - 10 square units and a width of (x + 10) units? The rectangle is a square. The rectangle has a length of (2x - 5) units. The perimeter of the rectangle is (10x + 18) units. The area of the rectangle can be represented by (4x2 + 20x - 2x - 10) square units.

The perimeter of the rectangle is (10x + 18) units.