{"questions":[{"uuid":"97534db1-e694-4653-92ee-8dbb9e59bc57","question":"What is the factorization of

6x^2 + 11x - 10

?","answer":"(3x - 2)(2x + 5)","alternatives":["(2x - 5)(3x + 2)","(6x - 5)(x + 2)","(x - 1)(6x + 10)"],"answerExplanation":"To factor

6x^2 + 11x - 10

, find two numbers that multiply to

6\\cdot(-10) = -60

and add to

11

. These numbers are

15

and

-4

. Rewrite the middle term,

11x

, as

15x - 4x

6x^2 + 15x - 4x - 10

. Factor by grouping:

(3x(2x + 5) - 2(2x + 5))

, so the factors are

(3x - 2)(2x + 5)

.","hint":"Consider factor pairs of the product of the first and last coefficients that add up to the middle coefficient.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"97534db1-e694-4653-92ee-8dbb9e59bc57"},{"uuid":"77d4b0a5-9239-45f4-9303-42811a197711","question":"What is the factorization of

8x^2 - 14x + 3

?","answer":"(4x - 1)(2x - 3)","alternatives":["(8x - 3)(x - 1)","(2x - 1)(4x + 3)","(4x + 1)(2x + 3)"],"answerExplanation":"To factor

8x^2 - 14x + 3

, find two numbers that multiply to

8\\cdot3 = 24

and add to

-14

. These numbers are

-12

and

-2

. Rewrite the middle term,

-14x

, as

-12x - 2x

8x^2 - 12x - 2x + 3

. Factor by grouping:

(4x(2x - 3) - 1(2x - 3))

, so the factors are

(4x - 1)(2x - 3)

.","hint":"Look for two numbers that multiply to the product of the quadratic and linear terms and add to the linear coefficient.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"77d4b0a5-9239-45f4-9303-42811a197711"},{"uuid":"38e1cf78-72e7-4e21-a7bf-e9ccc5b5b498","question":"What is the factorization of

12x^2 + 7x - 10

?","answer":"(3x - 2)(4x + 5)","alternatives":["(4x - 5)(3x + 2)","(2x - 5)(6x + 10)","(6x - 5)(2x + 1)"],"answerExplanation":"To factor

12x^2 + 7x - 10

, find two numbers that multiply to

12\\cdot(-10) = -120

and add to

7

. These numbers are

15

and

-8

. Rewrite the middle term,

7x

, as

15x - 8x

12x^2 + 15x - 8x - 10

. Factor by grouping:

(3x(4x + 5) - 2(4x + 5))

, so the factors are

(3x - 2)(4x + 5)

.","hint":"Consider factor pairs of the product of the leading coefficient and the constant term that sum to the middle coefficient.","imageEnabled":false,"duration":30,"latexEnabled":false,"audioEnabled":false,"htmlEnabled":true,"questionId":"38e1cf78-72e7-4e21-a7bf-e9ccc5b5b498"}]}

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