{"id":"act_quizme:math:q1:05","source_id":"act_quizme","source_item_id":"math-q1-05","external_id":"75c450896804d794","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":5,"scored":true,"layout_warning":null,"stem":"Which of the following expressions is equivalent to x squared minus x minus 30 x 2 - x - 30 ?","stimulus":"","stimulus_html":null,"stem_html":"

Which of the following expressions is equivalent to x squared minus x minus 30x2-x-30?

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A. Incorrect. For any product of two binomials (x+a)(x+b)=x2+(a+b)x+ab, the coefficient of the linear term will be a+b and the constant term will be the product ab. You may have known ab=-30 needed to be true but forgot that a+b=-1 also needed to be true.

B. Incorrect. For any product of two binomials (x+a)(x+b)=x2+(a+b)x+ab, the coefficient of the linear term will be a+b and the constant term will be the product ab. You may have known ab=-30 needed to be true but thought that a+b=1 also needed to be true. Instead, a+b=-1 needs to be true.

C. Correct. Note that the trinomial x2-x-30 can be factored as the product of two binomials. For any product of two binomials (x+a)(x+b)=x2+(a+b)x+ab, the coefficient of the linear term will be a+b and the constant term will be the product ab. To factor the quadratic polynomial x2-x-30, identify two real numbers a and b such that a+b=-1 and ab=-30. Among the answer choices, a=-6 and b=5 give the desired results. Therefore, x2-x-30=(x+(-6))(x+5)=(x-6)(x+5).

D. Incorrect. You may have thought that the factors of a trinomial would be the constant term divided by 2, 302=15. Instead, try identifying a product of two binomials, (x+a)(x+b), which simplify to yield the given trinomial.

","correct_answer":["C"],"equiv_key":"fab8ba78b7a7069f846bbb24","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"

(x+3) (x minus 10)(x+3)(x-10)

","ord":0},{"label":"B","content_html":"

(x+6) (x minus 5)(x+6)(x-5)

","ord":1},{"label":"C","content_html":"

(x minus 6) (x+5)(x-6)(x+5)

","ord":2},{"label":"D","content_html":"

(x minus 15) (x minus 15)(x-15)(x-15)

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