{"id":"cb_practice_pdf:t5-math-m1-q27","source_id":"cb_practice_pdf","source_item_id":"t5-math-m1-q27","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-5","module_number":1,"position":27,"stem":"The function g is defined by g(x) = x(x−2)(x+6)^2. 7−w The value of g is 0, where w is a constant. What is the sum of all possible values of w?","stimulus":"","stimulus_html":null,"stem_html":"<p>The function g is defined by g(x) = x(x−2)(x+6)^2. 7−w The value of g is 0, where w is a constant. What is the sum of all possible values of w?</p>","rationale_html":"<p>25 - The correct answer is . The value of g^7 wh is the value of g^xh when = - - x 7 w, where w is a constant. Substituting 7 w for x in the given equation 7- = 7- 7- -2 7- +6 2 yields g^ wh ^ wh^ w h^ w h , which is equivalent to 7- = 7- 5- 13- 2 - g^ wh ^ wh^ wh^ wh . It’s given that the value of g^7 wh is 0. - 7- = 7- 5- 13- 2 Substituting 0 for g^7 wh in the equation g^ wh ^ wh^ wh^ wh 0= 7- 5- 13- 2 yields ^ wh^^ wh wh . Since the product of the three factors on the right-hand side of this equation is equal to 0, at least one of these three factors must be equal to 0. Therefore, the possible values of w can be found by setting 7- =0 each factor equal to 0. Setting the first factor equal to 0 yields w . Adding = w to both sides of this equation yields 7 w. Therefore, 7 is one possible value 5- =0 of w. Setting the second factor equal to 0 yields w . Adding w to both = sides of this equation yields 5 w. Therefore, 5 is a second possible value of w. 13- 2=0 Setting the third factor equal to 0 yields ^ wh . Taking the square root of 13- =0 both sides of this equation yields w . Adding w to both sides of this 13= 13 equation yields w. Therefore, is a third possible value of w. Adding the 7+5+13 25 three possible values of w yields , or . Therefore, the sum of all 25 possible values of w is . 41 SAT PRACTICE TEST #5 ANSWER EXPLANATIONS</p>","correct_answer":["7"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}