Interactive multiple-choice quiz: Solve by Factoring - Reveal
This worksheet focuses on solving quadratic equations using the factoring method. It covers various forms of trinomials where the leading coefficient is one, such as simple monic trinomials, as well as the difference of squares and factoring out common variables. Students are required to find the roots or solution sets for equations in different variables including x, a, p, and n, reinforcing their algebraic manipulation skills and understanding of the zero-product property.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Factoring the quadratic expression x2 - 9x + 20 gives (x - 4)(x - 5) = 0. Applying the zero-product property, we get x - 4 = 0 or x - 5 = 0, which results in x = 4 and x = 5.
Question 2
DB ID: 1063
Points: 1
Solve by factoring: x2 + 3x - 18 = 0
Explanation
Factoring the quadratic expression x2 + 3x - 18 gives (x + 6)(x - 3) = 0. Setting each factor to zero gives x = -6 and x = 3.
Question 3
DB ID: 1064
Points: 1
Solve for a by factoring: a2 + 2a - 24 = 0
Explanation
Factoring a2 + 2a - 24 results in (a + 6)(a - 4) = 0. The roots are a = -6 and a = 4.
Question 4
DB ID: 1065
Points: 1
Solve by factoring: a2 - 9a + 8 = 0
Explanation
Factoring a2 - 9a + 8 yields (a - 8)(a - 1) = 0. Solving for a gives a = 8 and a = 1.
Question 5
DB ID: 1066
Points: 1
Solve by factoring: p2 + 12p + 35 = 0
Explanation
Factoring p2 + 12p + 35 gives (p + 7)(p + 5) = 0. The solutions are p = -7 and p = -5.
Question 6
DB ID: 1067
Points: 1
Solve by factoring: n2 - 15n + 56 = 0
Explanation
Factoring n2 - 15n + 56 gives (n - 7)(n - 8) = 0. The solutions are n = 7 and n = 8.
Question 7
DB ID: 1068
Points: 1
x2 - 6x - 7 = 0
Explanation
The expression factors into (x - 7)(x + 1) = 0, giving roots x = 7 and x = -1.
Question 8
DB ID: 1069
Points: 1
n2 + 6n - 27 = 0
Explanation
The expression factors into (n + 9)(n - 3) = 0, giving roots n = -9 and n = 3.
Question 9
DB ID: 1070
Points: 1
x2 + 15x + 44 = 0
Explanation
The expression factors into (x + 11)(x + 4) = 0, giving roots x = -11 and x = -4.
Question 10
DB ID: 1071
Points: 1
Solve: n2 - 2n = 0
Explanation
Factoring out the common term n gives n(n - 2) = 0. Thus n = 0 or n - 2 = 0, meaning n = 0 and n = 2.
Question 11
DB ID: 1072
Points: 1
Solve: 16a2 - 9 = 0
Explanation
This is a difference of squares: (4a)2 - 32 = 0, which factors to (4a - 3)(4a + 3) = 0. Solving for a gives \(a = \frac{3}{4}\) and \(a = -\frac{3}{4}\).
Question 12
DB ID: 1073
Points: 1
Solve for x by factoring: x2 - 8x + 12 = 0
Explanation
Factoring the quadratic gives (x - 2)(x - 6) = 0. The solutions are x = 2 and x = 6.
Question 16
DB ID: 1074
Points: 1
n2 - n - 90 = 0
Explanation
Factoring n2 - n - 90 gives (n - 10)(n + 9) = 0. Setting each factor to zero results in n = 10 and n = -9.
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