اختبار اختيار من متعدد تفاعلي: 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
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
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
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
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
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
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
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
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
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
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
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 13
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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