By Princeton Review
UNLOCK THE secrets and techniques OF ALGEBRA II with THE PRINCETON REVIEW.
Algebra could be a daunting topic. That’s why our new highschool Unlocked sequence specializes in providing you with a variety of key ideas that will help you take on topics like Algebra II. If one procedure does not "click" for you, you should use an alternate method of comprehend the idea that or challenge, rather than painfully making an attempt a similar factor persistently with out luck. belief us—unlocking the secrets and techniques of algebra does not have to hurt!
With this ebook, you’ll realize the hyperlink among summary suggestions and their real-world purposes and construct self assurance as your talents enhance. alongside the best way, you’ll get lots of perform, from absolutely guided examples to self sustaining end-of-chapter drills and test-like samples.
Everything you must learn about Algebra II.
• advanced recommendations defined in transparent, common ways
• Walk-throughs of pattern difficulties for all topics
• transparent objectives and self-assessments that will help you pinpoint parts for extra review
• step by step examples of alternative how one can process difficulties
Practice Your technique to Excellence.
• Drills and perform questions in each chapter
• entire solution reasons to spice up understanding
• ACT- and SAT-like questions for hands-on adventure with how Algebra II might sound on significant exams
High university Algebra II Unlocked covers:
• complicated numbers and polynomials
• graphing and fixing structures of equations
• radical and rational expressions and inequalities
• trigonometric equations
• logarithmic features and operations
• statistical modeling
... and extra!
Read or Download High School Algebra II Unlocked: Your Key to Mastering Algebra II PDF
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Extra info for High School Algebra II Unlocked: Your Key to Mastering Algebra II
Sample text
To factor, look back at the function’s original form, t = (−1/10 p2 + 490)(p) − 10(−1/10 p2 + 490). The binomial is a common factor in the two terms. t = (−1/10 p2 + 490)(p − 10) Factor out the binomial. t = −1/10 (p2 − 4900)(p − 10) Factor out −1/10. t = −1/10 (p + 70)(p − 70)(p − 10) Factor the difference of squares. If 0 = −1/10 (p + 70)(p − 70)(p − 10), then p = −70, p = 70, or p = 10. The function t has zeros of −70, 10, and 70, so these are the x-intercepts (p-intercepts) of its graph. The function generally looks like this.
3x(x − 2)(_____) Factor out (x − 2). At this point, we should be able to recognize that the other factor is (x + 5). However, even if we still don’t see it, we can fall back on the good old quadratic formula. Here is how you may see polynomial factoring on the SAT. Which of the following represents all zeros of the function f(x) = + 9x? A) 3 only B) −3, 3 C) −3, 0, 3 D) −3, 0, 2, 3 We had already found the root 2, so this work with the quadratic formula gave us the other root, −5. The full factorization of the polynomial is −3x(x − 2)(x + 5).
The correct answer is (C). This method is called completing the square, and it’s the same method we use to rewrite quadratic functions in vertex form (see Example 13). To check our work, let’s expand the expression (x6 − 7)2 + 3 to make sure it is equivalent to x12 − 14x6 + 52. (x6 − 7)2 + 3 = (x6)2 − 2(x6)(7) + 72 + 3 Expand the squared binomial using the polynomial identity (a − b)2 = a2 − 2ab + b2. = x12 − 14x6 + 49 + 3 Evaluate exponents and products. = x12 − 14x6 + 52 Combine like terms. You could also expand using FOIL, just in case you have misremembered the identity used here.