subject: Homeroom guidance
Processing Questions: On a sheet of paper, answer the following questions.
1 What are your thoughts and feelings while doing the activity?
2. What are your strengths and weaknesses that you discovered recently?
3. How did your skills, interests, talents, abilities and values help you in discovering your strengths and weaknesses?
4. How does this pandemic affect your thoughts and feelings about yourself?
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Answer:
\huge\purple{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: < /p > < p > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}}
</p><p>
DIRECTIONS :
\begin{gathered} \\ \end{gathered}
Factor the following polynomial
\huge\purple{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: < /p > < p > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}}
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SOLUTION :
\begin{gathered} \\ \end{gathered}
A). 6x - 18
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Factor out \rm\green{6}6 so the answer would be \rm\green{6\left(x-3\right) }6(x−3)
\begin{gathered} \\ \end{gathered}
B). x² - 36
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Rewrite x² - 36 as x² - 6² . the difference of squares can be factored using the rule : a² - b² = ( a - b ) ( a + b ) so therefore the answer is \rm\green{(x-6) (x+6)} .(x−6)(x+6).
\begin{gathered} \\ \end{gathered}
C). x² - 12x + 36
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Factor out common term x - 6 by using distributive property, \rm\green{( x - 6 ) ( x - 6 ).}(x−6)(x−6). then rewrite as a binomial square like this\rm\green{ (x-6) ².}(x−6)².
\begin{gathered} \\ \end{gathered}
D). x²- 6x + 5
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Factor out common term x - 5 by using distributive property so the answer is \rm\green{(x-5) (x-1). }(x−5)(x−1).
\begin{gathered} \\ \end{gathered}
E). x² - x - 12
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Factor out common term x - 4 by using distributive property so the answer is \rm\green{\left(x-4\right)\left(x+3\right) }(x−4)(x+3)
\begin{gathered} \\ \end{gathered}
F). 64x² - 1
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Rewrite 64x² - 1 as (8x)² - 1². The difference of squares can be factored using the rule a² - b² = ( a - b ) ( a + b ) so therefore the answer is \rm\green{\left(8x-1\right)\left(8x+1\right) }(8x−1)(8x+1)
\begin{gathered} \\ \end{gathered}
G). 5x² - 7x - 6
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Factor out common term x - 2 by using distributive property so the answer is \rm\green{\left(x-2\right)\left(5x+3\right) }(x−2)(5x+3)
\begin{gathered} \\ \end{gathered}
H). x³ - 4x² + 4x - 3
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By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}
q
p
, where p divides the constant term -3 and q divides the leading coefficient 1. One such root is 3. Factor the polynomial by dividing it by x - 3. Polynomial x² - x + 1 is not factored since it does not have any rational roots so therefore the answer is \rm\green{\left(x-3\right)\left(x^{2}-x+1\right) }(x−3)(x
2
−x+1)
\huge\purple{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}}
#CarryOnLearning
\begin{gathered}\begin{gathered}\tiny\boxed{\begin{array} {} \red{\bowtie} \:\:\:\:\:\:\: \red{\bowtie}\\ \fcolorbox{color}{skyblue}{\tt{} > < }\\ \: \smile\end{array}}\end{gathered}\end{gathered}
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Explanation:
✏️FACTORING ============================== Directions: Factor the following polynomials. a) 6x - 18 b) x² - 36 c) x²-12x + 36 d) x²- 6x + 5 e) x² - x - 12 f) 64x² - 1 g) 5x² - 7x - 6 h) x³ - 4x² + 4x - 3 Answers: a) \: \tt \large \green{6(x-3)}6(x−3) b) \: \tt \large \green{(x + 6)(x - 6)}(x+6)(x−6) c) \: \tt \large \green{(x - 6)(x - 6)}(x−6)(x−6) d) \: \tt \large \green{(x - 5)(x - 1)}(x−5)(x−1) e) \: \tt \large \green{(x + 3)(x - 4)}(x+3)(x−4) f) \: \tt \large \green{(8x + 1)(8x - 1)}(8x+1)(8x−1) g) \: \tt \large \green{(5x + 3)(x - 2)}(5x+3)(x−2) h) \: \tt \large \green{(x - 3)(x^2-x + 1)}(x−3)(x 2 −x+1) ============================== #CarryOnLearning (ノ^_^)ノ