Directions: Read each item carefully. Write the letter of the correct answer on the answer sheet provided. Write the solution in a separate sheet.
1. The answer is letter A.
Factoring the expression x² + 5x + 4
x² + 5x + 4
x² + (4x + x) + 4
(x² + 4x) + (x + 4)
x(x + 4) + 1(x +4)
»(x + 1)(x + 4)
2. The answer is letter A.
Factoring the expression 2a² + 5a - 12
2a² + 5a - 12
2a² + (8a - 3a) - 12
(2a² + 8a) + (-3a - 12)
2a(a + 4)+ -3(a + 4)
»(2a - 3)(a + 4)
3. The answer is letter B.
This is a perfect square trinomial because we see that
the first and last terms are perfect squares, and
the middle term is twice the product of the square root of the first and last term.
In factoring these kinds of polynomials, we just focus only on finding the square roots of the first and last terms.
√81x² = 9x
√25y² = 5y
The sign of the second term of the resulting factor depends on the sign of the trinomial being factored.
» The factors are (9x - 5y) and (9x - 5y), or simply, (9x - 5y)²
4. The answer is letter B.
Let y be the second number. Since the sum of the first number x and the second number is 15, we represent this mathematically as:
x + y = 15. Now we solve for y in terms of x.
» y = 15 - x
5. The answer is letter C.
(1) x + y = 17
(2) x² + y² = 169
Solving y in equation 1 in terms of x, we have
y = 17 - x
x² + (17 - x)² = 169
x² + (289 - 34x + x²) = 169
2x² - 34x + 289 = 169
2x² - 34x + 289 - 169 = 0
» 2x² - 34x + 120 = 0
6. The answer is letter C.
We find the last term from the middle term.
2ab = 10
2(1)b = 10
2b = 10
b = 10/2 = 5
We find the last term by squaring b.
b² = 5² = 25
» c = 25
7. The answer is letter C.
Since we assume that the trinomial being factored is a perfect square trinomial, we just focus on finding the square root of the last term to find the second term of the resulting factor/s.
» Second term = √36 = 6
8. The answer is letter C.
Based on the given clues, the trinomial is assumed to be a perfect square trinomial. So, we just focus on squaring the first term of the binomial factor/s to find the first term of the perfect square trinomial.
Answers & Comments
Assessment
Directions: Read each item carefully. Write the letter of the correct answer on the answer sheet provided. Write the solution in a separate sheet.
1. The answer is letter A.
Factoring the expression x² + 5x + 4
» (x + 1)(x + 4)
2. The answer is letter A.
Factoring the expression 2a² + 5a - 12
» (2a - 3)(a + 4)
3. The answer is letter B.
This is a perfect square trinomial because we see that
In factoring these kinds of polynomials, we just focus only on finding the square roots of the first and last terms.
The sign of the second term of the resulting factor depends on the sign of the trinomial being factored.
» The factors are (9x - 5y) and (9x - 5y), or simply, (9x - 5y)²
4. The answer is letter B.
Let y be the second number. Since the sum of the first number x and the second number is 15, we represent this mathematically as:
» y = 15 - x
5. The answer is letter C.
Solving y in equation 1 in terms of x, we have
» 2x² - 34x + 120 = 0
6. The answer is letter C.
We find the last term from the middle term.
We find the last term by squaring b.
» c = 25
7. The answer is letter C.
Since we assume that the trinomial being factored is a perfect square trinomial, we just focus on finding the square root of the last term to find the second term of the resulting factor/s.
» Second term = √36 = 6
8. The answer is letter C.
Based on the given clues, the trinomial is assumed to be a perfect square trinomial. So, we just focus on squaring the first term of the binomial factor/s to find the first term of the perfect square trinomial.
» First term = (4x)² = 16x²
9. The answer is letter B.
Factor the expression 18x² + 12x + 2
» 2(3x + 1)²
10. The answer is letter A.
Factor the expression 20x⁴ - 60x³ + 45x².
» 5x²(2x - 3)²
#CarryOnLearning
#LanazaQueenzy
(ノ^_^)ノ