Podcast
Questions and Answers
Factor the quadratic equation $x² + 22x + 121 = 0$. What are its factors?
Factor the quadratic equation $x² + 22x + 121 = 0$. What are its factors?
(x + 11)(x + 11) or (x + 11)²
Calculate the profit made on a bicycle that costs $180 and is sold for $240. What is the profit amount?
Calculate the profit made on a bicycle that costs $180 and is sold for $240. What is the profit amount?
$60
Simplify the expression $3 - \frac{2}{8}$ into a single fraction. What is the simplified result?
Simplify the expression $3 - \frac{2}{8}$ into a single fraction. What is the simplified result?
$\frac{22}{8}$ or $\frac{11}{4}$
What are the cube roots of 729? Provide the answer.
What are the cube roots of 729? Provide the answer.
Find the value of 'x' for the equation $x² - 19x + 60 = 0$. What are the roots?
Find the value of 'x' for the equation $x² - 19x + 60 = 0$. What are the roots?
Flashcards
Factorize x² + 22x + 121
Factorize x² + 22x + 121
Rewrite the equation as (x + 11)² = 0. This involves finding two numbers that add to 22 and multiply to 121. In this case, 11 + 11 = 22 and 11 * 11 = 121. This is a perfect square trinomial.
Find x in x² + 9x + 22 = 0
Find x in x² + 9x + 22 = 0
Factor the quadratic equation to get (x + 11)(x + 2) = 0, leading to the solutions x = -11 or x = -2.
√256
√256
The square root of 256 is 16 because 16 multiplied by itself equals 256.
³√1331
³√1331
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Factor (4m - 6my - 18mz)
Factor (4m - 6my - 18mz)
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Study Notes
Equations and Factoring
- Factorize equations: x² + 22x + 121 = 0, x² - 3x - 28 = 0, x² + 9x + 22 = 0, x² - 19x + 60 = 0
- Find 'x' in equations
- Find square roots without calculators: √256, √289, √361, √625
- Calculate seconds in 2 hours
- Find profit when a bicycle is sold for $240 with a cost of $180
- Find cube roots without calculators: ³√1331, ³√125, ³√64, ³√729
Cost and Profit
- Calculate pen cost if nine pens cost $29
- Calculate the value of 'a' if a: 400 = 6:24
- Find the values for HCF of 168 and 140
Calculations
- Evaluate expressions: 12 + 6²−8, 6×3 + 8², 12 + 8 ÷ (9−5)
- Convert 72 km/h to m/s
- Evaluate expressions: 63 + 0.9, 0.4 × 0.06, 10 − 7.56, 5.6 + 0.08
Prime Factorization and Fractions
- Express 154 as a product of its prime factors
- Express fractions in simplest form (e.g., 3/2, 1½/ 8, 1½ x 1/3)
Factorization (Polynomial Equations)
- Completely factorize: 4m−6my−18mz, 8ax+12y-4az
- Factorize expressions: 81x² − 27x = 0, (x-3)² = 9, h² - 400 = 0, 400 = t - 250
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