Example Question - factorization method
Here are examples of questions we've helped users solve.
Solving a Quadratic Equation
\[ \begin{align*} 2x^2 - 4x - 6 &= 0\\ x^2 - 2x - 3 &= 0 \quad \text{(Divide by 2)}\\ (x - 3)(x + 1) &= 0\\ x - 3 &= 0 \ \text{or} \ x + 1 = 0\\ x &= 3 \ \text{or} \ x = -1 \end{align*} \]
Finding the Greatest Common Divisor (GCD)
To find the greatest common divisor (GCD) or "faktor sepunya terbesar (FSTB)" as indicated in the question for a set of numbers, we need to find the largest number that divides each of the numbers without leaving a remainder. In the image, it looks like you're interested in solving option (e) which lists the numbers 42, 105, and 126. Let's find the GCD of these numbers: The prime factors for each number are: - 42 = 2 × 3 × 7 - 105 = 3 × 5 × 7 - 126 = 2 × 3^2 × 7 The GCD is the product of the lowest powers of common primes among these numbers. In this case, the common prime factors are 3 and 7. So, we take the lowest power of 3 that is common to all, which is 3^1 (since 3^2 is not a factor of 42 and 105), and the lowest power of 7, which is 7^1. Now multiply these together to find the GCD: 3^1 × 7^1 = 3 × 7 = 21 So, the greatest common divisor of 42, 105, and 126 is 21.
Factoring a Difference of Squares
The expression in the image is: \[ 100 - 121x^2 \] This is a difference of squares, which can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a^2 = 100 \) and \( b^2 = 121x^2 \). Therefore, the square roots are \( a = 10 \) and \( b = 11x \). The factored form is: \[ (10 - 11x)(10 + 11x) \]
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