This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Sawa, Mbari. Hizi hapa njia za kuweka usemi katika vigawo. a) Weka x^2 - x - 20 katika vigawo. Step 1: Tambua namba mbili zinazojumlisha -1 na kuzidisha -20. Namba hizo ni -5 na 4. -5 + 4 = -1 -5 × 4 = -20 Step 2: Andika usemi katika vigawo. x^2 - x - 20 = (x-5)(x+4) Jibu: (x-5)(x+4) b) Weka 3x^2 - 7x - 6 katika vigawo. Step 1: Tafuta namba mbili zinazozidisha 3 × (-6) = -18 na kujumlisha -7. Namba hizo ni -9 na 2. -9 + 2 = -7 -9 × 2 = -18 Step 2: Andika upya neno la kati na weka katika vigawo kwa kupanga. 3x^2 - 7x - 6 = 3x^2 - 9x + 2x - 6 = 3x(x - 3) + 2(x - 3) = (3x + 2)(x - 3) Jibu: (3x+2)(x-3) c) Weka x^2 - 64 katika vigawo. Step 1: Tambua kuwa huu ni tofauti ya miraba miwili (a^2 - b^2). Hapa, a^2 = x^2 a = x na b^2 = 64 b = 8. Step 2: Tumia fomula ya tofauti ya miraba miwili: a^2 - b^2 = (a-b)(a+b). x^2 - 64 = (x-8)(x+8) Jibu: (x-8)(x+8) d) Weka x^2 - 25 katika vigawo. Step 1: Tambua kuwa huu ni tofauti ya miraba miwili (a^2 - b^2). Hapa, a^2 = x^2 a = x na b^2 = 25 b = 5. Step 2: Tumia fomula ya tofauti ya miraba miwili: a^2 - b^2 = (a-b)(a+b). x^2 - 25 = (x-5)(x+5) Jibu: (x-5)(x+5) That's 2 down. 3 left today — send the next one.