Tuliskan daftar faktor-faktor suku a dan suku c. Tuliskan dua set tanda kurung dengan tempat kosong. Isilah tempat kosong di depan x dengan pasangan faktor-faktor yang mungkin untuk nilai a. Isilah dua tempat kosong setelah x dengan pasangan faktor-faktor untuk konstanta. Tentukan tandanya (tambah atau kurang) yang ada di antara variabel x dan angkanya. Ujilah pilihanmu menggunakan perkalian pertama-luar-dalam-terakhir (PLDT). Gantilah pilihanmu jika diperlukan. Baliklah urutannya jika diperlukan. Periksa dua kali tandamu jika diperlukan.

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Using the expression format ax2 + bx + c = 0, identify the a and c terms and list out what factors they have. For 3x2 + 2x - 8, that means:a = 3 and has one set of factors: 1 * 3 c = -8 and has four sets of factors: -2 * 4, -4 * 2, -8 * 1, and -1 * 8. You'll be filling in the constants for each expression into the space you've made:(  x    )(  x    ) For the a term in our example, 3x2, there is only one possibility for our example: (3x   )(1x   ) Let's say we chose 8 and 1. Write it in:(3x  8)(x  1) Depending on the signs in the original expression, it's possible to figure out what the signs for the constants should be. Let's call the two constants for our two factors h and k:If ax2 + bx + c then (x + h)(x + k) If ax2 - bx - c or ax2 + bx - c then (x - h)(x + k) If ax2 - bx + c then (x - h)(x - k) For our example, 3x2 + 2x - 8, the signs must be:(x - h)(x + k), giving us the two factors:(3x + 8) and (x - 1) A quick first test to run is to see if the middle term is at least the correct value. If it is not, you may have chosen the wrong c factors. Let's test our answer:(3x + 8)(x - 1) By multiplication, we arrive at:3x2 - 3x + 8x - 8 Simplifying this expression by adding the like terms (-3x) and (8x), we get:3x2 - 3x + 8x - 8 = 3x2 + 5x - 8 We know now that we must have identified the wrong factors:3x2 + 5x - 8 ≠ 3x2 + 2x - 8 In our example, let's try 2 and 4 instead of 1 and 8:(3x + 2)(x - 4) Now our c term is a -8, but our outside/inside product (3x * -4) and (2 * x) is -12x and 2x, which will not combine to make the correct b term of +2x.-12x + 2x = 10x 10x ≠ 2x Let's try moving the 2 and 4 around:(3x + 4)(x - 2) Now, our c term (4 * 2 = 8) is still okay, but the outside/inside products are -6x and 4x. If we combine them:-6x + 4x = 2x 2x ≠ -2x We're pretty close to the 2x we were aiming for, but it's the wrong sign. We're going to stick with the same order, but swap which one has the minus:(3x - 4)(x + 2) Now the c term is still okay, and the outside/inside products are now (6x) and (-4x). Since:6x - 4x = 2x...