Please use a caret (^) to exhibit exponents in undeniable textual content. x3 is technically multiplication of x by technique of three. because the elementary convention is to placed a coefficient earlier a letter, maximum individuals receives what you recommend, yet a large number of individuals received't. (x^3 ? 3x² ? 4x + 12) ÷ (x + 2) first of all divide by technique of x + 2. this may seem difficult, yet undergo in ideas lengthy branch. regardless of if that is difficult to placed up lengthy branch on the position, i visit target to :-P it really is type of comparable to one hundred forty four ÷ 12, notwithstanding it truly is utilising polynomials truly of coefficients. you probably did this by technique of: a million. wearing down a digit of one hundred forty four, until eventually you had a quantity higher than or equivalent to twelve. 2. searching the most important assorted of 12 that replaced into below or equivalent to the digits that you presently have. 3. putting the dept of that assorted by technique of 12, over the dept container. 4. Subtracting this assorted by technique of the digits that you've. 5. Repeat step a million until eventually you've a quantity that elevated by technique of 12 provides one hundred forty four. So operating example: Run a million, step a million: carry down the digits, you've 14, that is higher than 12. step 2: the optimal assorted is 12. step 3: 12 ÷ 12 = a million, placed a million on correct. step 4: 14 ? 12 = 2, step 5: Repeat. Run 2, step 2: carry down the digits, you've 24, that is higher than 12. step 2: the optimal assorted is 24. step 3: 24 ÷ 12 = 2, placed 2 on correct, giving 12. step 4: 24 ? 24 = 0 step 5: end, your answer is 12, which elevated by technique of 12 provides one hundred forty four. this may be mathematically expressed as: one hundred forty four / 12 = (10·12 + 24)/12 = 10 + 24/12 = 10 + 2 = 12 With that in ideas, enable's proceed: (x^3 ? 3x² ? 4x + 12) / (x + 2) = (x²·(x + 2) ? 5x² ? 4x + 12) / (x + 2) = end, x^3 ? 3x² = x²·(x + 2) ? 5x², (x + 2) is the dividend (like 12 in our previous social gathering), x² is the quotient (like 10 in our previous social gathering), and ? 5x² is the the relax (like 24 in our previous social gathering). Simplify. x² + (?5x² ? 4x + 12) / (x + 2) = Now use that branch approach. x² + (?5x·(x + 2) + 6x + 12) / (x + 2) = Simplify. x² ? 5x + (6x + 12) / (x + 2) something cancels out, x + 2 on correct, and x + 2 on the bottom, ensuing in 6. x² ? 5x + 6 you are able to now in simple terms use the foil approach. what quantity 2 numbers multiply to 6 and upload as a lot as ?5? ?3 and ?2. Your answer is (x^3 ? 3x² ? 4x + 12) / (x + 2) = (x ? 3)(x ? 2).
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Verified answer
X^3 - 3X^2 + 4X - 12
(take X^2 common in the first 2 terms; 4 common in the next 2 terms)
= X^2 (X-3) + 4 (X-3)
(now take X-3 common from both terms)
= (X-3) [X^2 + 4 ]
I guess this should be the answer.
Please use a caret (^) to exhibit exponents in undeniable textual content. x3 is technically multiplication of x by technique of three. because the elementary convention is to placed a coefficient earlier a letter, maximum individuals receives what you recommend, yet a large number of individuals received't. (x^3 ? 3x² ? 4x + 12) ÷ (x + 2) first of all divide by technique of x + 2. this may seem difficult, yet undergo in ideas lengthy branch. regardless of if that is difficult to placed up lengthy branch on the position, i visit target to :-P it really is type of comparable to one hundred forty four ÷ 12, notwithstanding it truly is utilising polynomials truly of coefficients. you probably did this by technique of: a million. wearing down a digit of one hundred forty four, until eventually you had a quantity higher than or equivalent to twelve. 2. searching the most important assorted of 12 that replaced into below or equivalent to the digits that you presently have. 3. putting the dept of that assorted by technique of 12, over the dept container. 4. Subtracting this assorted by technique of the digits that you've. 5. Repeat step a million until eventually you've a quantity that elevated by technique of 12 provides one hundred forty four. So operating example: Run a million, step a million: carry down the digits, you've 14, that is higher than 12. step 2: the optimal assorted is 12. step 3: 12 ÷ 12 = a million, placed a million on correct. step 4: 14 ? 12 = 2, step 5: Repeat. Run 2, step 2: carry down the digits, you've 24, that is higher than 12. step 2: the optimal assorted is 24. step 3: 24 ÷ 12 = 2, placed 2 on correct, giving 12. step 4: 24 ? 24 = 0 step 5: end, your answer is 12, which elevated by technique of 12 provides one hundred forty four. this may be mathematically expressed as: one hundred forty four / 12 = (10·12 + 24)/12 = 10 + 24/12 = 10 + 2 = 12 With that in ideas, enable's proceed: (x^3 ? 3x² ? 4x + 12) / (x + 2) = (x²·(x + 2) ? 5x² ? 4x + 12) / (x + 2) = end, x^3 ? 3x² = x²·(x + 2) ? 5x², (x + 2) is the dividend (like 12 in our previous social gathering), x² is the quotient (like 10 in our previous social gathering), and ? 5x² is the the relax (like 24 in our previous social gathering). Simplify. x² + (?5x² ? 4x + 12) / (x + 2) = Now use that branch approach. x² + (?5x·(x + 2) + 6x + 12) / (x + 2) = Simplify. x² ? 5x + (6x + 12) / (x + 2) something cancels out, x + 2 on correct, and x + 2 on the bottom, ensuing in 6. x² ? 5x + 6 you are able to now in simple terms use the foil approach. what quantity 2 numbers multiply to 6 and upload as a lot as ?5? ?3 and ?2. Your answer is (x^3 ? 3x² ? 4x + 12) / (x + 2) = (x ? 3)(x ? 2).