Question
Use synthetic division to divide. (x^3+14x^2+8x-9)/(x+5) (x^3+14x^2+8x-9)/(x+5)=square (Simplify your answer. Do not factor.)
Solution
4.5
(230 Votos)
André
Elite · Tutor por 8 anos
Resposta
To use synthetic division to divide
, we first need to rewrite the divisor
in the form
. In this case,
.The coefficients of the polynomial
are
.Now, we set up the synthetic division:
Here's the step-by-step process:1. Bring down the first coefficient (1).2. Multiply -5 by the value just written below the line (1), which gives -5. Write this under the next coefficient (14).3. Add the values in the second column: \(14 + (-5) = 9\).4. Multiply -5 by the new value (9), which gives -45. Write this under the next coefficient (8).5. Add the values in the third column: \(8 + (-45) = -37\).6. Multiply -5 by the new value (-37), which gives 185. Write this under the next coefficient (-9).7. Add the values in the fourth column:
.The final row gives the coefficients of the quotient polynomial and the remainder. The quotient polynomial is
and the remainder is 176.So, the result of the division is:
In simplified form, without factoring the remainder, the answer is: