How do you use synthetic division to divide $4 a^{2} + 19 a + 21$ $4a^2 + 19a + 21$ by $a + 1$ $a+1$ ?

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How do you use synthetic division to divide $4 a^{2} + 19 a + 21$ $4a^2 + 19a + 21$ by $a + 1$ $a+1$ ?

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Answer 1 · 2015-10-14T18:06:00

$4 a^{2} + 19 a + 21$ $4a^2 + 19a + 21$ divided by $a + 1$ $a+1$

$a + 1 = a - (- 1)$ $a+1=a-(-1)$

$-1 ∣ ∣$ $"-1" ||$ $41921$ $"4 " " " "19 " " " "21 "$
$+$ $+$ $-4 -15$ $"" " " " " "" "-4" " " " -15" "$
$"" " "$ $- - - - - -$ $------$
$415 ∣ 6$ $" "" "4" "15" "|6" "$

The quotient is $4 a + 15$ $4a+15$ and the remainder is $6$ $6$

We can check our answer by finding:

$(a + 1) (4 a + 15) + 6$ $(a+1)(4a+15) + 6$

$= 4 a^{2} + 15 a + 4 a + 15 + 6$ $= 4a^2+15a+4a+15 + 6$

$= 4 a^{2} + 19 a + 21$ $= 4a^2+19a+21$ which is the dividend.

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How do you use synthetic division to divide $4 a^{2} + 19 a + 21$ $4a^2 + 19a + 21$ by $a + 1$ $a+1$ ?

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