Divide using long division
(4x²+x-3) by (x-3)

The quotient is [tex]4x + 13[/tex] with a remainder [tex]\bold{36}[/tex].       [tex]\begin{gathered}4x + 13 \\\\x - 3 \overline{) 4x^{2} + x - 3} \\\\\quad - \underline{4x^{2} - 12x} \\\\\quad \quad 13x - 3 \\\\\quad \quad - \underline{13x - 39} \\\\\quad \quad \quad 36 \\\end{gathered}[/tex]This shows:Divide the first term [tex]4x^2[/tex] by [tex]x[/tex] to get [tex]4x[/tex].Multiply [tex]4x[/tex] by divisor [tex]x - 3[/tex] to get [tex]4x^2 - 12x[/tex].Subtract to get the new dividend [tex]13x - 3[/tex].Divide [tex]13x[/tex] by [tex]x[/tex] to get [tex]13[/tex].Multiply [tex]13[/tex] by divisor [tex]x - 3[/tex] to get [tex]13x - 39[/tex].Subtract to get remainder [tex]36[/tex].

Answered by Sefton | 2025-08-27