Question

18. Without actual division, show that (r-3x2 - 13x +15) is exactly
divisible by (x² + 2x - 3).​

Answer 1

Answer:

Here's your answer :-

\begin{gathered} {x}^{2} + 2x - 3 \\ = {x}^{2} + 3x - x - 3 \\ = x(x + 3) - 1(x + 3) \\ = (x + 3)(x - 1)\end{gathered}

x

2

+2x−3

=x

2

+3x−x−3

=x(x+3)−1(x+3)

=(x+3)(x−1)

\begin{gathered}x + 3 = 0 \\ = > x = - 3\end{gathered}

x+3=0

=>x=−3

\begin{gathered}( { - 3})^{3} - 3 \times( { - 3})^{2} - 13 \times - 3 + 15 \\ = > - 27 - 3 \times 9 + 39 + 15 \\ = > - 27 - 27 + 54 \\ = > - 54 + 54 \\ = > 0\end{gathered}

(−3)

3

−3×(−3)

2

−13×−3+15

=>−27−3×9+39+15

=>−27−27+54

=>−54+54

=>0

\begin{gathered}x - 1 = 0 \\ = > x = 1\end{gathered}

x−1=0

=>x=1

\begin{gathered} {1}^{3} - 3 \times {1}^{2} - 13 \times 1 + 15 \\ = > 1 - 3 - 13 + 15 \\ = > - 16 + 16 \\ = > 0\end{gathered}

1

3

−3×1

2

−13×1+15

=>1−3−13+15

=>−16+16

=>0

\begin{gathered}as \: x + 3 \: and \: x - 1 \: is \: divisible \: by \: {x}^{3} - 3 {x}^{2} - 13x + 15 \: \\ so \: {x}^{2} + 2x - 3 \: is \: also \: divisible\end{gathered}

asx+3andx−1isdivisiblebyx

3

−3x

2

−13x+15

sox

2

+2x−3isalsodivisible

Hope it helps

Step-by-step explanation:

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