Without actual division show that x cube -3x square -13x+15 is exactly divisible by x square +2x -3

answer:

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Explanation:

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g(x)=x²+2x-3

=x²+3x-x-3

=x(x+3)-1(x+3)

=(x-1)(x+3)

f(x)=x³-3x²-13x+15

=x³-x²-2x²+2x-15x+15

=x²(x-1)-2x(x-1)-15(x-1)

=(x-1)(x²-2x-15)

=(x-1){x²-5x+3x-15}

=(x-1){x(x-5)+3(x-5)}

=(x-1)(x+3)(x-5)

Hence, f(x) is completely divisible by g(x)

Here's your answer :-

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

x + 3 = 0 \\ = > x = - 3

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

x - 1 = 0 \\ = > x = 1

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

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

Hope it helps

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see the answer above. .

solving and finding the roots of quadratic equation...=> x^2-3x+2

=> x^2-2x-x+2

=> x(x-2)-1(x-2)

=> x=1,2

now putting these values and cheack weather it is satisfying the cubic question or not...

Step-by-step explanation:

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Step-by-step explanation:

put x^2+3x+2=0

x^2+2x+x+2=0

x(x+2)+1(x+2)

(x+2)(x+1) therefore x=-2,-1

f(x)=2x^4-6x^3+3x^2+3x-2

put x=-2

f(x)=2×-2^4-6×-2^3+3×-2^2+3×-2-2

f(x)=2×16-6×-8+3×4-6-2

f(x)=32+48+12-2

f(x)=80+10=90

x=-2 is not a factor

put x=-1

2×-1^4-6×-1^3+3×-1^2+3×-1-2

2×1-6×-1+3×1+3×-1-2

2+6+3-3-2

8-2

6

x=-1is also not a factor

answer:

step-by-step explanation:

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step-by-step explanation:

2x-y/5+6=0

2x-y=0

2x-y+1=0

hope it .