If the price of sugar is increased by 7%, then by how much percent should a housewife reduce her consumption of sugar, to have no extra expenditure?&nbsp;

What do we get after factorizing&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup><mo>+</mo><mo>&nbsp;</mo><mn>8</mn><msup><mi mathvariant="normal">y</mi><mn>3</mn></msup><mo>+</mo><mo>&nbsp;</mo><msup><mi mathvariant="normal">z</mi><mn>3</mn></msup><mo>&nbsp;</mo><mo>–</mo><mo>&nbsp;</mo><mn>6</mn><mi>xyz</mi></math>?

Factorise:&nbsp;<math class="SCXW164504537 BCX2" xmlns="http://www.w3.org/1998/Math/MathML"><mroot class="SCXW164504537 BCX2"><mn class="SCXW164504537 BCX2">2</mn><mrow>&nbsp;</mrow></mroot><msup><mi class="SCXW164504537 BCX2" mathvariant="normal">x</mi><mn class="SCXW164504537 BCX2">2</mn></msup><mo class="SCXW164504537 BCX2">−</mo><mn class="SCXW164504537 BCX2">3</mn><mi class="SCXW164504537 BCX2" mathvariant="normal">x</mi><mo class="SCXW164504537 BCX2">−</mo><mn class="SCXW164504537 BCX2">9</mn><mroot class="SCXW164504537 BCX2"><mn class="SCXW164504537 BCX2">2</mn><mrow>&nbsp;</mrow></mroot></math>&nbsp;

What is the value so k, if (x - 2) is a factor of&nbsp;<math class="SCXW65635256 BCX2" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi class="SCXW65635256 BCX2" mathvariant="normal">x</mi><mn class="SCXW65635256 BCX2">2</mn></msup><mo class="SCXW65635256 BCX2">−</mo><mn class="SCXW65635256 BCX2">4</mn><mi class="SCXW65635256 BCX2" mathvariant="normal">x</mi><mo class="SCXW65635256 BCX2">+</mo><mi class="SCXW65635256 BCX2" mathvariant="normal">k</mi><mo>.</mo></math>.

Find the value of k, if (x - 3) is a factor of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">k</mi><mo>.</mo></math>

If (2x -1) is a factor of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>(</mo><mi mathvariant="normal">x</mi><mo>)</mo><mo>=</mo><mn>8</mn><msup><mi mathvariant="normal">x</mi><mn>4</mn></msup><mo>+</mo><mn>4</mn><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup><mo>-</mo><mn>16</mn><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo>+</mo><mn>10</mn><mi mathvariant="normal">x</mi><mo>+</mo><mi mathvariant="normal">m</mi></math>, then what is the value of m?

If the price of sugar is increased by 7%, then by how much percent should a housewife reduce her consumption of sugar, to have no extra expenditure?

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