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Factor Quadratics with Leading Coefficient more than 1 (3)Factor Quadratics with Leading Coefficient more than 1 (3)
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Question 1 of 4
1. Question
Factorise.`10x^2+29x-72`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `10x^2+29x-72`Start by drawing a cross.
Now, find two values that will multiply into `10x^2` and write them on the left side of the cross.`5x` and `2x` fits this description.
Next, find two numbers that will multiply into `-72` and, when cross-multiplied to the values to the left side, will add up to `29x`.Product Sum when Cross-Multiplied `-9` and `8` `-72` `(5xtimes8)+[2xtimes(-9)]=22x` `-8` and `9` `-72` `(5xtimes9)+[2xtimes(-8)]=29x` `-8` and `9` fits this description.Now, write `-8` and `9` on the right side of the cross.Finally, group the values in a row with a bracket and combine the brackets.
Therefore, the factorised expression is `(5x-8)(2x+9)`.`(5x-8)(2x+9)` -
Question 2 of 4
2. Question
Factorise.`18x^2-33x+9`Hint
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When factorising trinomials, use the Cross Method.First, find the Highest Common Factor (HCF) of the three terms.Start by listing down their factors.Factors of `18x^2`: `3``times6timesxtimesx`Factors of `-33x`: `3``times-11timesx`Factors of `9`: `3``times3`All the terms have `3` as their factor, so it is the HCF.Next, factorise by placing `3` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `3`, then simplify.`3[(18x^2div3)-(33xdiv3)+(9div3)]` `=` `3(6x^2-11x-3)` Now, use the cross method to factorise `6x^2-11x+3`Start by drawing a cross.For the left side, find two values that will multiply into `6x^2` and write them on the left side of the cross.While for the right side, find two numbers that will multiply into `3` and, when cross-multiplied to the values to the left side, will add up to `-11x`.Left Side Product Right Side Product Sum when Cross-Multiplied `6x` and `x` `6x^2` `-3` and `-1` `3` `(6xtimes-1)+(xtimes-3)=-3x` `3x` and `2x` `6x^2` `-3` and `-1` `3` `(3xtimes-1)+(2xtimes-3)=-9x` `3x` and `2x` `6x^2` `-1` and `-3` `3` `(3xtimes-3)+(2xtimes-1)=-11x` `3x` and `2x` fits the left side and `-1` and `-3` fits the right side.Now, write the chosen values on the sides of the cross.Finally, group the values in a row with a bracket and combine the brackets.Remember to add the `HCF` before the brackets.Therefore, the factorised expression is `3(3x-1)(2x-3)`.`3(3x-1)(2x-3)` -
Question 3 of 4
3. Question
Factorise.`12y^2-24y-63`Hint
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When factorising trinomials, use the Cross Method.First, find the Highest Common Factor (HCF) of the three terms.Start by listing down their factors.Factors of `12y^2`: `3``times4timesytimesy`Factors of `24y`: `3``times8timesy`Factors of `63`: `3``times21`All the terms have `3` as their factor, so it is the HCF.Next, factorise by placing `3` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `3`, then simplify.`3[(12y^2div3)-(24ydiv3)-(63div3)]` `=` `3(4y^2-8y-21)` Now, use the cross method to factorise `4y^2-8y-21`Start by drawing a cross.For the left side, find two values that will multiply into `4y^2` and write them on the left side of the cross.While for the right side, find two numbers that will multiply into `-21` and, when cross-multiplied to the values to the left side, will add up to `-8y`.Left Side Product Right Side Product Sum when Cross-Multiplied `4y` and `y` `4y^2` `3` and `-7` `-21` `(4ytimes-7)+(3timesy)=-25y` `2y` and `2y` `4y^2` `3` and `-7` `-21` `(2ytimes-7)+(2ytimes3)=-8y` `2y` and `2y` fits the left side and `3` and `-7` fits the right side.Now, write the chosen values on the sides of the cross.
Finally, group the values in a row with a bracket and combine the brackets.Remember to add the `HCF` before the brackets.Therefore, the factorised expression is `3(2y+3)(2y-7)`.`3(2y+3)(2y-7)` -
Question 4 of 4
4. Question
Factorise.`15-u-2u^2`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `15-u-2u^2`Start by drawing a cross.For the left side, find two values that will multiply into `15` and write them on the left side of the cross.While for the right side, find two numbers that will multiply into `-2u^2` and, when cross-multiplied to the values to the left side, will add up to `-u`.Left Side Product Right Side Product Sum when Cross-Multiplied `3` and `5` `15` `2u` and `-u` `-2u^2` `(3times-u)+(5times2u)=7u` `3` and `5` `15` `u` and `-2u` `-2u^2` `(3times-2u)+(5timesu)=-u` `3` and `5` fits the left side and `5a` and `4a` fits the right side.Now, write the chosen values on the sides of the cross.
Finally, group the values in a row with a bracket and combine the brackets.
Therefore, the factorised expression is `(3+u)(5-2u)`.`(3+u)(5-2u)`
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