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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+29x72`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `10x^2+29x72`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 crossmultiplied to the values to the left side, will add up to `29x`.Product Sum when CrossMultiplied `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 `(5x8)(2x+9)`.`(5x8)(2x+9)` 
Question 2 of 4
2. Question
Factorise.`18x^233x+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``times11timesx`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^211x3)` Now, use the cross method to factorise `6x^211x+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 crossmultiplied to the values to the left side, will add up to `11x`.Left Side Product Right Side Product Sum when CrossMultiplied `6x` and `x` `6x^2` `3` and `1` `3` `(6xtimes1)+(xtimes3)=3x` `3x` and `2x` `6x^2` `3` and `1` `3` `(3xtimes1)+(2xtimes3)=9x` `3x` and `2x` `6x^2` `1` and `3` `3` `(3xtimes3)+(2xtimes1)=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(3x1)(2x3)`.`3(3x1)(2x3)` 
Question 3 of 4
3. Question
Factorise.`12y^224y63`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^28y21)` Now, use the cross method to factorise `4y^28y21`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 crossmultiplied to the values to the left side, will add up to `8y`.Left Side Product Right Side Product Sum when CrossMultiplied `4y` and `y` `4y^2` `3` and `7` `21` `(4ytimes7)+(3timesy)=25y` `2y` and `2y` `4y^2` `3` and `7` `21` `(2ytimes7)+(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)(2y7)`.`3(2y+3)(2y7)` 
Question 4 of 4
4. Question
Factorise.`15u2u^2`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `15u2u^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 crossmultiplied to the values to the left side, will add up to `u`.Left Side Product Right Side Product Sum when CrossMultiplied `3` and `5` `15` `2u` and `u` `2u^2` `(3timesu)+(5times2u)=7u` `3` and `5` `15` `u` and `2u` `2u^2` `(3times2u)+(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)(52u)`.`(3+u)(52u)`
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