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Factorise Trinomials (Quadratics) w Coefficient more than 1>
Factorise Trinomials (Quadratics) w Coefficient more than 1 (1)Factorise Trinomials (Quadratics) w Coefficient more than 1 (1)
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Question 1 of 4
1. Question
Factorise.`3m^2+24m+36`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 `3m^2`: `3``timesmtimesm`Factors of `24m`: `3``times8timesm`Factors of `36`: `3``times12`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[(3m^2div3)+(24mdiv3)+(36div3)]` `=` `3(m^2+8m+12)` Now, use the cross method to factorise `m^2+8m+12`Start by drawing a cross.
Then, find two numbers that will multiply into `12` and add up to `8`Product Sum `3` and `4` `12` `7` `2` and `6` `12` `8` `2` and `6` fits this description.Write `2` and `6` on the right side of the cross.
Now, find two values that will multiply into `m^2` and write them on the left side of the cross.`m` and `m` fits this description.
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(m+2)(m+6)`.`3(m+2)(m+6)` -
Question 2 of 4
2. Question
Factorise.`5b^2-30b-135`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 `5b^2`: `5``timesbtimesb`Factors of `30b`: `5``times6timesb`Factors of `135`: `5``times27`All the terms have `5` as their factor, so it is the HCF.Next, factorise by placing `5` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `5`, then simplify.`5[(5b^2div5)-(30bdiv5)-(135div5)]` `=` `5(b^2-6b-27)` Now, use the cross method to factorise `b^2-6b-27`Start by drawing a cross.Then, find two numbers that will multiply into `-27` and add up to `-6`Product Sum `1` and `-27` `-27` `-26` `3` and `-9` `-27` `-6` `3` and `-9` fits this description.Write `3` and `-9` on the right side of the cross.
Now, find two values that will multiply into `b^2` and write them on the left side of the cross.`b` and `b` fits this description.
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 `5(b+3)(b-9)`.`5(b+3)(b-9)` -
Question 3 of 4
3. Question
Factorise.`4x^2-32x+60`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 `4x^2`: `4``timesxtimesx`Factors of `32x`: `4``times8timesx`Factors of `60`: `4``times15`All the terms have `4` as their factor, so it is the HCF.Next, factorise by placing `4` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `4`, then simplify.`4[(4x^2div4)-(32xdiv4)+(60div4)]` `=` `4(x^2-8x+15)` Now, use the cross method to factorise `x^2-8x+15`Start by drawing a cross.
Then, find two numbers that will multiply into `15` and add up to `-8`Product Sum `1` and `-15` `-15` `-14` `-3` and `-5` `15` `-6` `-3` and `-5` fits this description.Write `-3` and `-5` on the right side of the cross.
Now, find two values that will multiply into `x^2` and write them on the left side of the cross.`x` and `x` fits this description.
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 `4(x-3)(x-5)`.`4(x-3)(x-5)` -
Question 4 of 4
4. Question
Factorise.`2m^2+7m+3`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `2m^2+7m+3`Start by drawing a cross.Now, find two values that will multiply into `2m^2` and write them on the left side of the cross.`2m` and `m` fits this description.
Next, find two numbers that will multiply into `3` and, when cross-multiplied to the values to the left side, will add up to `7m`.Product Sum when Cross-Multiplied `3` and `1` `3` `(2mtimes1)+(mtimes3)=4m` `1` and `3` `3` `(2mtimes3)+(mtimes1)=7m` `1` and `3` fits this description.Now, write `1` and `3` 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 `(2m+1)(m+3)`.`(2m+1)(m+3)`
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