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Factorise a Polynomial with Integers>
Factorise a Polynomial with IntegersFactorise a Polynomial with Integers
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Question 1 of 6
1. Question
Factor.`-18x+9`Hint
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A Greatest Common Factor is the factor of two terms with the highest value.First, find the Greatest Common Factor (GCF) of the two terms.Factors of `18x`: `1``times2times``9``times x`Factors of `9`: `1``times``9`Collect the common factors and multiply them all to get the GCF.GCF `=` `1``times``9` `=` `9` Since the first term is negative, we can make the GCF negative as well to make the factorising easier.Therefore, the GCF that we will use is `-9`.Finally, factor by placing `-9` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `-9`, then simplify.`-9[(-18xdiv(-9))+(9div(-9))]` `=` `-9[2x+(-1)]` `=` `-9(2x-1)` `-9(2x-1)` -
Question 2 of 6
2. Question
Factor.`-2m-6`Hint
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A Greatest Common Factor is the factor of two terms with the highest value.First, find the Greatest Common Factor (GCF) of the two terms.Factors of `2m`: `2``times m`Factors of `6`: `2``times3`Since the first term is negative, we can make the GCF negative as well to make the factorising easier.Therefore, the GCF that we will use is `-2`.Finally, factor by placing `-2` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `-2`, then simplify.`-2[(-2mdiv(-2))-(6div(-2))]` `=` `-2[m-(-3)]` `=` `-2(m+3)` `-2(m+3)` -
Question 3 of 6
3. Question
Factor.`-6ab^2+30ab`Hint
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A Greatest Common Factor is the factor of two terms with the highest value.First, find the Greatest Common Factor (GCF) of the two terms.Factors of `6ab^2`: `6``times``a``times``b``times b`Factors of `30ab`: `5times``6``times``a``times``b`Collect the common factors and multiply them all to get the GCF.GCF `=` `6``times``a``times``b` `=` `6ab` Since the first term is negative, we can make the GCF negative as well to make the factorising easier.Therefore, the GCF that we will use is `-6ab`.Finally, factor by placing `-6ab` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `-6ab`, then simplify.`-6ab[(-6ab^2div(-6ab))+(30abdiv(-6ab))]` `=` `-6ab[b+(-5)]` `=` `-6ab(b-5)` `-6ab(b-5)` -
Question 4 of 6
4. Question
Factor.`-20m-10m^2`Hint
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A Greatest Common Factor is the factor of two terms with the highest value.First, find the Greatest Common Factor (GCF) of the two terms.Factors of `20m`: `2times``10``times``m`Factors of `10m^2`: `1times``10``times``m``times m`Collect the common factors and multiply them all to get the GCF.GCF `=` `10``times``m` `=` `10m` Since the first term is negative, we can make the GCF negative as well to make the factorising easier.Therefore, the GCF that we will use is `-10m`.Finally, factor by placing `-10m` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `-10m`, then simplify.`-10m[(-20mdiv(-10m))-(10m^2div(-10m))]` `=` `-10m(2+m)` `-10m(2+m)` -
Question 5 of 6
5. Question
Factor.`-8x^2+20x`Hint
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A Greatest Common Factor is the factor of two terms with the highest value.First, find the Greatest Common Factor (GCF) of the two terms.Factors of `8x^2`: `2times``4``times``x``times x`Factors of `20x`: `4``times5times``x`Collect the common factors and multiply them all to get the GCF.GCF `=` `4``times``x` `=` `4x` Since the first term is negative, we can make the GCF negative as well to make the factorising easier.Therefore, the GCF that we will use is `-4x`.Finally, factor by placing `-4x` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `-4x`, then simplify.`-4x[(-8x^2div(-4x))+(20xdiv(-4x))]` `=` `-4x[2x+(-5)]` `=` `-4x(2x-5)` `-4x(2x-5)` -
Question 6 of 6
6. Question
Factor.`-26b^2c-39bc^2`Hint
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A Greatest Common Factor is the factor of two terms with the highest value.First, find the Greatest Common Factor (GCF) of the two terms.Start by listing down their factors.Factors of `26b^2c`: `2times``13``times` `b` `times b times` `c`Factors of `39bc^2`: `3times``13``times` `b` `times` `c``times c`Collect the common factors and multiply them all to get the GCF.GCF `=` `13``times``b``times``c` `=` `13bc` Since the first term is negative, we can make the GCF negative as well to make the factorising easier.Therefore, the GCF that we will use is `-13bc`.Finally, factor by placing `-13bc` outside a bracket.Also, place the given polynomial inside the bracket with each term divided by `-13bc`, then simplify.`-13bc[(-26b^2cdiv-13bc)+(-39bc^2div-13bc)]` `=` `-13bc[2b+(3c)]` `=` `-13bc(2b+3c)` `-13bc(2b+3c)`
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- Factorise Difference of Two Squares 3
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- Factorise Difference of Two Squares (Harder) 2
- Factorise Difference of Two Squares (Harder) 3
- Factorise Trinomials (Quadratics) 1
- Factorise Trinomials (Quadratics) 2
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