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Question 1 of 6
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Multiply the terms in the numerator and then in the denominator.
3 x 2 4 x × 5 x 2 10 x 3
=
3 x 2 × 5 x 2 4 x × 10 x 3
=
( 3 × 5 ) x 2 + 2 ( 4 × 10 ) x 1 + 3
Multiply the constants and the variables
=
15 x 4 40 x 4
Apply Multiplication Rule of Exponents
=
15 40
=
3 8
Express in lowest terms
Question 2 of 6
Multiply
m 2 - 5 m - 6 m - 2 × 4 m - 8 m - 6
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Look for polynomials that can be factorised before proceeding with the operation. Since the numerator of the first term is in standard form ( a x 2 + b x + c = 0 ) we can factorise using the cross method.
To factorise, we need to find two numbers that add to - 5 and multiply to - 6
- 6 and 1 fit both conditions
Read across to get the factors.
Do the same for the numerator of the second term.
Rewrite the expression with the factors.
m 2 - 5 m - 6 m - 2 × 4 m - 8 m - 6
=
( m - 6 ) ( m + 1 ) m - 2 × 4 ( m - 2 ) m - 6
=
( m + 1 ) × 4
Cancel out m - 6 and m - 2
=
4 ( m + 1 )
Simplify
Question 3 of 6
Multiply
4 x 2 + 4 x 5 x 2 - 5 x - 60 × x 2 - 6 x + 8 x 2 - 2 x
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Look for polynomials that can be factorised before proceeding with the operation.
4 x 2 + 4 x
=
4 x ( x + 1 )
5 x 2 - 5 x - 60
=
5 ( x 2 - x - 12 )
x 2 - 2 x
=
x ( x - 2 )
The denominator of the first term is in standard form ( a x 2 + b x + c = 0 ) so we can factorise using the cross method.
To factorise, we need to find two numbers that add to - 1 and multiply to - 12
- 4 and 3 fit both conditions
Read across to get the factors.
The numerator of the second term is also in standard form ( a x 2 + b x + c = 0 ) so we can factorise using the cross method.
To factorise, we need to find two numbers that add to - 6 and multiply to 8
- 4 and - 2 fit both conditions
Read across to get the factors.
Rewrite the expression with the factors.
4 x 2 + 4 x 5 x 2 - 5 x - 60 × x 2 - 6 x + 8 x 2 - 2 x
=
4 x ( x + 1 ) 5 ( x - 4 ) ( x + 3 ) × ( x - 4 ) ( x - 2 ) x ( x - 2 )
=
4 ( x + 1 ) 5 ( x + 3 )
Cancel out x , x - 4 and x - 2
Question 4 of 6
Divide
6 a 2 + 11 a - 10 3 a - 2 ÷ ( 2 a + 5 )
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Since the numerator of the first term is in standard form ( a x 2 + b x + c = 0 ) we can factorise using the cross method.
To factorise, we need to find two numbers that add to 11 and multiply to - 10
3 a , 2 a , - 2 and 5 fit both conditions
Read across to get the factors.
6 a 2 + 11 a - 10 3 a - 2 ÷ ( 2 a + 5 )
=
( 3 a - 2 ) ( 2 a + 5 ) 3 a - 2 ÷ ( 2 a + 5 )
=
( 3 a - 2 ) ( 2 a + 5 ) 3 a - 2 × 1 2 a + 5
Apply Division Formula
=
1
3 a - 2 and 2 a + 5 cancel out in the denominator
Question 5 of 6
Divide
3 x 2 - 9 x x 2 - 12 x + 36 ÷ x 3 - 9 x x - 6
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Since the denominator of the first term is in standard form ( a x 2 + b x + c = 0 ) we can factorise using the cross method.
To factorise, we need to find two numbers that add to - 12 and multiply to 36
- 6 and - 6 fit both conditions
Read across to get the factors.
Factorise remaining expressions.
3 x 2 - 9 x
=
3 x ( x - 3 )
Factor 3 x out
x 3 - 9 x
=
x ( x 2 - 9 )
Factor x out
=
x ( x - 3 ) ( x + 3 )
x 2 - 9 = ( x - 3 ) ( x + 3 )
3 x 2 - 9 x x 2 - 12 x + 36 ÷ x 3 - 9 x x - 6
=
3 x 2 - 9 x x 2 - 12 x + 36 × x - 6 x 3 - 9 x
Apply Division Formula
=
3 x ( x - 3 ) ( x - 6 ) ( x - 6 ) × x - 6 x ( x - 3 ) ( x + 3 )
Show factors
=
3 ( x - 6 ) ( x + 3 )
Cancel out like terms
Question 6 of 6
Divide
m 2 + 2 m - 8 m 2 - 3 m + 2 ÷ m 2 + 5 m + 4 m 2 - 4 m + 3
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Since the given polynomials are in standard form ( a x 2 + b x + c = 0 ) we can factorise using the cross method.
To factorise, we need to find two numbers that add to 2 and multiply to - 8
4 and - 2 fit both conditions
Read across to get the factors.
Do the same for the remaining polynomials.
To factorise, we need to find two numbers that add to - 3 and multiply to 2
- 2 and - 1 fit both conditions
Read across to get the factors.
To factorise, we need to find two numbers that add to 5 and multiply to 4
4 and 1 fit both conditions
Read across to get the factors.
To factorise, we need to find two numbers that add to - 4 and multiply to 3
- 3 and - 1 fit both conditions
Read across to get the factors.
m 2 + 2 m - 8 m 2 - 3 m + 2 ÷ m 2 + 5 m + 4 m 2 - 4 m + 3
=
m 2 + 2 m - 8 m 2 - 3 m + 2 × m 2 - 4 m + 3 m 2 + 5 m + 4
Apply Division Formula
=
( m + 4 ) ( m - 2 ) ( m - 2 ) ( m - 1 ) × ( m - 3 ) ( m - 1 ) ( m + 4 ) ( m + 1 )
Show factors
=
m - 3 m + 1
Cancel out like terms