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In this lesson, we will learn how to factor quadratics where the coefficient of the leading term is greater than one.

Q1:

Factorise fully 4 π₯ β 3 2 π₯ + 2 8 2 .

Q2:

Factorise fully 6 π₯ β 1 9 π₯ + 1 0 2 .

Q3:

Solve the equation 4 π‘ β 3 2 π‘ + 6 4 = 0 2 by factoring.

Q4:

Find the solution set of the equation 1 8 π₯ + 1 8 π₯ β 3 6 = 0 2 in β .

Q5:

Find the solution set of in .

Q6:

Given that β 1 0 is a root of the equation 2 π₯ + 1 3 π₯ β 7 0 = 0 2 , what is the other root?

Q7:

Find the solution set of 2 π₯ + 5 π₯ β 7 = 0 2 in β .

Q8:

Solve the equation 2 ( π₯ + 1 ) + 5 ( π₯ + 1 ) = 0 2 .

Q9:

Find the solution set of ( 2 π¦ + 4 ) + ( π¦ + 2 ) = 5 2 2 in β .

Q10:

Find the solution set of π₯ ( π₯ + 5 ) 4 β π₯ ( π₯ + 1 ) 8 β 3 ( π₯ + 4 ) 2 + 1 = 0 in β .

Q11:

Find the solution set of β 7 ( π₯ + 7 ) + 9 ( π₯ + 7 ) = 0 2 in β .

Q12:

The roots of the equation π₯ β 1 0 π₯ + 1 6 = 0 2 are πΏ and π , where πΏ > π . Find, in its simplest form, the quadratic equation whose roots are πΏ β 7 and 2 π β 6 2 .

Q13:

Find the solution set of the equation 3 π₯ β 9 π₯ + 6 = 0 2 , giving values to the nearest tenth.

Q14:

Find the solution set of π₯ + 9 3 π₯ + 3 8 = 1 2 2 in β .

Q15:

Find the solution set of ( 3 π₯ + 6 ) = ( 5 π₯ β 1 1 ) 2 2 in β .

Q16:

Find the solution set of 1 4 4 π₯ = 3 6 ο¨ in β .

Q17:

Find the solution set of 2 οΉ π₯ + 3 2 ο = 7 2 2 in β .

Q18:

Given that π¦ + 1 π¦ = 7 9 2 2 , find π¦ + 1 π¦ .

Q19:

Answer the following.

Solve 1 6 π₯ β 2 4 π₯ + 9 = 0 2 .

Deduce from the previous question the solution to 1 6 π₯ β 2 4 π₯ + 9 = 0 2 , using a change of variable.

Q20:

Find the solution set of 5 π₯ + 1 2 π₯ = β 7 2 in β .

Q21:

Find the solution set of β 2 π₯ + 2 = 0 4 in β .

Q22:

Given that π π = π π = 2 , find the solution set of the equation π π₯ β 2 π π₯ + π = 0 2 .

Q23:

Solve the equation ( 2 π₯ β 3 ) ( 3 π₯ + 4 ) = 0 .

Q24:

Solve the equation 4 π₯ + 4 0 π₯ + 4 0 = β 6 0 2 by factoring.

Q25:

Solve the equation 5 π₯ β 1 4 π₯ + 1 0 = 1 5 2 by factoring.

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