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In this lesson, we will learn how to use different strategies for solving polynomial equations of degree greater than two.

Q1:

Solve the equation ( 3 ๐ฅ โ 1 ) ( 5 ๐ฅ + 6 ) ( 3 ๐ฅ โ 4 ) ( 8 ๐ฅ + 7 ) = 0 .

Q2:

Which of the following is a factorized form of ๐ฅ + 2 ๐ฅ โ 1 6 ๐ฅ โ 3 2 3 2 ?

Q3:

Given that ๐ ( ๐ฅ ) = ๐ฅ + 3 ๐ฅ โ 1 3 ๐ฅ โ 1 5 3 2 and ๐ ( โ 1 ) = 0 , find the other roots of ๐ ( ๐ฅ ) .

Q4:

Which of the following is a factorised form of ?

Q5:

By factoring, find all the solutions to ๐ฅ + 2 ๐ฅ โ 1 7 ๐ฅ โ 1 8 ๐ฅ + 7 2 = 0 4 3 2 , given that ( ๐ฅ โ 3 ) and ( ๐ฅ + 4 ) are factors of ๐ฅ + 2 ๐ฅ โ 1 7 ๐ฅ โ 1 8 ๐ฅ + 7 2 4 3 2 .

Q6:

Find the values of ๐ , ๐ , and ๐ given that ( ๐ฅ + 3 ) , ( ๐ฅ โ 2 ) , and ( ๐ฅ + 4 ) are factors of ๐ฅ + ๐ ๐ฅ + ๐ ๐ฅ + ๐ 3 2 .

Q7:

How many roots does the polynomial 3 ๐ฅ โ 2 ๐ฅ + ๐ฅ + 4 ๐ฅ โ 2 6 3 2 have?

Q8:

Solve the equation ( ๐ฅ โ 1 ) ( ๐ฅ + 6 ) ( ๐ฅ โ 4 ) ( ๐ฅ + 7 ) = 0 .

Q9:

Factor the expression 4 ๐ โ 2 8 โ 6 ๐ 6 3 fully.

Q10:

Factor the expression 7 5 ๐ ๐ + 6 0 ๐ ๐ + 1 2 ๐ 4 2 fully.

Q11:

Find the solution set of ๐ฅ โ 2 5 ๐ฅ + 1 4 4 = 0 4 2 in โ .

Q12:

Given that ๐ฅ is in โ , find the value of ๐ฅ which satisfies the following equation ๏น 3 ๐ฅ โ 6 ๏ ๏น ๐ฅ + 9 ๏ = 0 3 2 . Give your answer to the nearest hundredth.

Q13:

Find the solution set of the equation ๏น ๐ฅ โ 5 0 6 ๏ ๏น ๐ฅ โ 5 8 ๏ = 0 3 2 in โ .

Q14:

According to the fundamental theorem of algebra, how many complex solutions does the equation ๐ฅ + 3 ๐ฅ โ 3 ๐ฅ + 2 = 0 ๏ฎ ๏ช ๏ฉ have, counted with multiplicity?

Q15:

How many roots does the equation ๐ฅ + ๐ฅ = 7 2 have?

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