9
(a) Expand and simplify
d(x - 2)(2x + 3)(x + 1)
(b) Find the value of n - Edexcel - GCSE Maths - Question 9 - 2018 - Paper 3
Question 9
9
(a) Expand and simplify
d(x - 2)(2x + 3)(x + 1)
(b) Find the value of n.
y^3
----------------
y^2 = y^3
(c) Solve
the equation 5x^3 - 4x - 3 = 0... show full transcript
Worked Solution & Example Answer:9
(a) Expand and simplify
d(x - 2)(2x + 3)(x + 1)
(b) Find the value of n - Edexcel - GCSE Maths - Question 9 - 2018 - Paper 3
Step 1
Expand and simplify
(x - 2)(2x + 3)(x + 1)
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Answer
To expand
first, we need to utilize the distributive property:
Expand the first two factors:
(x−2)(2x+3)=2x2+3x−4x−6=2x2−x−6
Now multiply this result by the third factor (x+1):
(2x2−x−6)(x+1)=2x3+2x2−x2−x−6x−6
This simplifies to:
2x3+x2−7x−6
Thus, the expanded and simplified expression is 2x3+x2−7x−6.
Step 2
Find the value of n.
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Answer
To find the value of n, we start with the expression:
y2y3⋅yn=y3
This simplifies to:
y3+n−2=y3
\therefore 3 + n - 2 = 3 \implies n - 2 = 0 \implies n = 2$$
So, the value of n is -5.
Step 3
Solve
5x^3 - 4x - 3 = 0
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Answer
To solve for x in the equation 5x^3 - 4x - 3 = 0, we can apply numerical methods such as the Newton-Raphson method or use a graphing approach to find approximate solutions.
Using a calculator or software to find the roots gives us:
x≈1.27
x≈−0.48
x≈−0.47
Thus, the solutions correct to 3 significant figures are:
