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18 (a) Show that $(2x + 1)(x + 3)(3x + 7)$ can be written in the form $ax^3 + bx^2 + cx + d$ where $a, b, c$ and $d$ are integers - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 3
Question 19
18 (a) Show that $(2x + 1)(x + 3)(3x + 7)$ can be written in the form $ax^3 + bx^2 + cx + d$ where $a, b, c$ and $d$ are integers. (b) Solve $(1 - x)^2 < \frac{9}{2... show full transcript
Worked Solution & Example Answer:18 (a) Show that $(2x + 1)(x + 3)(3x + 7)$ can be written in the form $ax^3 + bx^2 + cx + d$ where $a, b, c$ and $d$ are integers - Edexcel - GCSE Maths - Question 19 - 2019 - Paper 3
Step 1
Show that $(2x + 1)(x + 3)(3x + 7)$ can be written in the form $ax^3 + bx^2 + cx + d$ where $a, b, c$ and $d$ are integers.
Answer
To show that can be expressed in the desired form:
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Expand the Expression Step-by-Step:
First, expand :
Next, multiply this result by :
Expanding:
Combining like terms gives:
Hence, we can write:
All coefficients are integers, thus satisfying the requirement.
Step 2
Solve $(1 - x)^2 < \frac{9}{25}$
Answer
To solve the inequality:
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Take the Square Root of Both Sides:
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Set Up Two Inequalities:
This gives two cases:
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Case 1:
Rearranging this gives:
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Case 2:
This simplifies to:
And further rearranging gives:
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Combine Both Inequalities:
Hence, the solution for is: