The internal stress in a structural component is modeled by the cubic polynomial S(x)=3x3+Ax2+Bx−10S(x) = 3x^3 + Ax^2 + Bx - 10S(x)=3x3+Ax2+Bx−10, where AAA and BBB are integer constants and xxx represents the position along the component.
It is known that:
Show that 3A+B=−53A + B = -53A+B=−5.
Given that the stress is zero at position x=23x = \frac{2}{3}x=32, such that (3x−2)(3x - 2)(3x−2) is a factor of S(x)S(x)S(x), find the value of AAA and the value of BBB.
Hence determine the quadratic expression Q(x)Q(x)Q(x) such that S(x)=(3x−2)Q(x)S(x) = (3x - 2)Q(x)S(x)=(3x−2)Q(x).
Practise Edexcel A Level Maths Algebraic Methods with exam-style questions for A Level Maths. 226 questions covering 1.1 Proof by Contradiction, 1.2 Algebraic Fractions, 1.3 Partial Fractions, 1.4 Repeated Factors, and 1.5 Algebraic Division, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
