The polynomial $P(x) = ax^3 + bx^2 - 19x + 4$, where $a$ and $b$ are constants, has a fac

Question

The polynomial $P(x) = ax^3 + bx^2 - 19x + 4$, where $a$ and $b$ are constants, has a factor $x + 4$ and is such that $2P(1) = 5P(0)$. Find the value of $a$ and of $b$.[4] Hence, factorise $P(x)$ completely.[2]

Accepted Answer

(a) $a=6, b=19$ (b) $P(x)=(x+4)(2x-1)(3x-1)$

CGSS 4AM 2021 Prelims P1 Q2

CGSS 4AM 2021 Prelims P1 Q2

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