因式分解 $x^2+5x-6$ 。答案 ... 由此，解方程 $(p-1)^2+5(p-1)-6=0$ 。答案 p = ...

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完整解法

1. Find the two factors and write the quadratic as a product of two linear brackets.

For $x^2+5x-6$ , find two numbers with product $-6$ and sum $5$ .

The numbers are $6$ and $-1$ .

So,
$x^2+5x-6=(x+6)(x-1).$

答案

$(x+6)(x-1)$

1. Apply the factorisation from part (a) to the expression with $x=p-1$.

From part (a),
$x^2+5x-6=(x+6)(x-1).$
Let $x=p-1$ .
$(p-1)^2+5(p-1)-6=((p-1)+6)((p-1)-1).$
So
$(p+5)(p-2)=0.$

2. Solve the factorised quadratic equation using the zero product property.

$(p+5)(p-2)=0$
Hence,
$p+5=0 \quad \text{or} \quad p-2=0.$
So
$p=-5 \quad \text{or} \quad p=2.$

答案

$p=-5$ or $p=2$

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