Fill in the gaps to factorise this
expression.

Ask by French Cox. in the United Kingdom

Mar 18,2025

Question

Fill in the gaps to factorise this expression. $$ x^{2}+6 x-27=\left(x-\_\right)\left(x+\_\right) $$

UpStudy AI · Accepted Answer

To factor the expression $$ x^{2}+6x-27 $$, we need to find two numbers that multiply to $$-27$$ (the constant term) and add up to $$6$$ (the coefficient of the linear term).

Let's denote the two numbers as $$a$$ and $$b$$. We have:

1. $$a \cdot b = -27$$
2. $$a + b = 6$$

Now, we can find the pairs of factors of $$-27$$ and check which pair adds up to $$6$$:

- $$1$$ and $$-27$$ (sum: $$-26$$)
- $$-1$$ and $$27$$ (sum: $$26$$)
- $$3$$ and $$-9$$ (sum: $$-6$$)
- $$-3$$ and $$9$$ (sum: $$6$$)

The pair that works is $$-3$$ and $$9$$.

Thus, we can fill in the gaps in the factorization:

$$
x^{2}+6x-27=\left(x-(-3)\right)\left(x+9\right) = \left(x-(-3)\right)\left(x+9\right) = \left(x-(-3)\right)\left(x+9\right) = \left(x-(-3)\right)\left(x+9\right)
$$

So the final factorization is:

$$
x^{2}+6x-27=\left(x-(-3)\right)\left(x+9\right) = \left(x+3\right)\left(x-9\right)
$$

Thus, the filled gaps are $$3$$ and $$9$$.
Fill in the gaps with $$3$$ and $$9$$: $$ x^{2}+6x-27=\left(x-3\right)\left(x+9\right) $$

Fill in the gaps to factorise this
expression.

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