Question

Math

Posted 3 months ago

```
Factor the quadratic expression completely.
$6 x^{2}-13 x+6=$
$\square$
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

To factor the quadratic expression $6x^2 - 13x + 6$, we look for two numbers that multiply to $6 \times 6 = 36$ and add up to $-13$

step 2

The numbers that satisfy these conditions are $-9$ and $-4$, because $-9 \times -4 = 36$ and $-9 + (-4) = -13$

step 3

We rewrite the middle term $-13x$ using $-9x$ and $-4x$: $6x^2 - 9x - 4x + 6$

step 4

Group the terms: $(6x^2 - 9x) + (-4x + 6)$

step 5

Factor by grouping: $3x(2x - 3) - 2(2x - 3)$

step 6

Factor out the common binomial $(2x - 3)$: $(3x - 2)(2x - 3)$

Answer

$(3x - 2)(2x - 3)$

Key Concept

Factoring Quadratic Expressions

Explanation

The quadratic expression $6x^2 - 13x + 6$ is factored by finding two numbers that multiply to the product of the coefficient of $x^2$ and the constant term, and add up to the coefficient of $x$. Then, the expression is rewritten and factored by grouping.

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