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

Question

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To factor the quadratic expression $6x^2 - 13x + 6$, we look for two numbers that multiply to $6 imes 6 = 36$ and add up to $-13$. ‖ ‖ step 2 ⋮ The numbers that satisfy these conditions are $-9$ and $-4$, because $-9 imes -4 = 36$ 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.⚹◊What are the roots of the quadratic equation $6x^2 - 13x + 6 = 0$?⍭ Generate me a similar question◊

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