Question

factor the following trinomial. 2x² - 7x + 6 (?x - 3)(x - )

Explanation:

Step1: Expand the given factored form

Let the first box be \(a\) and the second box be \(b\). Then \((ax - 3)(x - b)=ax^{2}-abx - 3x + 3b=ax^{2}-(ab + 3)x + 3b\).

Step2: Compare with the original trinomial

The original trinomial is \(2x^{2}-7x + 6\). Comparing the constant terms: \(3b = 6\), so \(b=\frac{6}{3}=2\).

Step3: Find the value of \(a\)

Comparing the coefficients of \(x^{2}\): \(a = 2\) (since the coefficient of \(x^{2}\) in the original trinomial is 2). We can also verify using the coefficient of \(x\): \(-(ab + 3)=-7\). Substituting \(b = 2\), we get \(-(2a+3)=-7\), which gives \(2a + 3 = 7\), so \(2a=4\) and \(a = 2\).

Answer:

The first box is \(2\) and the second box is \(2\), so the factored form is \((2x - 3)(x - 2)\).