Question

factor the polynomial, if possible. drag the expressions into the box if they are part of the factored form of the polynomial. if the polynomial cannot be factored, drag prime. $2x^2 - 9x + 7$

Explanation:

Step1: Use factoring by grouping

For the quadratic polynomial \(2x^2 - 9x + 7\), we need to find two numbers that multiply to \(2\times7 = 14\) and add up to \(-9\). The numbers are \(-7\) and \(-2\).
Rewrite the middle term: \(2x^2 - 2x - 7x + 7\)

Step2: Group and factor

Group the first two and last two terms: \((2x^2 - 2x) + (-7x + 7)\)
Factor out the GCF from each group: \(2x(x - 1) - 7(x - 1)\)

Step3: Factor out the common binomial

Factor out \((x - 1)\): \((2x - 7)(x - 1)\)

Answer:

\((2x - 7)(x - 1)\)