Questions: Factor 15 x^2-16 x+4 by grouping. Each answer box needs to be filled, enter coefficients of 1 and constants of 0. 'x- 'x 'x- ソ

Transcript text: Factor ` $15 x^{\wedge} 2-16 x+4$ ` by grouping. Each answer box needs to be filled, enter coefficients of 1 and constants of 0. ` $\square$ 'x- $\square$ $x$ $\square$ 'x- $\square$ ソ

Solution

Solution Steps

To factor the trinomial $15x^2 - 16x + 4$ by grouping, we first need to find two numbers that multiply to the product of the leading coefficient (15) and the constant term (4), which is 60, and add up to the middle coefficient (-16). Once we find these numbers, we can split the middle term and group the terms to factor by grouping.

Step 1: Identify the Trinomial

We start with the trinomial $15x^2 - 16x + 4$.

Step 2: Factor the Trinomial

To factor the trinomial, we find two binomials that multiply to give us the original expression. The factored form is: \[ (3x - 2)(5x - 2) \]

Step 3: Verify the Factorization

We can verify the factorization by expanding the binomials: \[ (3x - 2)(5x - 2) = 3x \cdot 5x - 3x \cdot 2 - 2 \cdot 5x + 2 \cdot 2 = 15x^2 - 6x - 10x + 4 = 15x^2 - 16x + 4 \] This confirms that our factorization is correct.