Question

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Explanation:

Step1: Recall factoring quadratic

We need to factor \(4x^2 + 4x - 3\) as \((2x - a)(2x + b)\). Multiply \((2x - a)(2x + b)=4x^2+(2b - 2a)x - ab\).

Step2: Compare coefficients

Compare with \(4x^2 + 4x - 3\). So we have:

1. Coefficient of \(x\): \(2b - 2a = 4\) (divide by 2: \(b - a = 2\))
2. Constant term: \(-ab=-3\) (so \(ab = 3\))

Solve \(b - a = 2\) and \(ab = 3\). Possible integer solutions for \(a,b\) (since \(3 = 1\times3\)): Let \(a = 1\), \(b = 3\) (check \(b - a=3 - 1 = 2\), which works).

So the factors are \((2x - 1)(2x + 3)\).

Answer:

First blank: \(1\), Second blank: \(3\)