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. 4x² + 23x + 15

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(4\times15 = 60\) and add up to \(23\). The numbers are \(20\) and \(3\) since \(20\times3 = 60\) and \(20 + 3=23\).

Step2: Rewrite the middle term

Rewrite \(23x\) as \(20x+3x\) in the polynomial: \(4x^{2}+20x + 3x+15\).

Step3: Group and factor

Group the first two terms and the last two terms: \((4x^{2}+20x)+(3x + 15)\). Factor out the greatest common factor from each group: \(4x(x + 5)+3(x + 5)\).

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 5)\): \((4x + 3)(x + 5)\).

Answer:

The factored form of the polynomial \(4x^{2}+23x + 15\) is \((4x + 3)(x + 5)\)