Factor each polynomial completely. See Example 6. x² - 2x - 15

Guida verificata passo dopo passo

Identify the quadratic polynomial to factor: $x^{2} - 2x - 15$.

Recall that to factor a quadratic of the form $x^{2} + bx + c$, we look for two numbers that multiply to $c$ and add to $b$.

Find two numbers that multiply to $-15$ and add to $-2$. Consider the factor pairs of $-15$: $(1, -15)$, $(-1, 15)$, $(3, -5)$, and $(-3, 5)$.

Determine which pair sums to $-2$. The pair $(3, -5)$ multiplies to $-15$ and adds to $-2$.

Write the factored form using these numbers: $(x + 3)(x - 5)$.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Factoring Quadratic Polynomials

Factoring quadratic polynomials involves expressing a quadratic expression as a product of two binomials. For a quadratic in the form x² + bx + c, the goal is to find two numbers that multiply to c and add to b. This process simplifies solving equations and analyzing functions.

Video consigliato:

Percorso guidato

6:08

Factoring

Finding Factors of the Constant Term

To factor a quadratic, identify pairs of factors of the constant term (here, -15) that combine to give the middle coefficient (-2). For example, factors of -15 include (1, -15), (-1, 15), (3, -5), and (-3, 5). Selecting the correct pair is essential for accurate factoring.

Video consigliato:

Percorso guidato

6:08

Factoring

Zero Product Property

Once factored, the quadratic can be set equal to zero and solved using the zero product property, which states that if a product of factors equals zero, at least one factor must be zero. This property is fundamental for solving quadratic equations after factoring.

Video consigliato:

Percorso guidato