Factor by any method. See Examples 1–7. 4z2+28z+49

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 101

1장, 문제 101

Factor by any method. See Examples 1–7. 4z²+28z+49

검증된 단계별 안내

Identify the quadratic expression to factor: $4z^2 + 28z + 49$.

Check if the quadratic is a perfect square trinomial by comparing it to the form $a^2 + 2ab + b^2$.

Find $a$ and $b$ such that $a^2 = 4z^2$ and $b^2 = 49$. Here, $a = 2z$ and $b = 7$.

Verify if the middle term \$28z$ equals $2ab = 2 \times 2z \times 7 = 28z$, confirming it is a perfect square trinomial.

Write the factored form as $(2z + 7)^2$.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Factoring Quadratic Expressions

Factoring quadratics involves rewriting a quadratic expression as a product of two binomials or other factors. This process simplifies expressions and solves equations. Recognizing patterns like perfect square trinomials or using methods such as factoring by grouping is essential.

Perfect Square Trinomials

A perfect square trinomial is a quadratic expression that can be written as the square of a binomial, typically in the form a² + 2ab + b² = (a + b)². Identifying this pattern helps factor expressions quickly and accurately.

Greatest Common Factor (GCF)

The GCF is the largest factor shared by all terms in an expression. Factoring out the GCF simplifies the expression and can make further factoring easier. Always check for a GCF before applying other factoring methods.