Math Problem Statement

Factorize 6x^2 + 11x - 10.

Solution

The problem given in the image asks to factorize the quadratic expression:

6x2+11x106x^2 + 11x - 10

Let's go step by step to factorize it.

Step 1: Multiply the coefficient of x2x^2 (which is 6) by the constant term (which is -10).

6×(10)=606 \times (-10) = -60

Step 2: Find two numbers that multiply to give -60 and add up to the middle term’s coefficient, which is 11.

The numbers are 15 and -4 because: 15×(4)=60and15+(4)=1115 \times (-4) = -60 \quad \text{and} \quad 15 + (-4) = 11

Step 3: Rewrite the middle term (11x) as a sum of 15x and -4x.

6x2+15x4x106x^2 + 15x - 4x - 10

Step 4: Group the terms in pairs.

(6x2+15x)(4x+10)(6x^2 + 15x) - (4x + 10)

Step 5: Factor out the greatest common factor (GCF) from each group.

3x(2x+5)2(2x+5)3x(2x + 5) - 2(2x + 5)

Step 6: Factor out the common binomial factor (2x+5)(2x + 5).

(3x2)(2x+5)(3x - 2)(2x + 5)

Thus, the factorization of 6x2+11x106x^2 + 11x - 10 is:

(3x2)(2x+5)(3x - 2)(2x + 5)

Would you like more details or have any further questions? Here are five related questions you might explore:

  1. How do you factorize quadratics with complex solutions?
  2. What methods can be used to check if a factorization is correct?
  3. How do you solve a quadratic equation after factorization?
  4. How does the discriminant of a quadratic relate to factorization?
  5. What are some examples of quadratics that cannot be factored with real numbers?

Tip: Always check your factorization by expanding the factors to ensure they give the original quadratic expression.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Factoring

Formulas

Factoring Quadratic Expressions: ax^2 + bx + c

Theorems

Zero Product Property

Suitable Grade Level

Grades 9-10