Solve by factoring x^2 x=7x 16? (2023)

What is the factoring method of X² 6x 16?

∴x2+6x−16=(x+8)(x−2).

You can look at discriminant D=b2−4ac, if it is a perfect square you can factorise the trinomial ax2+bx+c as a product of two factors with rational coefficients. If D=b2−4ac isn't a perfect square, then ax2+bx+c still can be factorised, but it includes factors with surds.

Answer:The roots of the equation x² + 7x + 10 = 0, is -5 and -2. Let's see how we will use the concept of factorization of a polynomial to find the roots of the equation.

⇒61(2x+1)(3x−1)

Factoring of a polynomial is the method of breaking the polynomial into a product of its factors. For example, x² – 16 can be factored as (x+4) (x-4).

Not every quadratic equation can be solved by factoring or by extraction of roots. For example, the expression x2+x−1 x 2 + x − 1 cannot be factored, so the equation x2+x−1=0 x 2 + x − 1 = 0 cannot be solved by factoring. For other equations, factoring may be difficult.

One way to check for factorability is the quadratic formula. It gives the solutions of quadratic equations in terms of roots and coefficients. If a polynomial is not factorable, then it cannot be factored by the quadratic formula. The most common reason for this is that it has roots in an infinite number of places.

Which Quadratic Expressions Are Factorable? BIG IDEA A quadratic expression with integer coefficients is factorable over the integers if and only if its discriminant is a perfect square.

∴x2+7x−18=(x−2)(x+9)

Which of the following is a factor of the polynomial 2x2 7x 6?

Hence the factored form of 2x2−7x+6 is (x−2)(2x−3) Q.

Therefore, the factorization of 16 is written as, 16 = 2 × 2 × 2 × 2 x 1.

The only solution of 2x² + 8x = x² - 16 is -4.

Arrange the tiles for x2 – 8x so that two sides of the figure are congruent. To make the figure a square, add 16 positive 1-tiles. x 2 – 8x + 16 is a perfect square.

Two solutions were found :

x =(16-√224)/2=8-2√ 14 = 0.517.

Find the Greatest Common Factor (GCF) of a polynomial. Factor out the GCF of a polynomial. Factor a polynomial with four terms by grouping. Factor a trinomial of the form.

Step 1: Group the first two terms together and then the last two terms together. Step 2: Factor out a GCF from each separate binomial. Step 3: Factor out the common binomial. Note that if we multiply our answer out, we do get the original polynomial.

Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions.

In algebra, factoring is used to simplify an algebraic expression by finding the greatest common factors that are shared by the terms in the expression.

What is the first rule of factoring?

RULE # 1: The First Rule of Factoring: Always see if you can factor something out of ALL the terms. This often occurs along with another type of factoring.

Factoring only works if the solutions to a quadratic equation are rational numbers.

Solve by factoring is used to solve equations that have an x² (or higher) term in them. Factoring is when something is broken into pieces that _multiply_ to give the original, for example 35 is factored as 5 * 7.

When asked to solve a quadratic equation that you just can't seem to factor (or that just doesn't factor), you have to employ other ways of solving the equation, such as by using the quadratic formula. The quadratic formula is the formula used to solve for the variable in a quadratic equation in standard form.

Prime numbers have two factors, themselves and 1, but those are the trivial factors that every number has. Because they cannot be factored in any other way, we say that they cannot be factored.

Factorization was first considered by ancient Greek mathematicians in the case of integers. They proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1.

A polynomial with integer coefficients that cannot be factored into polynomials of lower degree , also with integer coefficients, is called an irreducible or prime polynomial .

Solved Examples on Factoring Expressions

The common factors are 3 and 5. Therefore, the greatest common factor of 15a and 30 is 3 × 5 = 15. Now, using the greatest common factor, we have to find the factor of the expression. Therefore, 15a + 30 can be factored as 15 ( a + 2 ) using GCF.

Any time you divide by a number (that number being a potential root of the polynomial) and get a zero remainder in the synthetic division, this means that the number is indeed a root, and thus "x minus the number" is a factor.

Hence, the factors of x 2 - 7 x + 12 obtained by using the common factor method is x - 3 x - 4 .

Which expression is the factored form of 2x² 7x 3?

Answer and Explanation: The quadratic expression 2x2 - 7x + 3 simplifies, or factors, to (2x - 1)(x - 3).

Factoring formulas are used to write an algebraic expression as the product of two or more expressions. Some important factoring formulas are given as, (a + b)² = a² + 2ab + b. (a - b)² = a² - 2ab + b.

Factoring of a polynomial is the method of breaking the polynomial into a product of its factors. For example, x² – 16 can be factored as (x+4) (x-4).

To do so first express the given equation as a difference of two squares. Hence , \[{x^2} - 16 = \left( {x + 4} \right)\left( {x - 4} \right)\]. Thus, the factors of \[{x^2} - 16\] are \[\left( {x + 4} \right)\] and \[\left( {x - 4} \right)\].

There are two ways to factorize x2−16 - one using identity a2−b2=(a+b)(a−b) . Other method is by splitting the middle term, which is 0 here and as product of coefficient of x2 and constant term is −16 . we need to do is to split middle term in 4 and −4 (as their sum is zero and product is −16 ).

In this method, we simply take out the common factors among each term of the given expression. Example: Factorise 3x + 9. Since, 3 is the common factor for both the terms 3x and 9, thus taking 3 as a common factor we get; 3x + 9 = 3(x+3).

If we have the equation x2 = 16, what are the solutions to the equation? Since the square of a positive or negative number are always positive, this equation has two solutions, namely x = -4 or x = 4.

So 1, 2, 4, and 8 are factors of 16.

The factors of 16 are the numbers that divide the number 16 completely without leaving any remainder. As the number 16 is a composite number, it has more than one factor. The factors of 16 are 1, 2, 4, 8 and 16. Similarly, the negative factors of 16 are -1, -2, -4, -8 and -16.

The factors of 16 include: 1, 2, 4, 8, and 16.

How do you solve polynomials step by step?

Thus, in the given problem x² + 16x. We have to add 8² = 64, to convert it into a perfect square. Therefore, 64 must be added to the expression to make it a perfect-square trinomial.