Simplifying Expressions
To simplify the expression 3x+5x, you combine like terms, resulting in this simplified expression.
What is 8x?
This is the process of writing a mathematical expression as a product of its factors.
What is factoring?
When multiplying two powers with the same base, you add the exponents. This property is known as this.
What is the product of powers property?
This formula is used to solve any quadratic equation of the form ax2+bx+c=0.
What is the quadratic formula?
To simplify the expression 4(2x+3), you apply this property to remove the parentheses.
What is the distributive property?
This term refers to the largest common factor that can be factored out of all the terms in an expression.
What is the greatest common factor (GCF)?
When dividing two powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator. This is called this property.
What is the quotient of powers property?
In the quadratic formula, this part under the square root, b2−4ac, is called the discriminant and determines the nature of the roots.
What is the discriminant?
When simplifying the expression 7x2−3x2+4x−5x, you combine the terms with the same powers of x, resulting in this simplified expression.
What is 4x2−x?
To factor the quadratic expression x2+7x+12, you look for two numbers that multiply to 12 and add to 7. This is the factored form.
What is (x+3)(x+4)?
Any non-zero number raised to this exponent is always equal to 1.
What is zero?
If the discriminant of a quadratic equation is positive, the equation has this many real solutions.
What are two real solutions?
To simplify the expression x2+5x+6, you factor it into two binomials, resulting in this factored form.
What is (x+2)(x+3)?
The expression x2−25 is a difference of squares and factors into these two binomials.
What is (x−5)(x+5)?
When raising a power to another power, you multiply the exponents. This property is called this.
What is the power of a power property?
If the discriminant of a quadratic equation is zero, the equation has this type of solution.
What is one real solution or a repeated root?
The expression x3⋅x4 can be simplified using this exponent rule, resulting in this expression.
What is x7, using the product of powers property?
To factor the expression 4x2+8x, you factor out the greatest common factor, which is 4x. This is the factored form.
What is 4x(x+2)?
A number raised to a negative exponent is equal to this.
What is the reciprocal of the number raised to the positive exponent?
To solve the quadratic equation x2−6x+5=0using the quadratic formula, you would first identify the values for a, b, and c. What are these values?
What are a=1, b=−6, and c=5?