2x³ + 2x² - 3 is the cubic trinomial that is expressed as the sum of 3x³ - 7x² +2 and -x³ +9x² - 5.
Given: To express the sum 3x³ - 7x² +2 and -x³ +9x² - 5 of as a trinomial.
What are algebraic equations?
Algebraic equations are a sequence or combination of characters containing variables, alphabets, numbers, symbols, etc. which are equated to some value.
What are polynomials?
Polynomials are algebraic expressions that consist of variables, coefficients, and operators. A polynomial is usually depicted as the sum of m terms for some unknown variable x, raised to the power of n with some constants.
For example: Let us consider p(x) to be a polynomial of degree n. The p(x) can be represented as
p(x) = Cₙ xⁿ + Cₙ₋₁xⁿ⁻¹ . . . . . . . + m terms . . . . . + K (where K is some constant and C's are coefficients of x)
What are trinomials?
Trinomials are algebraic expressions that consist of three non-zero terms or monomials.
For example: f(x) = x + y + z is a linear trinomial of 3 variables x, y, and z.
f(x) = x² + 4x + 1 is a quadratic trinomial of 1 variable x and so on.
Let's solve the problem:
Consider f(x) = 3x³ - 7x² +2 and g(x) = -x³ +9x² - 5
We have to express it as a sum of trinomials.
We can see both f(x) and g(x) are Cubic trinomials of one variable x and the lower degrees of x are the same.
So f(x) + g(x) will also given a cubic trinomial of one variable x
f(x) + g(x) = (3x³ - 7x² +2) + (-x³ +9x² - 5)
Grouping similar terms
f(x) + g(x) = (3x³ - x³) + (-7x² + 9x²) + (2 - 5)
f(x) + g(x) = 2x³ + 2x² - 3
Therefore, the required trinomial is 2x³ + 2x² - 3.
Hence 2x³ + 2x² - 3 is the cubic trinomial that is expressed as the sum of 3x³ - 7x² +2 and -x³ +9x² - 5.
Know more about "trinomials" here: brainly.com/question/16347049
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