Consider the cubic polynomial 2.r + 5x2 –r - 6. a) Given that 2r +3 is a factor, use polynomial division to show that 2.a + 5x? – x – 6 = (2x + 3)(x+2)(r - 1). b) Using your result from Part a, solve the inequality 2a + 5x – r – 6 < 0 for r.

Q: Given P(x) = 3æ° – 5x + x° – 23x? – 44x – 12, and - - - that 2i is a zero, write P in factored form…

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Q: Find numbers x and y with sum 10 and product 24. Hint: Find a quadratic polynomial satisfied by x.

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Q: Find the remainder when 6x3 – 10x + 1 is divided by a) x – 2 b) x + 3 c) 2x – 1 please assist with…

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Q: b) Solve the following cubic polynomial equation using the Zero Product Property. Clearly show all…

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Q: What will be the remainder of f(x) = 3x - 2x? - 5x - 6 if it is divided by x - 2? *

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Q: Find the quadratic polynomial if the zeroes of it are 2 and 1/3 respectively.

A: Find the quadratic polynomial

Q: What is the degree of this polynomial? f(x)= 5x5-2x7+12x2+38

A: Degree of polynomial

Q: x² + 2x - 7 1) has how many terms? 2) what degree a polynomial is it?

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Q: 4. Consider this polynomial: P(z) = 2r² – 72² – 5z +4 a) By the Rational Zeros Theorem, list all…

A: The given problem is to find the possibile rational zeros, then find the rational zeros and rewrite…

Q: Use synthetic division method to find the quotient of each the following. Show the solution on the…

A: 1. (x3-3x2+5x+3)÷(x-3) Using synthetic division, The quotient is q(x)=x2+5. The remainder is…

Q: 9) Determine if x-3 is a factor of 2x-2x2 + 4x- 3. Explain how you arrived at your answer.

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Q: Find all the real zeros of the polynomial. Use the quadratic formula if necessary. 1.…

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Q: Q10.  Find the roots algebraically by factoring:  a) x3 – 8x2-3x +90 b) x3 – 64

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Q: 2. Solve the polynomial equation for all zeros. x4 + 5x2 =z?

A: Simplify the polynomial equation x4 + 5x2 = x3 as follows.

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.