(a) Factorise z6 + 1 over the real numbers.

Q: Example 4: Factoring ax² + bx + c x² + 4x – 12 -

A:

Q: Factor completely over the real numbers. 21. f(x)=5x' +19x² +16x–4

A:

Q: What is the quickest way to factor a polynomial with three terms?

A:

Q: Find the factor of x^2-8x+16

A:

Q: Find a QR-factorisation of 1 1 -1 1 | 1 1 1 1 0 -

A: The given question is solved below.

Q: (a) 5x-3(x-2)-3(x+1)-x (b) 4-10 and use interval notation in the answer. (c) Use factoring: 2x² + 5x…

A: a) 5x-3x-2=3x+1-xb) 4-x2≤10c) 2x2+5x=3

Q: Find the last term to make the trinomial into a perfect square: 6x + - When this is factored, it…

A: For trinomial term ax2+bx+__, to make it perfect square last term should be c=(Middle term)24(First…

Q: Cannot be factored, say so. 1. x-x-2 2. x? + 4: + 3 3. x-4x + 3 4. x - 5x + 6 5. x+x-2 6. x?- 5x + 4…

A:

Q: Factor out −1 from the polynomial.  −3ab − 5ac + 6bc

A: To factor out −1 from the given polynomial. -3ab-5ac+6bc

Q: factor 3x^3-x^2-147x+49=0

A: Given, 3x3-x2-147x+49=0

Q: Explain why the degree of the product of two nonzero polynomials equals the sum of their degrees.

A: Let the two polynomials be of degree m & n respectively. Then, the highest power of x in the…

Q: Determine the coefficients of the product: (2- 3)(2 – 2)(x – 1)= 23+

A: Solution:-  the given expression is  f(x)=(x-3)(x-2)(x-1)

Q: How can the Factor Theorem be used to determine if x - 1 is a factor of x3 - 2x2 - 11x + 12?

A: Given: the polynomial function fx=x3-2x2-11x+12.

Q: What is the completely factored form of xy – xn

A: Given : xy3 - x3y

Q: Why is x-3 a factor of m(x) x^3-x^2-5x-3

A: It is  polynomial equation.

Q: 2. Factor the polynomial: 300y z- 60-4x +432°. _

A: The solution for the above question is as shown below.

Q: Find k so that 4x + 3 is a factor of 20x3 + 23x2 - 10x + k.

A: If 4x+3 is a factor, then on plugging -34 for x in the given expression, the result is 0.

Q: Factor the algebraic expressi 7x +63 -

A:

Q: Which of the following is the correct complete factorization of x4 - 1? (x-1)^{2}(x+1)^{2}

A: Given, x4-1

Q: 1. x =6x + 91 (Factoring) 2. -2x² +146 = -34 3. x -14x + 53 = 9 (Completing the Square) 4. 3x +6x-62…

A: According to our company policy we can answer only first three sub parts and rest of the questions…

Q: 5.26 st factor out th 2x + 2x-24 ect the correc A. 2x +2x

A: In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero,…

Q: Factor fully the polynomial 4x^4+4x^3-35x^2-36x-9

A:

Q: Find the sum of the polynomials: 8x3 - 2x2 + 6x - 2 and 3x4 - 2x3 + x2 + x

A: To find the sum of polynomials: 8x3-2x2+6x-2 and 3x4-2x3+x2+x Solution: (8x3-2x2+6x-2 )+…

Q: 1) x² + 5xy - 3x (Common Monomial Factor) 2) 25ax? - 9a (Difference of Two Squares) 3) 125x'- 8y…

A:

Q: x²-11x+28

A:

Q: Q2. Factorise completely (i) 3x − 6y + ax − 2ay (ii) p2 − 1 (iii) x2 − x − 12 (iv) 2x2 − 5x − 7

A:

Q: 1. Write the complete factored form of f(x). y 8. y = f(x) 4 -2 2 3 -8

A: Note  Factor form of a function is given by  f(x) =(x-a)(x-b)(x-c)....... and so on Where  a,b,c are…

Q: (d) Show that x² – 4 is a factor of x* – 5x³ + 2x? + 20x – 24.

A:

Q: If (x +3) is a factor of x³ – 13x – 12, what are the other factors.

A: The objective is to find the remaining factors of the given polynomial

Q: Factor 10a+15a. ?

A:

Q: 7x 6 completely if (x 1) is a factor Factor

A: Given that (x+1) is a factor of x3-7x-6. Divide the polynomial x3-7x-6 by x+1 as follows.

Q: A = 7x- 3x + 10 B = -4x2 + 6x - 4 А - В %3D Your answer should be a polynomial in standard form.

A: Given: To Find:

Q: b. Find a QR-factorisation of 1 -1 1 1 1 1 -1 0 |

A: Step:-1 Given matrix  is  110-1010111-10 Let  A= 110-1010111-10 Now, we'll apply Gram-Schmidt…

Q: (x - 2) is a factor for x2 - 5x + 6. صواب (خطأ

A: For   x-a to be a factor of a quadretic equation then x=a is a solution of the quadretic equation.

Q: 19. What is the largest value of the quadratic form 5(x,)? - 3(x2)² if x²x = 1. 20. What is the…

A:

Q: 9. What is the possible equation of the following polynomial in factored form?

A:

Q: Solve this strictly by Factor Theorem.  3x3 + 7x2 + 2x - 4

A: use the definition of factor theorem .

Q: Based on the factor theorem, a factor of x4 - 5x2 + 4 is:

A: Introduction: When factoring polynomials completely, the factor theorem is used in mathematics. It…

Q: Find the factor of x^2-7x+10

A: We have to find the factor of  x2 - 7x + 10  = x2 - 5x - 2x + 10

Q: Which of the following are perfect square trinomials? Select the two correct answers.     x2+9x+20…

A: Perfect square trinomial: An algebraic expression with 3 terms which is a perfect square.

Q: How do I express (x+1)squared as a trinomial in standard form?

A: The general form of trinomials with a leading coefficient of a is ax2 + bx + c.

Q: If x – 2 is a factor of x3- 4x2 + 8x + k then the value of k is

A: Given: x-2 is a factor of x3-4x2+8x+k.

Q: The binomials (x- 2) and (2x +3) are the factors of which polynomial?

A: We have to find the polynomial which the binomials (x - 2) and (2x + 3) are the factors . Then ,…

Q: Write the complex factors for 4x2 - 12x +25

A: Given:     To determine: complex factors for 4x2 - 12x +25

Q: Use the Binomial Theorem to simplify (x – 2)3 as a polynomial ax3 + bx? + cx + d.

A:

Q: Factorise x6 + 1 as a product of three quadratic polynomials with real coefficients.

A:

Q: Completely Factor over the real numbers a^3 + 2a^2-4a-8

A: The given function is  = a^3 + 2a^2-4a-8

Q: Completely factor over the real numbers 18x^3 + 15x^2y- 12xy^2

A: We have to factor the given expression.