Using remainder theorem, factorise: \(2x^3-13x^2+26x-15\)

For what value of k, (x+1) is a factor of \(p(x)=kx^2-x-4?\)

Find the value of k such that (x-1) is a factor of \(5x^3+4x^2-6x+2k.\)

Factorise \(y^2-5y+6\) by using the Factor Theorem.

Examine whether x+2 is a factor of \({ x }^{ 3 }+3{ x }^{ 2 }+5x+6\) and 2x+4. 

Polynomials \(kx^3+3x^2-3\) and \(2x^3-5x+k\), when divided by (x-4) leave the same remainder in each case. Find the value of k.

If the polynomial \(f(x)=x^4-2x^3-9x+3a-7,\)when divided by x+1 leaves the remainder 20, then find the value of a. Also, find the remainder when f(x) is divided by x+2.

If the polynomial \(p(x)=x^4-2x^3+3x^2-ax+8\)is divided by (x-2), it leaves a remainder 10, Find the value of a.

Find the remainder, when \(x^3-3x^2+3x-1\)  is divided by(x-1)

Find a zero of the polynomial p(x)=2x+1

Point out which of the following polynomials are monomials, binomials or trinomials?
\({ x }^{ 3 }+2x-3\)

Find the degree of the polynomials given below:
​​​​​​​\(2-{ y }^{ 2 }-{ y }^{ 3 }+{ 2y }^{ 8 }\)

Write the coefficient of x³ of the following polynomials:
\(4x+{ x }^{ 3 }+{ x }^{ 6 }-{ 7x }^{ 2 }\)

Write the coefficient of x³ of the following polynomials:
\(1+{ x }^{ 2 }+{ x }^{ 4 }-x-{ x }^{ 3 }\)