Question

10 Expand: (2x+3)3

11 Evaluate: [(35)³ + (-20)³ + (-15)3³).

Section C-Short Answer Questions [Type ] 12 If the polynomial f(x) = px³ + 5x²+x+q is divided by (x-1) and (x + 2) leaves the remainders 11 and 5 respectively. Find the values of p and q. 13. Factorise: 4x2 +9y2 + 1622 + 12xy-24yz - 16xz.

14 Verify that : x +y³+2³-3xyz = 2(x+y+z) [x - y)² + (y-2)² + (z − x)²]. 15 Ifx+y=7 and x² + y2 = 25, find the value of x3 + 3³.

Section D-Long Answer Questions

16. If both (x-3) and (x-3) are the factors of px2 + 5x+r; then show that p-r=0.

17. Factorise the polynomial p(x) = x³ + 13x²+31x - 45.

1 18. If x4 + =727, find the values of:

(1) x² + x2

(ii) x 1

1 (iii) x3​

Answer 1

Step-by-step explanation:

10)

(2x+3)^3

(a+b)^3 =a^3 +b^3 +3ab(a+b)

⇒(2x) 3+(3) 3+3(2x)(3)(2x+3)

⇒8x^3 +27+18x(2x+3)

⇒8x^3 +27+36x^2 +54x

⇒8x^3 +36x^2+54x+27.

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