Hits: 53
Hits: 53 Question i. The polynomial , where and are constants, is denoted by . It is given that and are factors of . Find the values of and . ii. When and have these values, find the quotient when p(x) is divided by x2 + x − 2. Solution i. […]
Hits: 63 Question The polynomial , where and are constants, is denoted by . It is given that is a factor of , and that when is divided by the remainder is 12. i. Find the values of a and b. ii. When a and b have these values, factorise p(x) completely. Solution […]
Hits: 67 Question The polynomial 4×3 + ax2 + 9x + 9, where a is a constant, is denoted by p(x). It is given that when p(x) is divided by (2x − 1) the remainder is 10. i. Find the value of a and hence verify that (x − 3) is a factor of […]
Hits: 37 Question The cubic polynomial is defined by where and are constants. It is given that is a factor of and that, when is divided by , the remainder is 24. i. Find the values of and . ii. When and have these values, factorise p(x) completely. Solution […]
Hits: 100 Question The cubic polynomial is defined by where and are constants. It is given that is a factor of and that, when is divided by , the remainder is 24. i. Find the values of and . ii. When and have these values, factorise p(x) completely. Solution […]
Hits: 121 Question The polynomial is defined by where is a constant. i. Given that is a factor of , find the value of . ii. When has the value found in part (i), find the quotient when is divided by . Solution i. We are given that; We are […]
Hits: 185 Question The curve C has equation y = (x +1)(x + 3)2 a. Sketch C, showing the coordinates of the points at which C meets the axes. b. Show that . The point A, with x-coordinate -5, lies on C. c. Find the equation of the tangent to C at A, giving your […]
Hits: 40 Question a. On the axes below, sketch the graphs of i. ii. showing clearly the coordinates of all the points where the curves cross the coordinate axes. b. Using your sketch state, giving a reason, the number of real solutions to the equation Solution a. i. We are required to sketch; We need to […]
Hits: 63 Question The polynomial is given by . a. Use the Remainder Theorem to find the remainder when is divided by . b. Use the Factor Theorem to show that is a factor of . c. i. Express in the form , where b and c are integers. ii. Hence show that the equation has exactly one real root. Solution a. Remainder […]
Hits: 47 Question a. i. Sketch the curve with equation ii. Show that the equation can be expressed as b. The polynomial is given by . i. Find the remainder when is divided by . ii. Use the Factor Theorem to show that is a factor of . iii. Express in the form , where b and c are integers. c. […]
Hits: 65 Question A circle has centre C(-3,1) and radius . a. i. Express the equation of the circle in the form ii. Hence find the equation of the circle in the form where m, n and p are integers. b. The circle cuts the y-axis at the points A and B. Find the distance AB. c. i. Verify […]