Using remainder theorem factorise 4x 3 + 7x 2 - 36x - 63 completely.

Substituting x = 3 in 4x 3 + 7x 2 - 36x - 63, we get : ⇒ 4x 3 + 7x 2 - 36x - 63 ⇒ 4(3) 3 + 7(3) 2 - 36(3) - 63 ⇒ 4 × 27 + 7 × 9 - 108 - 63 ⇒ 108 + 63 - 108 - 63 ⇒ 0. So, x - 3 is the factor of 4x 3 + 7x 2 - 36x - 63. On dividing 4x 3 + 7x 2 - 36x - 63 by (x - 3) we get, ∴ 4x 3 + 7x 2 - 36x - 63 = (x - 3)(4x 2 + 19x + 21) = (x - 3)(4x 2 + 12x + 7x + 21) = (x - 3)[4x(x + 3) + 7(x + 3)] = (x - 3)(4x + 7)(x + 3). Hence, 4x 3 + 7x 2 - 36x - 63 = (x - 3)(4x + 7)(x + 3).

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Vertex A of triangle ABC is (-3, 5) and mid-points of the sides AB and AC are (-4, 4) and (2, -2) respectively. Find :
(i) co-ordinates of vertices B and C.
(ii) equation of line through vertex C and parallel to side AB.

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Prove that :
sin A(1 + tan A) + cos A(1 + cot A) = sec A + cosec A

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Mathematics

Using remainder theorem factorise 4x³ + 7x² - 36x - 63 completely.

Factorisation

Related Questions

Vertex A of triangle ABC is (-3, 5) and mid-points of the sides AB and AC are (-4, 4) and (2, -2) respectively. Find :
(i) co-ordinates of vertices B and C.
(ii) equation of line through vertex C and parallel to side AB.

Prove that :
sin A(1 + tan A) + cos A(1 + cot A) = sec A + cosec A

Mathematics

Using remainder theorem factorise 4x3 + 7x2 - 36x - 63 completely.

Factorisation

Related Questions

Vertex A of triangle ABC is (-3, 5) and mid-points of the sides AB and AC are (-4, 4) and (2, -2) respectively. Find :(i) co-ordinates of vertices B and C.(ii) equation of line through vertex C and parallel to side AB.

Prove that :sin A(1 + tan A) + cos A(1 + cot A) = sec A + cosec A

Using remainder theorem factorise 4x³ + 7x² - 36x - 63 completely.

Vertex A of triangle ABC is (-3, 5) and mid-points of the sides AB and AC are (-4, 4) and (2, -2) respectively. Find :
(i) co-ordinates of vertices B and C.
(ii) equation of line through vertex C and parallel to side AB.

Prove that :
sin A(1 + tan A) + cos A(1 + cot A) = sec A + cosec A