Question

(7x2-11x+10)(x3 -x2) find the product.....​

Answer 1

Answer:

Two equations are given

x

3

−7x

2

+14x−8=0 ......... (1) and x

3

−6x

2

+11x−6=0 ........ (2)

We have used synthetic division to solve the given equations.

From part (A), we get the factor of equation (1)

∴ x

3

−7x

2

+14x−8=(x−1)(x

2

−6x+8)

=(x−1)(x

2

−4x−2x+8)

=(x−1)(x(x−4)−2(x−4))

=(x−1)(x−4)(x−2)

∴ x

3

−7x

2

+14x−8=(x−1)(x−2)(x−4) .................. (3)

From part (B), we get the factor of equation (2)

∴ x

3

−6x

2

+11x−6=(x−1)(x

2

−5x+6)

=(x−1)(x

2

−3x−2x+6)

=(x−1)(x(x−3)−2(x−3))

=(x−1)(x−2)(x−3)

∴ x

3

−6x

2

+11x−6=(x−1)(x−2)(x−3) .................. (4)

From equation (3) and (4),

(x−1)(x−2) is the H.C.F(highest common factor) of given equations (1) and (2).

Explanation:

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