Question

11.Factorise 8x² +19x - 15​

Answer 1

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➡ 8x² + 19x - 15 = 0

➡ 8x² + 24x - 5x - 15 = 0

➡ 8x(x + 3) - 5(x + 3) = 0

➡ (x + 3)(8x - 5) = 0

➡ x + 3 = 0 ; 8x - 5 = 0

➡ x = 0 - 3 ; 8x = 0 + 5

➡ x = - 3 ; 8x = 5

➡ x = - 3 ; x = 5/8

∴ x = - 3 or 5/8

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Answer 2

Solution:

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Simplifying

8x2 + -19x + -15 = 0

Reorder the terms:

-15 + -19x + 8x2 = 0

Solving

-15 + -19x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-5 + -8x)(3 + -1x) = 0

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Extras:

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Subproblem 1

Set the factor '(-5 + -8x)' equal to zero and attempt to solve:

Simplifying

-5 + -8x = 0

Solving

-5 + -8x = 0

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + -8x = 0 + 5

Combine like terms: -5 + 5 = 0

0 + -8x = 0 + 5

-8x = 0 + 5

Combine like terms: 0 + 5 = 5

-8x = 5

Divide each side by '-8'.

x = -0.625

Simplifying

x = -0.625

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying

3 + -1x = 0

Solving

3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0

0 + -1x = 0 + -3

-1x = 0 + -3

Combine like terms: 0 + -3 = -3

-1x = -3

Divide each side by '-1'.

x = 3

Simplifying

x = 3

Solution

x = {-0.625, 3}

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