Question

4x^2-15x-4

factorise please ​

Answer 1

`\boxed{4x^2-15x-4=(x-4)(4x+1)}`

Solution Steps:

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1.) Change the equation using factored transformation:

• 
  `4x^2-15x-4=0`

- Quadratic polynomial can be factored using the transformation
`ax^2+bx+c=a(x-x_(1))(x-x_(2))`, where
`x_(1)` and
`x_(2)` are the solutions of the quadratic equation
`ax^2+bx+c=0`.

- This steps basically means change you current equation using the formula
`ax^2+bx+c=0`.

2.) Turn the factored form into the quadratic equation form:

• 
  `x=\frac{-(-15)\frac{+}{}\sqrt{(-15)^2-4\bold{x}4(-4)}}{2\bold{x}4}`

- All equations of the form
`ax^2+bx+c=0` can be solved using the quadratic formula:
`\sqrt{\frac{-b\frac{+}{}√(b^2-4ac)}{2a} }`.

- The quadratic equation formula gives two solutions, one when
`\frac{+}{}` is addition and one when it is subtraction.

3.) Square -15:

• 
  `-15^2=225`

Equation at the end of Step 3:

• 
  `x=\frac{-(-15)\frac{+}{}\sqrt{225-4\bold{x}4(-4)}}{2\bold{x}4}`

4.) Multiply −4 times 4:

• 
  `-4` ×
  `4=-16`

Equation at the end of Step 4:

• 
  `x=\frac{-(-15)\frac{+}{}√(225-16(-4))}{2\bold{x}4}`

5.) Multiply −16 times −4:

• 
  `-16` ×
  `-4=64`

Equation at the end of Step 5:

• 
  `x=\frac{-(-15)\frac{+}{}√(225+64)}{2\bold{x}4}`

6.) Add 225 to 64:

• 
  `225+64=289`

Equation at the end of Step 6:

• 
  `x=\frac{-(-15)\frac{+}{}√(289)}{2\bold{x}4}`

7.) Take the square root of 289:

• 
  `√(289)=17`

Equation at the end of Step 7:

• 
  `x=\frac{-(-15)\frac{+}{}17}{2\bold{x}4}`

8.) Change -15 to positive 15:

• 
  `-15=15`

Equation at the end of Step 8:

• 
  `x=\frac{15\frac{+}{}17}{2\bold{x}4}`

9.) Multiply 2 by 4:

• 
  `2` ×
  `4=8`

Equation at the end of Step 9:

• 
  `x=\frac{15\frac{+}{}17}8}`

10.) Now Solve:

Now solve the equation
`x=\frac{15\frac{+}{}17}8}` when
`\frac{+}{}` is plus.

Add 15 to 17:

• 
  `15+17=32`

• 
  `x=(32)/(8)`

Divide 32 by 8:

• 
  `32` ÷
  `8=4`

• 
  `x=4`

Now solve the equation
`x=\frac{15\frac{+}{}17}8}` when
`\frac{+}{}` is minus.

Subtract 15 by 17:

• 
  `15-17=-2`

• 
  `x=(-2)/(8)`

Reduce the fraction to lowest terms by extracting and canceling out 2:

• 
  `-2` ÷
  `-2=-1`

• 
  `8` ÷
  `-2=-4`

• 
  `x=-(1)/(4)`

11.) Factor the expression:

Factor the original expression using
`ax^2+bx+c=a(x-x_(1))(x-x_(2))`. Substitute 4 for
`x_(1)` and
`-(1)/(4)` for
`x_(2)`:

• 
  `4x^2-15x-4=4(x-4)(x-(-(1)/(4)))`

Simplify all the expressions of the form
`p-(-q)` to
`p+q`:

• 
  `4x^2-15x-4=4(x-4)(x+(1)/(4))`

Add
`(1)/(4)` to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible:

• 
  `4x^2-15x-4=4(x-4)\bold{x}((4x+1)/(4))`

Cancel out 4, the greatest common factor in 4 and 4:

• 
  `4x^2-15x-4=(x-4)(4x+1)`

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