Question

4x^2-15x-4factorise please ​

Answer 1

Answer:

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

Solution Steps:

______________________________

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: $\sqrt{\frac{-b\frac{+}{}\sqrt{b^2-4ac}}{2a} }$.

 - 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:

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

5.) Multiply −16 times −4:

• $-16$ × $-4=64$

Equation at the end of Step 5:

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

6.) Add 225 to 64:

• $225+64=289$

Equation at the end of Step 6:

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

7.) Take the square root of 289:

• $\sqrt{289}=17$

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:

• $15+17=32$

• $x=\frac{32}{8}$

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:

• $15-17=-2$

• $x=\frac{-2}{8}$

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

• $-2$ ÷ $-2=-1$

• $8$ ÷ $-2=-4$

• $x=-\frac{1}{4}$

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 $-\frac{1}{4}$ for $x_{2}$:

• $4x^2-15x-4=4(x-4)(x-(-\frac{1}{4}))$

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

• $4x^2-15x-4=4(x-4)(x+\frac{1}{4})$

Add $\frac{1}{4}$ to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible:

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

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

• $4x^2-15x-4=(x-4)(4x+1)$

______________________________