Question

p^2 + 14p - 12

factorise it

Answer 1

Hi.

Question ✏

FACTORISE

==> p² + 14p - 12

While trying with splitting the middle term method...,

We got,

First term is p² Coefficient is 1,
Second term is 14p with coefficient 14,
and the constant term is (-12)

Now,

Multiplying the first term's coefficient with the constant term,

we have,

==> 1 X (-12) = -12

Now,

finding out the two factors, whose sum is 14 (coefficient of the middle term).

Since,

there were no two factors found,

Let us try it with the quadratic formula,

On comparing above equation with,

==> ax² + bx - c,

we have,

a = 1, b = 14, c = -12

Thus,

we know,

the quadratic formula,

i.e. x = (-b ± √b² - 4ac)/2a

==> x = (-14 ± √(14)² - 4(1)(-12))/2(1)

==> x = (-14 ± √196 - (-48)/2

==> x = (-14 ± √244)/2

We Know,

√244 = 2√61 .........{on prime factorisation}

==> x = (-14 + 2√61)/2 or x = (-14 - 2√61)/2

x = -7 + √61 or x = -7 - √61

x = 0.810 or x = - 14.810

HENCE, FACTORISED.

HOPE IT HELPS YOU.