Question

factorise the quadratic trinomials :
${x}^{2} + 13x + 40$
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Answer 1

Step-by-step explanation:

its yur solution dear...

Answer 2

AnswEr:-

Given Quadratic trinomial:-

$\tt\longrightarrow {x}^{2} + 13x + 40.$

So here we have to factorize the given quadratic polynomial:-

Therefore we will factorize the polynomial by factorization method:-

So Here,

$\mapsto$ Coefficient of x²×constant term,

$\tt = 1\times40 \\ \\ \tt = 40. \\ \\ \tt also \\ \\ \tt\mapsto40 = 2 \times 2 \times 2 \times 5 . \\ \\ \tt and \\ \\ \tt\mapsto(2 \times 2 \times 2) + 5 \\ \\ \tt = 8 + 5. \\ \\ \tt = 13= middle \: term.$

So let's splitt the middle term:-

$\tt\mapsto {x}^{2} + (8 + 5)x + 40. \\ \\ \tt\mapsto {x}^{2} + 8x + 5x + 40. \\ \\ \tt\mapsto x(x + 8) + 5(x + 8). \\ \\ \tt\mapsto(x + 8)(x + 5).$

$\therefore$ The factors of given polynomial are (x+8) and (x+5).

$\rule{200}2$

We can also find the value of x:-

$\because$ x+8 and x+5 are factors.

Therefore both the factors must be equal to 0.

$\tt\longrightarrow(x + 8) = 0 \: \: and \: \: (x + 5) = 0. \\ \\ \tt\longrightarrow x = - 8 \: \: and \: \: x = - 5.$

So two values of x are possible which are -8 and -5.