Question

5x²+70.x+245 factorization must be done in this question please answer fast
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Answer 1

$\Large\textrm{Given to solve: -}$

$5x^{2}+70x+245$

The factorization starts with the factorization of common factors.

$5x^{2}+70x+245$

$=5(x^{2}+14x+49)$

$=5(x+7)^{2}$

$\Large\textrm{Factorization tricks: -}$

Suppose we have large coefficients, in this case, we can use an approach with the factorization formula.

$x^{2}-38x+217$

Then we apply complete the square method here. Let's see what happens.

$x^{2}-38x+217$

$=(x^{2}-38x+19^{2})-19^{2}+217$

$=(x^{2}-38x+19^{2})-361+217$

$=(x^{2}-38x+19^{2})-144$

$=(x-19)^{2}-12^{2}$

$\textbf{Difference of two squares}$

$\cdots\longrightarrow\boxed{a^{2}-b^{2}=(a+b)(a-b)}$

$(x-19)^{2}-12^{2}$

$=(x-19+12)(x-19-12)$

$=(x-7)(x-31)$

Suppose we have a very large coefficient on the leading term.

$243x^{2}+99x-20$

No worries. We can substitute in $t=9x$ as we see the HCF of two leading terms.

$243x^{2}+99x-20$

$=3t^{2}+11t-20$

$=(3t-4)(t+5)$

$=(27x-4)(9x+5)$

Answer 2

Answer:

Step-by-step explanation:

Given that,

5x² + 70x + 245

= 5x² + 35x+ 35x + 245

= 5x ( x + 7 ) + 35 ( x + 7 )

= ( x + 7 ) ( 5x + 35 ) is the answer.