How do you factor $3 x^{2} - 10 x + 7$ $3x^2-10x+7$ ?

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Answer 1 · 2016-06-19T09:14:30

$= (3 x - 7) (x - 1)$ $= color(blue)( (3x - 7 ) ( x -1)$

$3 x^{2} - 10 x + 7$ $3x^2 - 10x + 7$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 3 \cdot 7 = 21$ $N_1*N_2 = a*c = 3 * 7 = 21$

AND

$N_{1} + N_{2} = b = - 10$ $N_1 +N_2 = b = -10$

After trying out a few numbers we get $N_{1} = - 7$ $N_1 = -7$ and $N_{2} = - 3$ $N_2 =-3$

$(- 7) \cdot (- 3) = 21$ $(-7) * ( -3) = 21$ , and $(- 7) + (- 3) = - 10$ $(-7) +(-3)= -10$

$3 x^{2} - 10 x + 7 = 3 x^{2} - 3 x - 7 x + 7$ $3x^2 - 10x + 7 = 3x^2 color(green)(- 3x -7x) + 7$

$= 3 x (x - 1) - 7 (x - 1)$ $= 3x ( x -1) -7 ( x- 1)$

$= (3 x - 7) (x - 1)$ $= color(blue)( (3x - 7 ) ( x -1)$

How do you factor 3x2−10x+73x^2-10x+7?