Factor completely. 3x^(2)-13 x+10 Answer:

Identify a, b, c: Identify a, b, and c in the quadratic expression 3x^2 - 13x + 10. Compare 3x^2 - 13x + 10 with ax^2 + bx + c. a = 3 b = -13 c = 10Find two numbers: Find two numbers whose product is a*c (3*10 = 30) and whose sum is b (-13). We need to find two numbers that multiply to 30 and add up to -13. -3 * -10 = 30 -3 + -10 = -13 Two numbers: -3, -10Rewrite middle term: Rewrite the middle term -13x using the two numbers found in Step 2. 3x^2 - 3x - 10x + 10Factor by grouping: Factor by grouping. Group the terms: (3x^2 - 3x) + (-10x + 10) Factor out the common factors from each group. 3x(x - 1) - 10(x - 1)Factor out common binomial: Factor out the common binomial factor (x - 1). (3x - 10)(x - 1)

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Q. Factor completely.

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3 x^{2}-13 x+10

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3x^2 - 13x + 10$ . Compare $3x^2 - 13x + 10$ with $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $3*10 = 30$ ) and whose sum is $b$ ( $-13$ ). $\newline$ We need to find two numbers that multiply to $30$ and add up to $-13$ . $\newline$ $-3 * -10 = 30$ $\newline$ $-3 + -10 = -13$ $\newline$ Two numbers: $-3$ , $-10$
Rewrite middle term: Rewrite the middle term $-13x$ using the two numbers found in Step $2$ . $\newline$ $3x^2 - 3x - 10x + 10$
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $(3x^2 - 3x) + (-10x + 10)$ $\newline$ Factor out the common factors from each group. $\newline$ $3x(x - 1) - 10(x - 1)$
Factor out common binomial: Factor out the common binomial factor $(x - 1)$ . $(3x - 10)(x - 1)$