Write this trinomial in factored form. 3b^2+b-14

Mathematics

1 answer:

Makovka662 [10]3 years ago

4 0

Answer:

(b - 2)(3b + 7)

Step-by-step explanation:

Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term

product = 3 × - 14 = - 42 and sum = + 1

The factors are - 6 and + 7

Use these factors to split the b- term

3b² - 6b + 7b - 14 ( factor the first/second and third/fourth terms )

= 3b(b - 2) + 7(b - 2) ← factor out (b - 2) from each term

= (b - 2)(3b + 7) ← in factored form

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Solve the system of equations. x+y=4 y=x^2 - 8x + 16 a) {(-3,7).(-4, 8)} b) [(4,0)} c) {(3,1),(4,0) d) {(3,7). (4.0)} e) none

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$x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

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$y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.$