SOLUTION: Students are trying to factor quadratic expressions using the guess-and-check method. Find the mistake in each student's work. Then give the correct answer. a) 𝑥(small 2)

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Question 1183025: Students are trying to factor quadratic expressions using the guess-and-check method. Find the mistake in each student's work. Then give the correct answer.
a) 𝑥(small 2)―𝑥―72=(𝑥―8)(𝑥+9)
b) 3𝑥(small 2)―19𝑥+28=(3𝑥―4)(𝑥―7)
c) 6𝑥(small 2)+25𝑥+4=(2𝑥+1)(3𝑥+4)
Found 3 solutions by MathLover1, greenestamps, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a)
x%5E2-x+-72=%28x-8%29%28x%2B9%29
%28x-8%29%28x%2B9%29....multiply
=x%2Ax%2B9x-8x-8%289%29
=x%5E2%2Bx-72
mistake was -x, should be x+
b)
3x%5E2-19x%2B28=%283x-4%29%28x-7%29
%283x-4%29%28x-7%29....multiply
=3x%2Ax%2B3x%28-7%29-4%2Ax-4%28-7%29
=3x%5E2-21x+-4x%2B28
=3x%5E2-25x+%2B28
mistake was -19x, should be +-25x


c)
6x%5E2%2B25x%2B4=%282x%2B1%29%283x%2B4%29
%282x%2B1%29%283x%2B4%29...multiply
=2x%2A3x%2B2x%2A4%2B1%2A3x%2B1%2A4
=6x%5E2%2B8x%2B3x%2B4
=6x%5E2%2B11x%2B4
mistake was 25x, should be 11x

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


a) 𝑥^2―𝑥―72=(𝑥―8)(𝑥+9)

The student's factorization, when multiplied back out, gives middle term "x" instead of the required "-x". Since the coefficient is the right magnitude but wrong sign, the correct factorization can be obtained by switching the signs of the two factors: x^2-x-72 = (x+9)(x-8)

b) 3𝑥^2―19𝑥+28=(3𝑥―4)(𝑥―7)

The student's factorization when multiplied back out gives the correct quadratic term and constant, but the linear term is -25x instead of the required -19x. Since the only way to get the 3x^2 in the product is with "x" and "3x" in the two linear factors, the only thing we can do to try to get the factorization is switch the constant terms in the two factors.

And that gives us the right factorization: (3x-7)(x-4) = 3x^2-19x+28

c) 6𝑥^2+25𝑥+4=(2𝑥+1)(3𝑥+4)

Again the student's factorization gives the correct quadratic term and constant in the product, but the coefficient of the linear term is 11x instead of the required 25x. Since the required linear coefficient 25 is "large", the linear terms in the two factors are probably going to have to be 6x and x instead of 3x and 2x.

And indeed the correct factorization is (6x+1)(x+4) = 6x^2+25x+4

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Students are trying to factor quadratic expressions using the guess-and-check method.
Find the mistake in each student's work. Then give the correct answer.
a) x(small 2)―x―72=(x―8)(x+9)
b) 3x(small 2)―19x+28=(3x―4)(x―7)
c) 6x(small 2)+25x+4=(2x+1)(3x+4)
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            @MathLover1 misread the problem.

            The task  IS  NOT  to check multiplications of binomials.

            The task is to check if the DECOMPOSITION/factoring is made correctly. 


(a)  x^2 - x - 72 = (x+8)*(x-9)



(b)  3x^2 - 19 + 28 = (3x-7)*(x-4)



(c)  6x^2 + 25x + 4 = (6x+1)*(x+4)


So, for your safety, you better ignore the post by @MathLover1.