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)�

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)   (Show Source): You can put this solution on YOUR website!

a)

....multiply
=
=
mistake was , should be
b)

....multiply
=
=
=
mistake was , should be

c)

...multiply
=
=
=
mistake was , should be

Answer by greenestamps(13200)   (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)   (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)
~~~~~~~~~~~~~~~~~~~~

            @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.

RELATED QUESTIONS
Two students both solved the equation -4x-0.5=6 incorrectly. The work of each student is (answered by MathLover1)
Two engineering students are solving a problem leading to a quadratic equation. One... (answered by Theo)
UNFINISHED Mary and Richard worked as a team to solve the following problem. (answered by Boreal)
How do you factor this trinomial using the Guess and Check Method 3x^2+16x+5? Thank you... (answered by richwmiller,Theo)
A class is taking a multiple-choice quiz that consists of 15 questions. Each question... (answered by mathmate)
One angle in a triangle is half the largest angle but three times the smallest. Find all (answered by stanbon)
A rectangle has area 60 cm2 and perimeter 38 cm. Use the "guess and check" method to... (answered by checkley71)
I am having a terrible time trying to solve this question, please help. Jelly bean Jar... (answered by solver91311)
Problem: "Using the numbers 9, 8, 7, 6, 5, and 4, once each. Find the smallest... (answered by Alan3354)