Let y = x + -3. Determine m so that m**2 + y*m**2 - 2*m**2 = 0.
0
Let l(r) be the second derivative of r**4/24 + r**3/12 + r. Factor l(b).
b*(b + 1)/2
Let z(i) be the second derivative of -i**2 - 1/6*i**4 + 7*i - 2/3*i**3 + 0. Determine n so that z(n) = 0.
-1
Let z(v) be the second derivative of 0*v**5 + 0 + 0*v**4 + 1/20*v**6 + 0*v**2 + 2*v + 0*v**3. Factor z(u).
3*u**4/2
Let v(y) be the first derivative of y**3/15 + y**2/5 - 3. Factor v(c).
c*(c + 2)/5
Find u such that 20/7*u**2 + 10/7*u**4 + 0 + 16/7*u - 46/7*u**3 = 0.
-2/5, 0, 1, 4
Let t(l) be the first derivative of 1/4*l**2 - 1/8*l**4 - 7 + 0*l + 0*l**3. Suppose t(s) = 0. What is s?
-1, 0, 1
Let m(q) be the first derivative of -q**5 + 5*q**4/4 - 19. Solve m(o) = 0 for o.
0, 1
Let f(p) be the third derivative of 0 - 1/60*p**6 + 1/4*p**4 + 0*p + 0*p**5 - 11*p**2 + 2/3*p**3. Factor f(x).
-2*(x - 2)*(x + 1)**2
Let s(u) be the third derivative of -u**6/30 + u**5/5 - u**4/3 + 7*u**2. Let s(j) = 0. What is j?
0, 1, 2
Let f(a) be the first derivative of -a**8/1680 - a**7/840 + a**6/180 + 5*a**3/3 + 4. Let k(d) be the third derivative of f(d). Factor k(r).
-r**2*(r - 1)*(r + 2)
Find c such that 0 + 3/2*c**3 + 3*c - 9/2*c**2 = 0.
0, 1, 2
Let x(m) = -m**2 + 6*m - 5. Let z be x(5). Suppose -3*u = -z*u. Factor -1/2*t - 1/2*t**2 + u.
-t*(t + 1)/2
Suppose 0 = s + 4*j - 20, 2*s - 24 = -3*s - j. Factor 1 + 3*m**5 - m + m + 5*m**s + 5*m - 2*m**5 + 10*m**3 + 10*m**2.
(m + 1)**5
Let d = -2719/445620 + 9/1061. Let u(f) be the third derivative of -2*f**2 + 0 - d*f**6 + 0*f - 1/210*f**5 + 1/21*f**3 + 1/84*f**4. Factor u(i).
-2*(i - 1)*(i + 1)**2/7
Let z = -9 - -9. Let n(a) = a**3 + 5*a**2 - a - 1. Let w be n(-5). Factor 0*i + z - 2/7*i**3 + 0*i**2 + 2/7*i**w.
2*i**3*(i - 1)/7
Let y(x) be the second derivative of -x**9/3780 + x**8/3360 + x**7/1440 + x**6/2880 - x**4/4 + 2*x. Let u(m) be the third derivative of y(m). Factor u(s).
-s*(s - 1)*(4*s + 1)**2/4
Let a(j) = -j**4 + j**3 - 6*j. Let s(n) = -n**4 + n**3 - 7*n. Let o(d) = 7*a(d) - 6*s(d). Suppose o(u) = 0. What is u?
0, 1
Let r(m) be the third derivative of -m**8/504 + m**7/315 + m**6/180 - m**5/90 - 5*m**2. Let r(o) = 0. What is o?
-1, 0, 1
Let x(f) be the second derivative of -f**5/5 + 7*f**4/3 - 10*f**3 + 18*f**2 - 18*f. Find z such that x(z) = 0.
1, 3
Factor -f - f**3 + 5*f**2 - 2*f**2 + 0*f**3 - f**2.
-f*(f - 1)**2
Let d be 3/(-15) + 2/10. Suppose d = z + 2*z. What is n in -6/7*n**3 + z + 6/7*n**2 - 2/7*n + 2/7*n**4 = 0?
0, 1
Let t(o) be the second derivative of o**8/1680 + o**7/630 - 5*o**4/12 - 7*o. Let a(c) be the third derivative of t(c). Factor a(j).
4*j**2*(j + 1)
Let j be 21 + -3 - (1 + 0). Factor -h**5 - j*h**3 - 2*h**5 - 8*h**4 + 2*h**4 + 14*h**3.
-3*h**3*(h + 1)**2
Factor -1/2*g**2 + 0*g + 1/2.
-(g - 1)*(g + 1)/2
Find t, given that 6*t - 15*t**2 - 6*t**5 - 4*t**4 + 6*t**3 + 31*t**2 + 4*t**5 + 2*t = 0.
-2, -1, 0, 2
Let j be ((-1)/(-3))/((-6)/162). Let a be j/(-132) + 2/11. Factor 1/4*s**5 + 0*s - 1/4*s**3 + 1/4*s**4 + 0 - a*s**2.
s**2*(s - 1)*(s + 1)**2/4
Suppose -4*k**5 + 28*k + 104*k**4 - 12*k**3 - 12*k**3 - 8*k**2 + 0*k**5 - 84*k**4 - 12 = 0. Calculate k.
-1, 1, 3
What is q in 1/7*q**3 + 1/7*q**4 - 1/7*q**5 - 1/7*q**2 + 0*q + 0 = 0?
-1, 0, 1
Let q be -9 + 0 + 3 + 0. Let k(s) = 5*s**2 + 3*s - 11. Let b(r) = -r**2 - r + 3. Let u(g) = q*k(g) - 22*b(g). Factor u(x).
-4*x*(2*x - 1)
Let b = 17 + -17. Let j(s) be the second derivative of 0 - 1/36*s**3 + b*s**2 - 1/36*s**4 - 1/120*s**5 + s. Let j(r) = 0. What is r?
-1, 0
Let u = -170 - -174. Let s = 131/483 - -1/69. Factor 2/7*f**u - s*f + 2/7*f**3 + 0 - 2/7*f**2.
2*f*(f - 1)*(f + 1)**2/7
Let t(m) be the first derivative of -m**4/3 + 8*m**2/3 - 7. Find y, given that t(y) = 0.
-2, 0, 2
Let a(d) = 7*d**2 - 15*d + 16. Let n(v) = -8*v**2 + 15*v - 17. Let o(w) = 5*a(w) + 4*n(w). Suppose o(m) = 0. What is m?
1, 4
Let b be (-12)/(-4) - (1 + 0). Factor 2 + 2 + b + 3*k**2 + 9*k.
3*(k + 1)*(k + 2)
Suppose 4*c + 4*v = -0*c, -2*v = 5*c. Let j(t) be the second derivative of c*t**2 + 0*t**3 + 0 + 1/4*t**4 + 3*t. Factor j(k).
3*k**2
Let z be 14/12 - (-2)/(-2). Let d(y) be the first derivative of z*y**2 + 3 - 1/6*y - 1/18*y**3. Factor d(b).
-(b - 1)**2/6
Suppose 3*c**2 - 18*c**4 + 21/2*c**5 + 0*c + 9/2*c**3 + 0 = 0. Calculate c.
-2/7, 0, 1
Factor 3/2*y**2 - 3/2 - 3/4*y**3 + 3/4*y.
-3*(y - 2)*(y - 1)*(y + 1)/4
Let q = 4 + -1. Suppose 2*v - 2 = 2*r, -q*r - 4 + 3 = -v. Solve 2/5*a + r - 2/5*a**2 = 0.
0, 1
Let f(i) be the third derivative of -i**7/630 + i**6/180 - i**4/36 + i**3/18 + 6*i**2. Factor f(k).
-(k - 1)**3*(k + 1)/3
Solve -1/3 + 2/3*i**2 + 2/3*i - 1/3*i**4 - 4/3*i**3 + 2/3*i**5 = 0 for i.
-1, 1/2, 1
Let b = -201/2 - -2419/24. Let i = 3/8 + b. Factor 0 - i*k**2 + 2/3*k**4 + 0*k**3 - 1/3*k + 1/3*k**5.
k*(k - 1)*(k + 1)**3/3
Let z be 4/(-6) + 8/12. Suppose m + 4*m = z. Factor h**5 + h**4 + 0*h**4 + m*h**5.
h**4*(h + 1)
Let o(h) be the third derivative of h**5/105 - h**4/7 - 12*h**2. Factor o(g).
4*g*(g - 6)/7
Let n = -63/10 + 34/5. Factor n*b - 1/4 - 1/4*b**2.
-(b - 1)**2/4
Let h = 15/2 - 43/6. Factor -1/3*i**3 + 0*i + 0 + h*i**2.
-i**2*(i - 1)/3
Let k(f) be the first derivative of -f**4/12 + f**2/2 - 3*f + 1. Let r(n) be the first derivative of k(n). Factor r(o).
-(o - 1)*(o + 1)
Let u(n) be the second derivative of 1/30*n**4 + 0*n**3 + 0*n**2 + 0 - 5*n + 1/50*n**5. Let u(y) = 0. Calculate y.
-1, 0
Let q(d) be the first derivative of d**3/36 + d**2/24 - 7. Let q(y) = 0. What is y?
-1, 0
Let b(i) be the third derivative of i**5/60 - i**4/6 + i**3/2 + 10*i**2. Solve b(z) = 0 for z.
1, 3
Factor -1/2*j - 3/4 + 1/4*j**2.
(j - 3)*(j + 1)/4
Let b = 353/5 - 352/5. Solve -b*j**3 - 4/5*j**2 - 2/5 - j = 0.
-2, -1
Let v(m) be the second derivative of -m**6/270 + 11*m**4/108 - m**3/3 + 4*m**2/9 - 7*m. Factor v(d).
-(d - 2)*(d - 1)**2*(d + 4)/9
Let c(j) = 2*j**2 + 5*j + 0 + 2 + 8*j**4 + 3 - 5*j**3. Let p(v) = v**4 - v**3 + v**2 + v + 1. Let u be (3 - 2) + 0/2. Let r(k) = u*c(k) - 5*p(k). Factor r(o).
3*o**2*(o - 1)*(o + 1)
Solve 0*t**5 + 2*t**5 + 4*t**4 - 2*t**3 + 3*t**3 + t**3 = 0 for t.
-1, 0
Suppose -2*d + 0*d - 6 = 0. Let i(t) = -t - 1. Let c be i(d). Determine a so that -4/5*a**3 + 0 + 0*a**4 + 0*a**c + 2/5*a**5 + 2/5*a = 0.
-1, 0, 1
Let u = -86 - -90. Let c(g) be the second derivative of 0 + 1/100*g**5 + 2*g - 3/20*g**u - 27/10*g**2 + 9/10*g**3. Factor c(o).
(o - 3)**3/5
Solve -9/4*h + 0 + 3/2*h**2 - 1/4*h**3 = 0 for h.
0, 3
Let k = 389 - 81689/210. Let q(j) be the third derivative of 1/84*j**4 + 0*j**3 - k*j**5 - 3*j**2 + 0*j + 0. Factor q(c).
-2*c*(c - 1)/7
Let r(p) be the third derivative of 0 + 0*p + 1/12*p**3 + 1/80*p**6 - 1/24*p**5 - p**2 + 1/48*p**4. Suppose r(x) = 0. Calculate x.
-1/3, 1
Let x(r) be the second derivative of r**6/720 - r**4/48 - r**3/6 + r. Let u(v) be the second derivative of x(v). Factor u(z).
(z - 1)*(z + 1)/2
Factor -75 + 38*a - 2*a + 48 - 81 - 3*a**2.
-3*(a - 6)**2
Let c(v) be the first derivative of -1/3*v**6 - v**2 + 0*v**5 + 1 + 0*v**3 + v**4 + 0*v. Factor c(p).
-2*p*(p - 1)**2*(p + 1)**2
Suppose 3*n - 52 = -7. Suppose -n = -2*p - 3*p. Factor -3*c**p + 6*c**3 - c**4 + 3*c**4 - c**3.
2*c**3*(c + 1)
Let x(t) be the second derivative of -t**6/15 - t**5/10 + t**4/6 + t**3/3 - 6*t. Suppose x(f) = 0. Calculate f.
-1, 0, 1
Let v be 4 + (-2)/(-1) + -2 + 1. Solve 0*i**3 + 1/4*i**4 + 0*i**2 + 0*i - 1/4*i**v + 0 = 0 for i.
0, 1
Let n be (1/5)/((-96)/(-720)). Suppose -9/4*s + 9/4*s**3 + 3/4*s**2 + 3/4*s**4 - n = 0. What is s?
-2, -1, 1
Let o(v) be the second derivative of v**7/105 + 13*v**6/900 + v**5/150 - v**3/6 + 3*v. Let k(t) be the second derivative of o(t). Solve k(f) = 0 for f.
-2/5, -1/4, 0
Determine l, given that -3*l + 10*l**2 + 0*l**3 - 8*l**2 + l**3 = 0.
-3, 0, 1
Suppose 0 = -4*q + 24 + 8. Let l = -5 + q. Factor 3 - l + 2*p**4 - 2*p**2.
2*p**2*(p - 1)*(p + 1)
Let b(n) be the third derivative of n**8/2688 - n**7/840 - n**6/960 + n**5/240 + 2*n**2. Find f, given that b(f) = 0.
-1, 0, 1, 2
Let r(d) = d**2 - 2*d + 3. Let o be r(2). Let b be (576/42)/(-6) + 4. Suppose b*h**4 - 8/7*h + 8/7 + 2*h**o - 26/7*h**2 = 0. Calculate h.
-2, -2/3, 1/2, 1
Let u(d) be the second derivative of -d**6/60 - d**5/10 - d**4/6 - 11*d. Factor u(j).
-j**2*(j + 2)**2/2
Let j be (-4)/10 - (-16)/40 - 0. Let a(n