, 2
Let q = -6 + 8. Let z(f) = f**3 - 2*f**2 + 2*f. Let u be z(q). Determine i, given that u - i**3 - 2*i**3 + 4*i**3 - 3*i**2 = 0.
-1, 2
Let s(r) = r**2 - 8*r - 7. Let z be s(9). Let b(c) = c**3 - c**2 - 1. Let m be b(z). Factor 0*l**2 + 1/2 + l**m - 1/2*l**4 - l.
-(l - 1)**3*(l + 1)/2
Find r, given that -3*r**4 - 9*r**3 + 6*r**4 - 2*r - r + 9*r**2 + 0*r**2 = 0.
0, 1
Factor 8/3*m + 2/3*m**2 - 8/3 - 2/3*m**3.
-2*(m - 2)*(m - 1)*(m + 2)/3
Factor 9/4 + 1/4*x**2 - 3/2*x.
(x - 3)**2/4
Let a(p) be the second derivative of p**7/6300 + p**6/1800 - p**5/150 + 7*p**4/12 - 7*p. Let q(b) be the third derivative of a(b). Factor q(v).
2*(v - 1)*(v + 2)/5
Let n(x) = x**2 - 5*x + 6. Let g be n(5). Factor g*d**2 - 13*d**2 + d**4 + 8*d**2 - 2*d**3.
d**2*(d - 1)**2
Factor 35*b - 12 - 30*b**4 - 24*b**3 + 3*b**5 - 14*b + 6*b**2 + 36*b**4.
3*(b - 1)**3*(b + 1)*(b + 4)
Let w = 12 - 8. Suppose c = i, -5*c = -0*i - 3*i - 8. Factor -3*j**4 + j**3 + 3*j**4 - j**w + 2*j**i - j**2 - j.
j*(j - 1)*(j + 1)**2
Determine s, given that -s**5 - 18*s**3 - 2*s**4 + 18*s**3 + 2*s**2 + 0*s**2 + s = 0.
-1, 0, 1
Let f(q) be the first derivative of -q**5/5 + 3*q**4/4 - 2*q**3/3 - 12. Factor f(l).
-l**2*(l - 2)*(l - 1)
Let x(n) be the second derivative of -2*n + 0 + 0*n**2 + 1/20*n**6 + 0*n**3 - 1/84*n**7 + 1/24*n**4 - 3/40*n**5. Factor x(t).
-t**2*(t - 1)**3/2
Let n(t) = 3*t**2 + 18*t + 12. Let z(a) = -1. Let w(i) = n(i) - 15*z(i). Let w(l) = 0. What is l?
-3
Let f(n) be the third derivative of n**5/360 - 5*n**4/36 + 25*n**3/9 - 36*n**2. Factor f(q).
(q - 10)**2/6
Let x(b) be the third derivative of -b**6/1440 - b**5/240 - b**4/96 - b**3/3 + b**2. Let g(p) be the first derivative of x(p). Determine k, given that g(k) = 0.
-1
Let h(y) be the third derivative of y**7/1890 - y**6/1080 - y**5/108 - y**4/72 + 19*y**2. Let h(u) = 0. What is u?
-1, 0, 3
Let c(a) be the first derivative of -a**4/4 + 2*a**2 - 17. Factor c(z).
-z*(z - 2)*(z + 2)
Let o(j) = -6*j**3 - 2*j**2 + 12*j - 8. Let q(n) = -13*n**3 - 5*n**2 + 24*n - 16. Let p(z) = -5*o(z) + 2*q(z). Solve p(g) = 0.
-2, 1
Factor 28*b - 53*b + 11*b**3 - 12*b**2 - 3*b**4 + 29*b.
-b*(b - 2)*(b - 1)*(3*b - 2)
Let j(a) be the first derivative of -a**6/1620 + a**5/540 + a**4/54 + a**3 - 1. Let r(q) be the third derivative of j(q). Determine i, given that r(i) = 0.
-1, 2
What is l in 0*l + 2/7*l**2 + 12/7*l**3 + 10/7*l**4 + 0 = 0?
-1, -1/5, 0
Let o(r) be the first derivative of -6*r**3 + 3*r**3 - 12*r + 2*r**3 + 0*r**3 + 6*r**2 - 1. Factor o(z).
-3*(z - 2)**2
Let a(o) be the second derivative of -4*o + 13/6*o**4 - 1/2*o**5 - 4/3*o**3 + 0 - 4*o**2. Factor a(i).
-2*(i - 2)*(i - 1)*(5*i + 2)
Suppose -4*i = -3*i + 3*s, i + s = 0. Let z(l) be the second derivative of -7/18*l**4 + i - 2*l - 2/3*l**2 + l**3. Find k, given that z(k) = 0.
2/7, 1
Factor 25*j + 10 - 34*j**3 - 5*j**5 - 5*j**2 - 20*j**4 + 18*j**2 - 3*j**2 + 14*j**3.
-5*(j - 1)*(j + 1)**3*(j + 2)
Suppose 0 = -h + 10 - 7. Factor 6*f**2 + 11*f**3 - f**h - f**3 + 9*f - 12*f.
3*f*(f + 1)*(3*f - 1)
Let m(b) be the second derivative of b**4/6 - 4*b**3/3 + 3*b**2 + 8*b. Determine n so that m(n) = 0.
1, 3
Let y(w) be the third derivative of w**9/7560 + w**8/4704 - w**7/4410 - w**4/24 + 4*w**2. Let z(p) be the second derivative of y(p). Solve z(x) = 0.
-1, 0, 2/7
Let u = -1 - -3. Solve 3*d**4 - 16*d**u + 3*d**3 + 16*d**2 = 0.
-1, 0
Suppose 24*u = 14*u + 40. Solve 0 + 2/3*y**3 + 0*y**2 + 2/3*y**u + 0*y = 0.
-1, 0
Let h(i) = i + 1. Let o be h(-7). Let l be 4/o - 8/(-6). Factor 0 - l*d**3 + 0*d - 2/3*d**2.
-2*d**2*(d + 1)/3
Let t(a) be the second derivative of -a**6/75 + 3*a**5/50 - a**4/10 + a**3/15 - a. Factor t(m).
-2*m*(m - 1)**3/5
Let k = 32/75 - -6/25. Factor -2/3*h**3 + k*h + 0*h**2 + 0.
-2*h*(h - 1)*(h + 1)/3
Let t(c) = c**2 + 49*c. Let x be t(-49). Factor 0*k**2 + x*k + 3/5*k**4 + 0 + 3/5*k**3.
3*k**3*(k + 1)/5
Factor 4*t**5 + 1691 - 1691 + 108*t**2 + 36*t**4 + 108*t**3.
4*t**2*(t + 3)**3
Let o(d) be the second derivative of -d**4/66 + 2*d**3/33 - d**2/11 - 8*d. Factor o(x).
-2*(x - 1)**2/11
Let 1/10*b**2 + 0 - 1/10*b**3 + 1/5*b = 0. Calculate b.
-1, 0, 2
Factor 7 - 6*y**3 + 6*y**2 + 3*y**3 - 7.
-3*y**2*(y - 2)
Let c(v) be the first derivative of -v**6/540 - v**5/90 - 4*v**3/3 + 4. Let q(y) be the third derivative of c(y). Find o such that q(o) = 0.
-2, 0
Let f(j) be the first derivative of j**5/15 - j**3/3 - j**2/3 - 31. Factor f(o).
o*(o - 2)*(o + 1)**2/3
Let t(n) be the third derivative of 1/12*n**5 + 2/3*n**3 + 1/120*n**6 + 0*n + 3*n**2 + 1/3*n**4 + 0. Factor t(g).
(g + 1)*(g + 2)**2
Let v(n) be the third derivative of n**6/30 - 4*n**5/15 + 2*n**4/3 - 3*n**2. Factor v(u).
4*u*(u - 2)**2
Let q(m) be the third derivative of m**5/84 + m**4/56 - m**3/21 + 6*m**2. Factor q(o).
(o + 1)*(5*o - 2)/7
Let o = -2 - -2. Let b = o + 3. What is q in -5*q - 8*q**b - 2*q**2 + 3*q - 8*q**2 = 0?
-1, -1/4, 0
Let f(s) be the second derivative of -1/6*s**3 - 2/75*s**6 + 0 + 1/210*s**7 + 1/25*s**5 + 10*s + 1/5*s**2 + 1/30*s**4. Factor f(t).
(t - 2)*(t - 1)**3*(t + 1)/5
Suppose -2 = -148*j + 147*j. Let m be 3 + (0 - (-1)/1). Solve -6/5*b**2 + 2/5*b**m - j*b - 4/5 + 2/5*b**3 = 0.
-1, 2
Let h(w) = w**4 + w**3 + w**2 - w + 1. Let y(v) = -v**4 - v**4 - v - 8*v**3 - 6 + 9*v - 2*v**2 - 2*v**2. Let z(k) = 4*h(k) + y(k). Factor z(t).
2*(t - 1)**3*(t + 1)
Let d(h) be the third derivative of -h**7/840 + h**6/120 + h**4/8 - h**2. Let k(m) be the second derivative of d(m). Determine v so that k(v) = 0.
0, 2
Suppose 2*a = 3*a. Let o = 115/93 + 3/31. Suppose -2/3*j**5 - 4/3*j**4 + o*j**2 + 0*j**3 + 2/3*j + a = 0. What is j?
-1, 0, 1
Let t(c) be the first derivative of -1/6*c**2 - 1 - c + 1/9*c**3 - 1/36*c**4. Let q(u) be the first derivative of t(u). Factor q(m).
-(m - 1)**2/3
Suppose -5*u + 6*n = 2*n - 203, 0 = 5*u - 3*n - 206. What is l in -39*l**4 - 6 + 2 + 4*l**3 - 35*l**5 + 31*l**3 + u*l**2 = 0?
-1, -2/5, 2/7, 1
Let j(c) be the first derivative of -2*c**6/3 + 16*c**5/5 - 5*c**4 + 8*c**3/3 + 4. Factor j(k).
-4*k**2*(k - 2)*(k - 1)**2
Let a(n) be the third derivative of 2*n**7/105 + n**6/30 - n**5/15 - n**4/6 - 6*n**2. Factor a(y).
4*y*(y - 1)*(y + 1)**2
Let c(u) = 3*u**3 + u**2 - 9*u + 7. Let y(s) = s**3 - s**2 + 1. Let g(t) = c(t) - 2*y(t). Solve g(j) = 0.
-5, 1
Let i = 327 + -322. Suppose 0*h**2 + 0 - 6/5*h**4 + 0*h - 2*h**i + 4/5*h**3 = 0. Calculate h.
-1, 0, 2/5
Let o(r) be the first derivative of 2*r**3/33 - 5*r**2/11 + 4. Factor o(g).
2*g*(g - 5)/11
Let d(x) be the second derivative of x**7/42 + x**6/30 - 10*x. Suppose d(m) = 0. Calculate m.
-1, 0
Let n(c) be the second derivative of -c**7/14 + 8*c**6/15 - 29*c**5/20 + 5*c**4/3 - 2*c**3/3 - 16*c. Find a such that n(a) = 0.
0, 1/3, 1, 2
Let r(h) = h**2 + h + 2. Let m(c) = 4*c**2 + 11 - 3*c**2 + 4*c**2 + 7*c - c. Let o(w) = -2*m(w) + 11*r(w). What is d in o(d) = 0?
0, 1
Let l(j) be the first derivative of -j**5/10 - j**4/4 + j**2/2 + j/2 - 9. Find f, given that l(f) = 0.
-1, 1
Let h(c) be the first derivative of c**6/420 + c**5/210 - c**4/84 - c**3/21 + c**2 + 2. Let l(v) be the second derivative of h(v). Factor l(u).
2*(u - 1)*(u + 1)**2/7
Let o(m) = -m - 10. Let t be o(-8). Let b = t - -5. Factor v + v**4 + 0*v**2 - 2*v**4 + 3*v**b - 3*v**2.
-v*(v - 1)**3
Suppose -u + 1 = 4*j - 10, -5*j = u - 13. Let n(x) be the second derivative of -2*x + 0*x**u + 0 + 1/36*x**4 + 0*x**2. Let n(y) = 0. What is y?
0
Let m(x) be the third derivative of x**9/20160 - x**8/26880 - x**7/1260 - x**6/720 + 5*x**4/24 + 5*x**2. Let u(g) be the second derivative of m(g). Factor u(w).
w*(w - 2)*(w + 1)*(3*w + 2)/4
Let u(j) be the first derivative of -1/5*j**3 + 3/25*j**5 + 0*j**2 + 0*j - 2/5*j**6 + 3/5*j**4 + 3. What is x in u(x) = 0?
-1, 0, 1/4, 1
Suppose 3*k + s = k + 19, 2*s - 31 = -3*k. Suppose -3 = 2*p - k. Factor 2/3*v + 1/3 + 1/3*v**p.
(v + 1)**2/3
Suppose -2*l = 8 - 32. Let z be (l/15)/(1 - -1). Determine n, given that -2/5*n**2 + 0 + z*n = 0.
0, 1
Let o(h) be the third derivative of -1/3*h**3 - 1/60*h**6 + 5*h**2 + 1/12*h**4 + 0 + 1/30*h**5 + 0*h. Factor o(u).
-2*(u - 1)**2*(u + 1)
Let x(o) = -2*o**4 + 2*o**3 + 2*o**2 - 2*o. Let n(z) = 6*z**4 - 4*z**4 - 2*z - 2*z**2 - 2*z**3 - z + 5*z. Let q(s) = 6*n(s) + 7*x(s). Factor q(t).
-2*t*(t - 1)**2*(t + 1)
Let b(r) be the third derivative of