t i = 191/9744 + 1/812. Let x(l) be the second derivative of 1/4*l**3 - i*l**4 + 0 + 3*l - 9/8*l**2. Suppose x(w) = 0. What is w?
3
Find j such that 2/7*j**2 - 6/7 - 11/7*j = 0.
-1/2, 6
Let m(y) be the second derivative of 1/28*y**4 - 1/42*y**3 - 1/70*y**6 + 0*y**2 - 7*y + 1/140*y**5 + 0. Let m(v) = 0. What is v?
-1, 0, 1/3, 1
Let p(d) be the second derivative of d**3/6 - 27*d. Let j(h) = -3*h**2 + 5*h + 1. Let o(w) = j(w) - 3*p(w). Factor o(v).
-(v - 1)*(3*v + 1)
Let l(p) be the third derivative of -p**8/1680 + p**7/840 + p**6/360 - p**5/120 - 5*p**3/6 - 3*p**2. Let t(r) be the first derivative of l(r). Factor t(m).
-m*(m - 1)**2*(m + 1)
Factor 3/7*c + 33/7*c**2 - 3/7*c**3 - 33/7.
-3*(c - 11)*(c - 1)*(c + 1)/7
Let w(q) be the first derivative of 2*q**3/27 - 196*q**2/9 + 19208*q/9 + 237. Factor w(j).
2*(j - 98)**2/9
Let y be -51 - -1*0/2*-1. Let l = 257/5 + y. Factor -2/5*c**4 + 2/5*c**2 - l*c**3 + 2/5*c + 0.
-2*c*(c - 1)*(c + 1)**2/5
Let s(u) be the first derivative of -u**3/3 - u + 26. Let x(a) = -3*a**4 + 3*a**3 - a**2 - 3*a - 4. Let y(q) = -4*s(q) + x(q). Factor y(g).
-3*g*(g - 1)**2*(g + 1)
Factor 3*a**2 + 6 + 5/2*a**3 - 23/2*a.
(a - 1)*(a + 3)*(5*a - 4)/2
Suppose -2*t + 16 = 3*m, 0 = m - 1 - 3. Factor 41*u - 14*u - 15 + 3*u**t + 39.
3*(u + 1)*(u + 8)
Let x be 6/(-3)*(-1 + -1). Suppose 33076 = -22*l + 33142. Let 8/5 - 16/5*t**l - 8/5*t**5 + 24/5*t + 6*t**x - 38/5*t**2 = 0. What is t?
-1, -1/4, 1, 2
Let n(q) be the second derivative of 0*q**4 - 2*q + 0*q**3 + 0*q**2 - 3/20*q**5 + 0. Suppose n(x) = 0. Calculate x.
0
Let r(c) be the first derivative of c**6/80 + 3*c**5/160 - 5*c**4/16 - c**3/4 + 9*c**2/2 - 19*c - 45. Let i(s) be the first derivative of r(s). Factor i(q).
3*(q - 2)**2*(q + 2)*(q + 3)/8
Let n be (-3)/((-63)/6) - 94/329. Let j(a) be the first derivative of 4 + 1/6*a**3 + 1/16*a**4 + 0*a**2 + n*a. Suppose j(q) = 0. Calculate q.
-2, 0
Let t(x) = -x**4 - x**2 - x + 1. Let i = 37 + -34. Let h(v) = -7*v**4 + 8*v**3 - 3*v**2 - 11*v + 7. Let f(s) = i*t(s) - h(s). Factor f(r).
4*(r - 1)**3*(r + 1)
Let g(x) = 3*x**2 - 391*x + 1880. Let v be g(5). Find z such that -4/3*z**2 - 1/3*z**5 + 0*z + 1/3*z**4 + 4/3*z**3 + v = 0.
-2, 0, 1, 2
Let l(v) = 2*v**2 - 9*v. Let x be (2/(-6))/((-3)/54). Let u be l(x). Factor -1 + 3 - 4 - 12*q**2 + 14*q - u*q**2 + 18*q**3.
2*(q - 1)*(3*q - 1)**2
Let n = -2693 - -2696. Determine x so that 0*x**2 - 9/2*x**5 - 1/2*x + 5*x**n + 0 + 0*x**4 = 0.
-1, -1/3, 0, 1/3, 1
Let x(l) = 2*l**2 + 4*l + 2. Let y(g) be the first derivative of -g**3/3 + g - 7. Let z(n) = x(n) + y(n). Factor z(p).
(p + 1)*(p + 3)
Let s(c) = 2*c + 2. Let p be s(0). Factor -p*u - 3*u**3 - 2*u**2 - 5*u**4 + 0*u**2 + 7*u**2 + u**5 + 4*u**4.
u*(u - 1)**3*(u + 2)
Let i(n) be the third derivative of n**5/210 + n**4/42 - 5*n**3/7 + 4*n**2 - 15*n. Factor i(v).
2*(v - 3)*(v + 5)/7
Let j(n) be the first derivative of -n**8/1848 + n**7/385 - n**6/330 + n**2 - 4. Let l(r) be the second derivative of j(r). Factor l(h).
-2*h**3*(h - 2)*(h - 1)/11
Let n(w) be the third derivative of -w**7/7560 - w**6/720 - 13*w**4/24 + 10*w**2. Let u(m) be the second derivative of n(m). Find o such that u(o) = 0.
-3, 0
Let u(t) be the third derivative of -1/1344*t**8 + 0 + 0*t**3 + 0*t**4 + 0*t**5 + 0*t + 2*t**2 + 1/840*t**7 + 0*t**6. Factor u(x).
-x**4*(x - 1)/4
Suppose 0 = -3*n - 2*n. Let b(z) be the first derivative of 4/3*z**3 + 4 + 4*z**2 + n*z. Factor b(d).
4*d*(d + 2)
Let t(k) = 8*k**2 - 13*k - 3. Let n be t(2). Factor 768/7 - 48/7*m**n + 288/7*m**2 - 768/7*m + 3/7*m**4.
3*(m - 4)**4/7
Let h(u) be the second derivative of u**8/448 + 11*u**7/840 - 15*u**4/4 - u - 28. Let k(p) be the third derivative of h(p). Solve k(m) = 0 for m.
-11/5, 0
Let m = 403/225 + -42/25. Factor -m*l**2 - 4/9*l**5 + 0*l + 0 - 2/3*l**3 - l**4.
-l**2*(l + 1)**2*(4*l + 1)/9
Determine o so that 11475*o**3 - 636*o**5 + 326 + 274 + 250*o**4 + 4660*o + 12330*o**2 - 1239*o**5 = 0.
-5/3, -2/5, 3
Let o**4 + 2*o**2 + 12*o**3 - 12*o - 3*o**4 - 9*o**3 + 3 + o**4 + 5 = 0. What is o?
-2, 1, 2
Suppose -8 = -3*i + 1. Suppose o = -4*p + i - 1, 0 = -2*o - 2*p + 4. Factor 24 + 4*h**o - 15 - 8*h - 9.
4*h*(h - 2)
What is f in 12*f**4 + 27*f**4 + 42 + 696*f + 267*f**3 - 963*f - 81*f**2 = 0?
-7, -1, 2/13, 1
Let w = -553 - -560. Let h(u) be the second derivative of 1/42*u**w + 0*u**2 + 1/10*u**5 + 0*u**4 + 0 + 4/45*u**6 - 7*u - 1/18*u**3. Factor h(c).
c*(c + 1)**3*(3*c - 1)/3
Let a be 96/(-15)*(-10)/4. Let s = -9 + a. Factor -s*q - 8 + 5*q + 2 - 7*q + 3*q**3.
3*(q - 2)*(q + 1)**2
Let x(a) be the third derivative of -a**7/105 + a**6/20 + a**5/30 - a**4/4 - 20*a**2 - a. Find i such that x(i) = 0.
-1, 0, 1, 3
Let z be (120/(-14))/(-15)*21/5. Suppose -a**3 - 18/5*a**2 + 8/5 - z*a = 0. Calculate a.
-2, 2/5
Let c(o) be the third derivative of 0*o**4 + 1/120*o**5 + 0*o**3 - 1/160*o**6 - 16*o**2 + 0 + 0*o**7 + 1/1344*o**8 + 0*o. Factor c(g).
g**2*(g - 1)**2*(g + 2)/4
Suppose 0 = -2*z + 77 - 31. Let t(u) = 2*u - 42. Let b be t(z). Suppose -2/9*k**b + 0 + 4/9*k**3 - 2/9*k**2 + 0*k = 0. What is k?
0, 1
Let k be 495/12 - (-10)/(-8). Let 464*i**4 - k*i + 20*i**2 + 7*i**3 - 469*i**4 + 3*i**3 = 0. What is i?
-2, 0, 2
Let h(b) be the first derivative of 0*b + 2/33*b**3 - 1 - 1/33*b**6 + 0*b**2 - 3/22*b**4 + 6/55*b**5. Suppose h(a) = 0. Calculate a.
0, 1
Suppose -3*v - v - 52 = 0. Let u = -1 - v. Factor -14 - 7 + 5 - 16*s + 12*s**3 + u*s**2 + 4*s**3 + 4*s**4.
4*(s - 1)*(s + 1)*(s + 2)**2
Factor 16*u**4 - 57*u**3 + 8*u**4 - 21*u**5 + 18*u**5 + 12*u**3.
-3*u**3*(u - 5)*(u - 3)
Let u(m) = -3*m**2 - 17*m + 4. Let r(p) = 4*p**2 + 19*p - 5. Let v(x) = -4*r(x) - 5*u(x). Determine j so that v(j) = 0.
0, 9
Let c(u) = u. Let g be c(0). Suppose g = -2*i + 4 + 2. Find q such that -4/7*q + 0 - 18/7*q**i - 10/7*q**4 - 2/7*q**5 - 2*q**2 = 0.
-2, -1, 0
Suppose 2 = j - f, 4*j = -j - 3*f + 26. Factor -1/2*y**3 + 1/2*y - 1/4*y**j - 3/4 + y**2.
-(y - 1)**2*(y + 1)*(y + 3)/4
Let f = 208 + -208. Let h(l) be the first derivative of -l**2 - 1 - 1/3*l**3 + f*l. Determine i so that h(i) = 0.
-2, 0
Let x(i) be the first derivative of -i**4/4 + i - 278. Let s = 7 - 4. Let v(y) = -7*y**3 - 8*y**2 - 4*y + 3. Let j(k) = s*x(k) - v(k). Factor j(r).
4*r*(r + 1)**2
Let w(f) be the second derivative of f**5/90 + 13*f**4/18 + 16*f**3 + 108*f**2 + 168*f. Find r, given that w(r) = 0.
-18, -3
Suppose 48*k - 66*k = -36. Suppose 2/5*l**3 - 6/5 - 2/5*l**2 - k*l = 0. What is l?
-1, 3
Suppose -894*w + 899*w = s + 6, 3*w - 14 = -2*s. Solve -13/4*k**3 - 1/2 + 5/4*k**4 + 9/4*k**w + 1/4*k = 0 for k.
-2/5, 1
Let c(t) be the third derivative of -t**7/210 + t**6/30 + 7*t**5/60 - 5*t**4/12 - 16*t**2. Factor c(i).
-i*(i - 5)*(i - 1)*(i + 2)
Let x(r) = 9*r - 83. Let a be x(10). Suppose -6*y + a = -17. Factor 0 - 1/2*w**5 + 0*w - 2*w**2 - 5/2*w**y - 4*w**3.
-w**2*(w + 1)*(w + 2)**2/2
Let g(a) be the third derivative of -a**5/20 + 5*a**4/4 - 21*a**3/2 - 128*a**2. Solve g(i) = 0.
3, 7
Suppose -4*t - 5*h = -0*h - 26, 4*t - h = 38. Suppose 7*c = t*c - 6. Solve 14*a**3 + 21*a**c - 4*a**2 - 37*a**3 = 0.
-2, 0
Let -30*n**2 + 0*n + 46/3*n**3 + 2/15*n**5 - 38/15*n**4 + 0 = 0. Calculate n.
0, 5, 9
Let h(i) = 5*i**2 - 23*i - 2. Let x(p) = -p**2 + p + 1. Let y(k) = -h(k) - 2*x(k). Factor y(l).
-3*l*(l - 7)
Let p(j) be the first derivative of 8/9*j + 7 + 4/9*j**2 - 2/9*j**3 - 2/9*j**4 - 2/45*j**5. Determine h so that p(h) = 0.
-2, -1, 1
Let s(m) = -7*m**2 - m + 6*m + 10*m**2 - 2*m**3 + m**3 - 4. Let j be s(4). Factor j - 2/5*g**2 + 2/5*g**4 + 0*g**3 + 0*g.
2*g**2*(g - 1)*(g + 1)/5
Let u(y) be the third derivative of 0*y**3 + 37*y**2 + 0*y**7 + 1/504*y**8 + 0 - 7/180*y**6 + 1/15*y**5 + 0*y**4 + 0*y. Let u(x) = 0. What is x?
-3, 0, 1, 2
Suppose -5*t - 5*k - 40 = 0, 4*t + 6*k - 11*k = 13. Let d be ((-204)/90 - -2)*t. Factor -4/5*s**2 + 3/5*s**3 - d*s - 1/5*s**5 + 0 + 2/5*s**4.
-s*(s - 2)**2*(s + 1)**2/5
Let j(x) = -x**4 - x**3 + x**2 + 5*x - 4. Let z(g) = -g + 1. Let m(u) = j(u) + 4*z(u). Determine k so that m(k) = 0.
-1, 0, 1
Let u(g) be the first derivative of 1/12*g**3 + 0*g**2 + 0*g - 14 - 1/16*g**4. Factor u(y).
-y**2*(y - 1)/4
Let x(c) be the second derivative of 0 + 3/5*c**5 + 34*c - 1/2*c**4 + 2/5*c**6 + 1/14*c**7 - 5/2*c**3 - 3*c**2. Factor x(i).
3*(i - 1)*(i + 1)**3*(i + 2)
Let v(s) be the s