 k(t) = -11*u(t) + 4*y(t). Solve k(i) = 0 for i.
-19, -1, 1
Suppose -5*a = -6*a - 3, 3*c = -3*a. Factor 15*k**2 - 6*k + 0*k + 7*k**3 - k**c - 15*k**4.
-3*k*(k - 1)*(k + 1)*(5*k - 2)
Factor -5*a**2 - 2140*a**4 + 5*a**2 + 2143*a**4 + 3*a**3.
3*a**3*(a + 1)
Suppose -5*b + 16 = -4, -3*c - 4*b + 1 = 0. Let g(r) = r**2 + 3*r - 6. Let m be g(c). Factor -2/5*a**3 + 1/5*a**5 - 2/5*a**2 + 1/5 + 1/5*a**m + 1/5*a.
(a - 1)**2*(a + 1)**3/5
Let o be ((0/(4 + -9))/10)/6. What is t in -2/3*t**2 + 8/3 + o*t = 0?
-2, 2
Suppose -s - 4*o = o + 10, -4 = 2*o. Solve -4*x**4 + 2*x + s*x**4 - 5*x**2 + 2*x**2 + 5*x**4 = 0 for x.
-2, 0, 1
Let f(t) be the first derivative of -3*t**3 + 2 + 45/4*t**4 + 3*t**6 - 51/5*t**5 - 3/2*t**2 + 0*t. Factor f(b).
3*b*(b - 1)**3*(6*b + 1)
Let t(s) be the second derivative of s**7/3150 - 2*s**5/75 + 5*s**4/4 - 5*s. Let a(x) be the third derivative of t(x). Factor a(c).
4*(c - 2)*(c + 2)/5
Suppose -14 - 1 = -3*g. Let n(q) be the second derivative of -2*q + 1/4*q**4 - 1/2*q**3 - 3/2*q**2 + 0 + 3/20*q**g. Suppose n(o) = 0. What is o?
-1, 1
Let g(l) = 23*l**4 - 36*l**3 + 61*l**2 - 38*l + 24. Let t(h) = -8*h**4 + 12*h**3 - 20*h**2 + 12*h - 8. Let y(q) = -6*g(q) - 17*t(q). Factor y(x).
-2*(x - 2)**2*(x - 1)**2
Let t be (4 - 4/(-2)) + 116/(-29). Let 4/3*z + 2/3*z**3 - 2*z**t + 0 = 0. What is z?
0, 1, 2
Determine p, given that 2/5*p**2 - 6/5*p - 4/5 + 2/5*p**4 + 6/5*p**3 = 0.
-2, -1, 1
Let j(i) be the first derivative of i**6/40 - 9*i**5/40 + 13*i**4/16 - 3*i**3/2 + 3*i**2/2 + 33*i + 19. Let h(u) be the first derivative of j(u). Factor h(x).
3*(x - 2)**2*(x - 1)**2/4
Let q(i) be the first derivative of -7*i**5/20 - 19*i**4/8 + 3*i**3 - 5*i**2/2 - 22. Let b(h) be the second derivative of q(h). Suppose b(x) = 0. Calculate x.
-3, 2/7
Let h(b) be the second derivative of 1/15*b**6 + 1/3*b**3 - 4*b + 0*b**2 - 1/4*b**4 + 0 - 3/20*b**5. Factor h(p).
p*(p - 2)*(p + 1)*(2*p - 1)
Let y = 25 + -38. Let r = 30 + y. Factor r*q**3 - 3*q**2 - 2 - q**2 - 18*q**3 - 5*q.
-(q + 1)**2*(q + 2)
Let k = -83 + 665/8. Let c be 21/120 - (180/(-25) + 7). Determine l, given that 1/8 + c*l**2 + k*l**3 + 3/8*l = 0.
-1
Determine v, given that -4*v**2 + 17/4*v - 1/4 = 0.
1/16, 1
Let l(t) be the first derivative of t**6/1800 + t**5/200 + t**4/60 + 8*t**3/3 - 5. Let m(r) be the third derivative of l(r). Suppose m(o) = 0. What is o?
-2, -1
Find b, given that 0 + 2/3*b**5 + 22/9*b**4 - 22/9*b**2 - 4/3*b + 2/3*b**3 = 0.
-3, -1, -2/3, 0, 1
Let x be 180/45*(-4)/(-8). Factor 1/2*j**x + 1/2*j**3 - 1/2*j**4 + 0 - 1/2*j.
-j*(j - 1)**2*(j + 1)/2
Let u(l) be the third derivative of l**5/90 - 20*l**4/9 + 1600*l**3/9 - 465*l**2. Factor u(t).
2*(t - 40)**2/3
Suppose 2*k = 2*l - 12, 0 = -l - k - k. Let m(x) = -3*x + 35. Let s be m(10). Determine d, given that s*d**4 - 31*d + 16 - 3*d**l - 14*d**3 + 36*d**2 - 9*d = 0.
1, 2
Suppose 8*g - 24/7*g**3 + 36/7*g**2 - 4/7*g**4 + 0 = 0. Calculate g.
-7, -1, 0, 2
Let y = 15 - 11. Suppose -y*r - 2 = h, 2*h + r = -0*r + 3. Determine t so that 6*t**3 - 49*t**2 + 8 + t**2 + 22*t**3 + h*t + 10*t = 0.
-2/7, 1
Let m = -111 + 101. Let d = m + 10. Let 3*x**3 - 3/2*x**5 + 0*x**4 - 3/2*x + 0*x**2 + d = 0. Calculate x.
-1, 0, 1
Let h(b) be the first derivative of -8*b + b**4 + 5 - 2*b**2 + 8/3*b**3. Solve h(t) = 0.
-2, -1, 1
Let k be (-3)/(6/(-8)) + -13. Let y be (4/(-3))/(k - -5). Solve y*w**2 + 2/3 - w = 0.
1, 2
Let b(s) be the third derivative of 0 - 1/240*s**5 - 1/48*s**4 - 4*s**2 + 0*s**3 + 0*s. Factor b(q).
-q*(q + 2)/4
Suppose 8*k + 7 - 39 = 0. Let s(z) be the third derivative of 0*z + 0 - 5*z**2 + 1/120*z**6 + 0*z**3 - 1/20*z**5 + 1/12*z**k. Determine x so that s(x) = 0.
0, 1, 2
Suppose -4*q + 7 + 9 = 0. Factor 74*u - 120 + 308 + q*u**2 - 10*u + 68.
4*(u + 8)**2
Let k(u) = -u**4 - u. Let y(b) = -102*b**4 + 10*b**3 + 3*b. Let m = -1 - -2. Let t(c) = m*y(c) + 3*k(c). What is o in t(o) = 0?
0, 2/21
Let t = 0 + 4. Suppose -2 = -t*y + 14. Solve 4*d**2 - d**3 - y*d**3 + d**3 + 2*d**3 - 2*d = 0.
0, 1
Suppose -13*y + 8*y + 2150 = 0. Suppose y = 8*f - 3*f. Factor -12*r**2 - 86 + 9*r**4 - 3*r**5 + f.
-3*r**2*(r - 2)**2*(r + 1)
Let c(f) = -f**3 + f**2 + f + 1. Let t(v) = -11*v**3 + 15*v - 33 + 3*v + 48 + 13*v**2 - v**3. Let s(q) = 22*c(q) - 2*t(q). Suppose s(j) = 0. Calculate j.
-1, 4
Let u(x) = 7*x + 25. Let r be u(-3). Let a(t) be the first derivative of 4 + 0*t + 0*t**5 + 0*t**2 + 1/30*t**6 + 0*t**3 - 1/20*t**r. Solve a(h) = 0.
-1, 0, 1
Let u be (7 - 10) + 45/(-5). Let c be u/(-28) - 12/28. Suppose -8/3*v + c + 28/3*v**2 = 0. Calculate v.
0, 2/7
Factor 32/9 + 4/3*t + 2/9*t**3 - 2*t**2.
2*(t - 8)*(t - 2)*(t + 1)/9
Factor 3*j**2 + 1/2*j**3 + 9/2*j + 2.
(j + 1)**2*(j + 4)/2
Suppose 2*y + 48 = -y. Let j = 18 + y. Find s, given that s**2 - 119*s**4 + j*s - 2*s**3 - 6*s**3 + 124*s**4 = 0.
-2/5, 0, 1
Let m(a) be the second derivative of 5*a**4/12 + 25*a**3/2 + 125*a**2 - 15*a - 6. Factor m(w).
5*(w + 5)*(w + 10)
Let v(d) be the second derivative of -d**7/4200 + d**5/200 - 3*d**4/4 - d**2 + 11*d + 2. Let j(w) be the third derivative of v(w). Find u such that j(u) = 0.
-1, 1
Let d = 61 - 38. Suppose 8 = 27*v - d*v. Find h, given that -1/3*h - 1/3*h**v + 1/3*h**4 + 1/3*h**3 + 0 = 0.
-1, 0, 1
Suppose -3*h + 6 = 3*o, -7*o = -5*h - 9*o + 4. Let j(f) be the second derivative of -1/12*f**3 - 1/48*f**4 + h*f**2 - 10*f + 0. Factor j(x).
-x*(x + 2)/4
Let j(a) be the second derivative of 2*a**6/15 + 12*a**5/5 + 46*a**4/3 + 40*a**3 + 50*a**2 + 43*a. Factor j(w).
4*(w + 1)**2*(w + 5)**2
Let v = 749 - 75647/101. Let s = 913/202 - v. Solve 3 - s*l + 3/2*l**2 = 0.
1, 2
Solve 3*l**2 - 3/2*l**3 + 0*l + 0 = 0.
0, 2
Let o = -84583/18 - -4701. Let z = 40/9 - o. Factor z*v**2 + v + 3/2*v**3 + 0.
v*(v + 1)*(3*v + 2)/2
Factor 9*b**3 + 98 + 1/2*b**4 + 109/2*b**2 + 126*b.
(b + 2)**2*(b + 7)**2/2
Let i(o) be the third derivative of 0*o + o**2 - 2*o**3 + 0 + 1/10*o**6 + 3/4*o**5 + 3/2*o**4. Find g, given that i(g) = 0.
-2, 1/4
Find b, given that 209 + 352*b**3 + 45*b**2 - 74 - 357*b**3 - 135*b = 0.
3
Let w(i) be the first derivative of 5/3*i**3 - 15*i**2 + 45*i - 3. Find d, given that w(d) = 0.
3
Let b(p) be the third derivative of p**8/2016 - p**7/180 - p**6/720 + 7*p**5/360 - 106*p**2 + 2. Factor b(z).
z**2*(z - 7)*(z - 1)*(z + 1)/6
Let n be -1*(7040/(-112))/20. Factor n*d - 2*d**2 + 2/7*d**3 - 10/7.
2*(d - 5)*(d - 1)**2/7
Let d = 379 + -368. Let c(t) be the third derivative of 1/180*t**5 + 0*t + 1/72*t**4 - 1/18*t**3 - d*t**2 + 0 - 1/360*t**6. Factor c(a).
-(a - 1)**2*(a + 1)/3
Let g(x) = -13*x - 283. Let c be g(-22). Factor 5/3*i**4 + 50/3*i**2 + 9*i**c + 12*i + 8/3.
(i + 1)*(i + 2)**2*(5*i + 2)/3
Let n(l) = -l**4 - 3*l**3 + 9*l**2 - 5*l - 3. Let u(k) = k**4 + 7*k**3 - 17*k**2 + 9*k + 5. Let v(i) = 5*n(i) + 3*u(i). Solve v(t) = 0.
0, 1
Let n(z) be the third derivative of -5*z**8/336 + 3*z**7/10 + 57*z**6/40 + 133*z**5/60 + 5*z**4/4 + 353*z**2. Suppose n(r) = 0. Calculate r.
-1, -2/5, 0, 15
What is w in 1/8 + 3/8*w**3 - 1/8*w**2 - 3/8*w = 0?
-1, 1/3, 1
Let z(k) be the second derivative of -k**4/32 - 5*k**3/8 - 122*k. Suppose z(j) = 0. What is j?
-10, 0
Let w be 1216/(-9) - (-10)/90. Let i be (-2)/(-9) + 30/w. Solve -1/3*n**4 + 0*n - 16/3*n**2 + 8/3*n**3 + i = 0.
0, 4
Let r(x) be the first derivative of -2197*x**6/12 - 3887*x**5/5 - 611*x**4 + 1720*x**3/3 - 148*x**2 + 16*x + 29. Find h, given that r(h) = 0.
-2, 2/13
Factor -56299 - 6*h**3 - 41157*h + 8773*h - 5653 + 2*h**3 - 712*h**2.
-4*(h + 2)*(h + 88)**2
Let b(u) be the second derivative of 1/12*u**3 + 0*u**2 + 63/40*u**5 + 49/60*u**6 + 5/8*u**4 + 0 + 3*u. Suppose b(v) = 0. What is v?
-1, -1/7, 0
Factor -3/8*r**2 + 0 + 345/4*r.
-3*r*(r - 230)/8
Let -2/3*y**2 + 0*y + 0 - y**5 + 2/3*y**4 + y**3 = 0. What is y?
-1, 0, 2/3, 1
Let v be (((-880)/24)/22)/((-10)/3). Factor 3/4*s**2 - v*s + 0 - 1/4*s**3.
-s*(s - 2)*(s - 1)/4
Let r(h) be the first derivative of -1/4*h**4 + h + h**3 + 4 - 3/2*h**2. Let r(j) = 0. Calculate j.
1
Let u(s) be the first derivative of 1/36*s**4 + 0*s**2 + 5/3*s**3 - 1/216*s**6 + 0*s + 1/120*s**5 - 3. Let x(a) be the third derivative of u(a). Factor x(p).
-(p - 1)*(5*p + 2)/3
Suppose 0 = 2*s - 4*u - 6, -3*s = 3*u - 3 - 6. Let m(f) be the first derivative of -32/3*f**6 + 0*f**2 - 48/5*f**5 - 3*f**4 + 2 - 1/3*f**s + 0*f. Factor