0, 1
Let n(q) be the third derivative of 7*q**5/60 - q**4/3 + q**3/6 + 9*q**2 - 5. Find v, given that n(v) = 0.
1/7, 1
Let d(p) = -p**4 + p**3 + p**2 + p - 3. Let o(a) = 2*a**4 + 2*a**3 - 10*a**2 + 9. Let i(v) = 6*d(v) + 2*o(v). Factor i(s).
-2*s*(s - 3)*(s - 1)**2
Let f(k) be the third derivative of -k**8/672 + k**7/420 + 5*k**6/24 - 5*k**5/12 - 625*k**4/48 + 625*k**3/12 + 450*k**2. Let f(q) = 0. What is q?
-5, 1, 5
Find u, given that -31/2*u - 1/2*u**2 + 0 = 0.
-31, 0
Let t = -395 + 224. Let m = 517/3 + t. Suppose -4 - 8/3*w + m*w**2 = 0. What is w?
-1, 3
Factor 6*x + 9 - 11/4*x**2 + 1/4*x**3.
(x - 6)**2*(x + 1)/4
Solve 4/3 - 4/3*v**2 + 2/3*v**3 - 2/3*v = 0.
-1, 1, 2
Let u(p) be the third derivative of p**5/150 - 3*p**4/20 + 8*p**3/15 + 31*p**2 + 1. Solve u(l) = 0 for l.
1, 8
Let u(i) be the second derivative of 0 + 1/90*i**6 - 2/3*i**2 - 11*i + 1/12*i**4 - 1/15*i**5 + 2/9*i**3. Solve u(z) = 0 for z.
-1, 1, 2
Let b(z) = 2*z**2 - 1. Let l(n) = -7*n**2 + 9*n - 25. Let c(g) = -5*b(g) - l(g). Determine s, given that c(s) = 0.
-5, 2
Suppose 5*h - 241 = 3*r - 103, 3*r - 12 = 0. Let o be h/10 + -1 + 5. Determine q, given that 3*q**3 + q**5 - o*q**3 + 3*q**3 = 0.
-1, 0, 1
Let m(r) = -3*r**3 - 19*r**2 - 12*r + 34. Let t(f) = 4*f**3 + 20*f**2 + 11*f - 35. Let k(o) = 3*m(o) + 2*t(o). Determine w, given that k(w) = 0.
-16, -2, 1
Let z(u) be the first derivative of 2/5*u**5 - 4/21*u**3 + 0*u - 5/14*u**4 - 17 + 0*u**2. Solve z(q) = 0 for q.
-2/7, 0, 1
Let o(u) be the first derivative of 2*u**3/45 + 109*u**2/15 + 428*u/15 - 874. Factor o(x).
2*(x + 2)*(x + 107)/15
Let m = 24 - 21. Let i = 102 + -102. Find r, given that -13/2*r**2 + i - r - 23/2*r**4 - 7/2*r**5 - 27/2*r**m = 0.
-1, -2/7, 0
Let o(f) = -2*f**4 - 14*f**3 - 28*f**2 - 19*f. Let t(y) = -10*y**4 - 70*y**3 - 140*y**2 - 94*y. Let j(c) = 14*o(c) - 3*t(c). Factor j(s).
2*s*(s + 1)*(s + 2)*(s + 4)
Let f be 4*(3 + (-18)/8). Let h be 2/(2/f) - 0. Factor 0*v**3 - 3 - 6*v**h + 6*v**2 + 2*v**3 + 1.
-2*(v - 1)**2*(2*v + 1)
Let a = -59 - -61. Factor 9*l**3 - 1829*l**2 - 12 + 1797*l**a + 46*l - 3*l**3.
2*(l - 3)*(l - 2)*(3*l - 1)
Let w(y) be the second derivative of -3/2*y**3 - 10*y + 0 - 1/4*y**4 - 3*y**2. Factor w(l).
-3*(l + 1)*(l + 2)
Let h(b) be the third derivative of -b**6/120 + 9*b**4/8 - 9*b**3 - 64*b**2. Let h(y) = 0. Calculate y.
-6, 3
Let w be 2/(-15)*(10 + -8 + -8). Factor -q**3 - 8/5 + 1/5*q**4 + 6/5*q**2 + w*q.
(q - 2)**3*(q + 1)/5
Suppose 0 = -2*z + 5*z - 6. Factor -d**4 + 2*d**2 + 0*d**4 + z*d**3 + 0*d**3 - 3*d**2.
-d**2*(d - 1)**2
Let t(f) = -8*f**2 + f + 1. Let w be t(-1). Let h be 2*((-76)/w + -1). Factor -9*v**5 - v**4 - v**3 - 7*v**5 + v**2 + h*v**5.
v**2*(v - 1)**2*(v + 1)
Let c(r) be the first derivative of -r**6/3 - 16*r**5/5 - 21*r**4/2 - 12*r**3 - 235. Factor c(x).
-2*x**2*(x + 2)*(x + 3)**2
Let d(m) be the second derivative of -m**9/13608 + m**8/3780 - 13*m**3/3 + 8*m. Let p(u) be the second derivative of d(u). Let p(s) = 0. What is s?
0, 2
Let n(m) = m**2 - 29*m - 57. Let u be n(-2). Let d(r) be the second derivative of 0 + 1/12*r**4 + 11*r + 1/30*r**u + 1/18*r**3 + 0*r**2. Factor d(v).
v*(v + 1)*(2*v + 1)/3
Let q(m) be the first derivative of 7/48*m**4 + 0*m - 1/6*m**3 + 1/60*m**5 - 7/240*m**6 - 8 + 3*m**2. Let j(w) be the second derivative of q(w). Factor j(x).
-(x - 1)*(x + 1)*(7*x - 2)/2
Let i be ((-28)/(-364))/((-2)/(-13)). Factor -3/2*v - 3/2*v**4 + i*v**5 + 1/2 + v**2 + v**3.
(v - 1)**4*(v + 1)/2
What is n in 328/5*n + 32 - 172/5*n**2 + 4*n**3 = 0?
-2/5, 4, 5
Let y(w) be the third derivative of 0*w + 0 + 1/20*w**5 - 1/40*w**6 + 0*w**4 - 22*w**2 + 0*w**3. Solve y(h) = 0.
0, 1
Let s(t) be the first derivative of -t**5/180 + 7*t**4/36 - 49*t**3/18 + t**2/2 - 6. Let x(k) be the second derivative of s(k). Determine c so that x(c) = 0.
7
Let a(q) = -12*q**2 + 36*q. Let n(p) = -p**3 - 9*p**2 - 11*p - 3. Let l be n(-8). Let c(y) = 3*y**2 - 9*y. Let h(k) = l*c(k) + 5*a(k). Factor h(d).
3*d*(d - 3)
Factor 63*v**2 - 888*v + 57*v**2 + 65712 - 117*v**2.
3*(v - 148)**2
Solve 24*s**4 + 18*s**3 - 60*s**2 - 6*s**4 - 117*s + 7135 - 7189 + 3*s**5 = 0.
-3, -1, 2
Let g(d) = d - 1. Let w be 1/(6/(-3))*-2. Suppose f = -5*h + 7, 2 = h + w. Let q(j) = -7*j**2 - 8*j - 5. Let u(o) = f*q(o) - 4*g(o). Let u(s) = 0. What is s?
-1, -3/7
Let d(s) = s**3 + s**2 - 8*s - 4. Let p be d(-3). Let t be (4 - (-12)/(-8) - 2)/p. Solve 0*c + t*c**2 + 0 - 1/4*c**3 = 0 for c.
0, 1
Let p be 1*17 - (-8)/8. Let s be 76/57*p/56. Solve 3/7*g**3 + 3/7*g**2 - 3/7*g**4 - s*g + 0 = 0 for g.
-1, 0, 1
Let t(q) = 8*q**2. Let f(c) = -5*c**3 - 55*c**2 + 65*c + 35. Let w(n) = f(n) + 10*t(n). Suppose w(v) = 0. What is v?
-1, 7
Let l(f) be the first derivative of -3*f**4/4 - 16*f**3 - 135*f**2/2 + 486*f + 327. Factor l(v).
-3*(v - 2)*(v + 9)**2
What is c in -5*c**2 - 11*c**2 + 32*c**2 + 21*c**2 - 8 + 43*c**2 - 28*c**3 - 44*c = 0?
-1/7, 1, 2
Solve 64/7 + 81/7*i**4 + 608/7*i + 1588/7*i**2 + 684/7*i**3 = 0 for i.
-4, -2/9
Let p(x) be the first derivative of -1/4*x**2 - 1/6*x**3 + 1/8*x**4 + 1/2*x - 8. Suppose p(t) = 0. What is t?
-1, 1
Factor 7/2*z + 1/6*z**2 + 0.
z*(z + 21)/6
Suppose 0 = -34*n - 14*n + 96. Factor -1/3*q - 5/6*q**n + 0.
-q*(5*q + 2)/6
Suppose 0 = 27*d - 20*d. Let h(l) be the second derivative of l**2 - 5*l - 1/6*l**4 + d*l**3 + 0. Let h(g) = 0. What is g?
-1, 1
Let x(n) be the third derivative of -n**5/140 + 3*n**4/56 + 5*n**3/7 - 7*n**2 - 2. What is a in x(a) = 0?
-2, 5
Let p(m) = 6 + 3*m - 2*m - 4*m - 9*m**2. Let c(h) = 4 + 6 - 2*h - 8*h**2 + 4 - 8. Let i(z) = 7*c(z) - 6*p(z). Determine k, given that i(k) = 0.
-1, 3
Suppose 0 = 3*m - 1 - 11. Factor -25*p + m + 5*p**2 + 21 - 2*p - 3*p.
5*(p - 5)*(p - 1)
Let d be (-4)/26 + 0 + (-72)/(-130). Let c(j) be the first derivative of d*j**3 + 0*j**2 + 5 + 0*j + 3/25*j**5 + 9/20*j**4. Factor c(z).
3*z**2*(z + 1)*(z + 2)/5
Let n(b) be the third derivative of b**7/1680 - b**6/360 - 5*b**3/3 + 4*b**2. Let r(u) be the first derivative of n(u). Let r(q) = 0. What is q?
0, 2
Let k(o) be the first derivative of -o**6/3 + 5*o**4/2 - 4*o**2 - 62. Find m, given that k(m) = 0.
-2, -1, 0, 1, 2
Let o(r) be the second derivative of 2401*r**6/45 - 7546*r**5/15 + 5929*r**4/3 - 37268*r**3/9 + 14641*r**2/3 - r + 3. Determine k so that o(k) = 0.
11/7
Let r(l) be the third derivative of l**7/105 + 3*l**6/10 + 18*l**5/5 + 18*l**4 + 65*l**2. Determine p so that r(p) = 0.
-6, 0
Let o = -5203 - -5205. Determine u, given that -3 - 4*u - 1/4*u**3 - 7/4*u**o = 0.
-3, -2
Let 0*i + 16/11*i**2 + 0 - 2/11*i**3 = 0. Calculate i.
0, 8
Let u(g) be the second derivative of g**7/42 - g**6/6 - 7*g**5/10 - g**4/6 + 13*g**3/6 + 7*g**2/2 - 261*g. Let u(t) = 0. Calculate t.
-1, 1, 7
Let p(h) be the first derivative of 2*h**3/3 - 34*h**2 - 70*h + 67. Factor p(o).
2*(o - 35)*(o + 1)
Let b(o) = 8*o - 86. Let t be b(11). Let v(d) be the second derivative of -1/165*d**6 + 1/66*d**4 + 2/33*d**3 + 0 + 10*d - 1/55*d**5 + 0*d**t. Solve v(i) = 0.
-2, -1, 0, 1
Let q(i) be the second derivative of -3/5*i**5 + 0 + 1/2*i**4 + 2*i**3 + 3/2*i**2 + i - 3/10*i**6. Find k such that q(k) = 0.
-1, -1/3, 1
Let p = 1 + 2. Let z be 51/21 + 8/14. Let -i**z - p - 4 + 7*i**2 + 3 - 4*i**2 = 0. Calculate i.
-1, 2
Let f(m) be the third derivative of m**5/12 - 35*m**4/24 - 15*m**2 + 4. Factor f(l).
5*l*(l - 7)
Solve 2/11*t**2 + 0*t + 0 = 0 for t.
0
Let -7*i**2 + 50 - 135*i**3 + 185*i - 8*i**2 + 7*i**3 - 57*i**3 - 35*i**4 = 0. Calculate i.
-5, -1, -2/7, 1
Factor 44/7 - 2/7*x**2 - 18/7*x.
-2*(x - 2)*(x + 11)/7
Let l(n) be the second derivative of 1/8*n**4 + 0 + 3/4*n**2 - 1/2*n**3 - 14*n. Factor l(u).
3*(u - 1)**2/2
Factor -6*g**3 + 868*g**4 - g**2 + g**3 + 12 - 867*g**4 + 17*g.
(g - 4)*(g - 3)*(g + 1)**2
Let n(l) be the first derivative of -l**3/3 + 13*l**2/2 - 36*l + 585. Factor n(s).
-(s - 9)*(s - 4)
Let q(p) be the second derivative of -p**7/840 + p**6/24 + 17*p**4/4 + p**3/3 - 10*p - 1. Let w(x) be the third derivative of q(x). Factor w(c).
-3*c*(c - 10)
Let a(w) = w**2. Let n be (0 - -1)/((-2)/(-6)). Let m(x) = 3*x**2 - 10*x + 4. Let l(r) = n*a(r) + m(r). Solve l(o) = 0.
2/3, 1
Let c(w) be the first derivative of -w**3/2 - 51*w**2/4 - 63*w - 246. Factor c(v).
-3*(v + 3)*(v + 14)/2
Determine c, given that -7*c**3 + 23*c**3 - 10*c**3 - 2*c**2 -