 z(q) be the third derivative of -7/24*q**4 - 1/120*q**6 + m*q - 1/2*q**3 + 10*q**2 + 0 - 1/12*q**5. Factor z(d).
-(d + 1)**2*(d + 3)
Suppose 1/4*x**2 + 31/4*x + 15/2 = 0. What is x?
-30, -1
Let f be (1 - -2)*(-12 + 17). Suppose -2 + 25*k - f*k**2 - 6 + 20*k**4 + 3 - 10*k**3 - 15*k**3 = 0. What is k?
-1, 1/4, 1
Let l(k) be the third derivative of k**6/30 + 41*k**5/15 + 220*k**4/3 + 800*k**3/3 + 10*k**2. Factor l(u).
4*(u + 1)*(u + 20)**2
Let f(u) be the first derivative of u**6/105 + u**5/35 + u**4/42 + 27*u + 5. Let b(l) be the first derivative of f(l). Let b(h) = 0. Calculate h.
-1, 0
Let m = 363 - 2913/8. Let d = 21/8 + m. Determine b so that 0 + 3/2*b**4 - 3/2*b**3 - 3/2*b**2 + d*b = 0.
-1, 0, 1
Let v(m) be the third derivative of m**5/420 - m**4/56 - 2*m**3/21 + 5*m**2. Factor v(a).
(a - 4)*(a + 1)/7
Let d = 113 + -115. Let c(f) = 15*f**5 - 63*f**3 + 15*f + 33. Let s(a) = -a**5 + 4*a**3 - a - 2. Let z(q) = d*c(q) - 33*s(q). Find m such that z(m) = 0.
-1, 0, 1
Suppose 6*h - 7*h + 8 = 0. Find n such that -2*n**2 - h*n + 2*n**2 - 4*n**2 = 0.
-2, 0
Factor -5*y**3 - 1142035 - 79496*y - 1695*y**2 - 27449*y - 80349*y - 6072450 - 4241*y.
-5*(y + 113)**3
Let u be 2/9 - 118/531. Let j(q) be the third derivative of u*q**6 + 0*q**3 + 0 + 0*q**4 - 1/840*q**7 - 6*q**2 + 0*q - 1/1344*q**8 + 0*q**5. Factor j(x).
-x**4*(x + 1)/4
Let o(q) = -q**2 + 18*q - 14. Let r be o(17). Solve -53*l**2 + 0*l**3 + 18*l**5 + 41*l**4 - 4*l**r + 28*l - 4 + 10*l**4 = 0.
-2, 1/3, 1/2
Let m be 1 + -2 + 32/24. Let v(j) be the first derivative of -m*j**3 - 2/5*j + 7/10*j**2 - 5. Factor v(h).
-(h - 1)*(5*h - 2)/5
Let w(p) be the third derivative of p**4/12 + 67*p**3/6 + 20*p**2. Let d be w(-32). What is q in -2/9 + 2/9*q**4 - 4/9*q + 0*q**2 + 4/9*q**d = 0?
-1, 1
Let r(l) = -2*l**2 - 4*l - 2. Let z(u) = u**3 + 7*u - 2. Let i(v) = v**2 + 1. Let m(a) = 5*i(a) + z(a). Let c(g) = 2*m(g) + 5*r(g). Suppose c(w) = 0. What is w?
-1, 2
Factor 0*l - 2/3*l**5 + 0 + 1/6*l**2 + 3/2*l**4 - l**3.
-l**2*(l - 1)**2*(4*l - 1)/6
Let k(d) be the third derivative of 3/20*d**5 + 0 + 0*d + 0*d**3 - 1/4*d**4 - 1/40*d**6 - 24*d**2. Factor k(s).
-3*s*(s - 2)*(s - 1)
Suppose 11*i = 18 - 7. Let f be (-480)/(-648)*(i - 1/(-2)). Factor -8/9*r**2 - 2/9*r**3 - 4/9 - f*r.
-2*(r + 1)**2*(r + 2)/9
Let m(p) be the second derivative of -41*p + 0*p**2 + 0 + 0*p**3 - 3/20*p**5 + 3/4*p**4. Factor m(j).
-3*j**2*(j - 3)
Suppose 0 = 5*y - 25, -5*x + 13 - 58 = -y. Let g be (-6)/21 - (x/(-21) - 1). What is f in -2/3*f**2 + g*f + 0 + 1/3*f**3 = 0?
0, 1
Let a(v) be the second derivative of 7*v**5/10 - 19*v**4/6 - 26*v**3/3 + 116*v. Suppose a(w) = 0. Calculate w.
-1, 0, 26/7
Let l(j) be the first derivative of 5*j**4/12 + 25*j**3/6 + 15*j**2 + 15*j - 14. Let r(n) be the first derivative of l(n). Factor r(u).
5*(u + 2)*(u + 3)
Let a = 4211/36 + -463/4. Let y = -5/9 + a. Factor 1/3*m**4 + 0 + 0*m + y*m**2 + m**3.
m**2*(m + 1)*(m + 2)/3
Let 31*f**3 - f**5 + 162*f - 75*f**2 + 5*f**5 - 186*f**2 - f**5 + 57*f**4 + 8*f**3 = 0. Calculate f.
-18, -3, 0, 1
What is b in -149*b**3 + 157*b**3 - 357*b - 2*b**4 + 369*b + 22*b**2 = 0?
-1, 0, 6
Let q(n) be the second derivative of -5*n**7/42 - n**6/6 + 3*n - 9. Factor q(m).
-5*m**4*(m + 1)
Let a(r) be the third derivative of r**8/11760 + r**7/1470 - 2*r**5/105 + r**4/6 - 6*r**2. Let y(t) be the second derivative of a(t). Factor y(p).
4*(p - 1)*(p + 2)**2/7
Suppose 0 = -p - b - 1, p + b + 17 = -4*b. Determine d so that -1 + 4*d**2 - p*d - 2 + 2 = 0.
-1/4, 1
Let p = -50 + 52. Find g, given that -6*g**p + 16*g**2 - g**5 + 7*g + 5*g**4 + 1 - 10*g**3 - 12*g = 0.
1
Let r(v) = 20*v**4 + 18*v**3 - 58*v**2 - 88*v - 34. Let h(b) = 20*b**4 + 19*b**3 - 57*b**2 - 88*b - 35. Let o(k) = -2*h(k) + 3*r(k). Factor o(w).
4*(w - 2)*(w + 1)**2*(5*w + 4)
Let i be (7 - (40/16 - -3)) + (0 - -1). Factor -i - 3*b - 1/2*b**2.
-(b + 1)*(b + 5)/2
Factor -4/5*v**2 + 0 - 4/5*v**3 + 4/5*v**5 + 0*v + 4/5*v**4.
4*v**2*(v - 1)*(v + 1)**2/5
Find s, given that 2*s**2 - 2*s**3 + 5*s**3 - 3*s**2 - 2*s**3 = 0.
0, 1
Suppose -140 = 26*p - 140. Let m(u) be the second derivative of -u**3 + 9/4*u**2 + 1/8*u**4 + p - 7*u. Factor m(x).
3*(x - 3)*(x - 1)/2
Let z(t) = 7*t. Let u be z(1). Suppose 0 = 4*q - u - 1. Suppose 6*s**5 + s**3 + 3*s**2 - 10*s**4 + s**3 - s**q = 0. Calculate s.
-1/3, 0, 1
Let t be (-75)/(-27) + 4/(-144)*-8. Let p(r) be the first derivative of 7 + 11/2*r**2 - r - 121/12*r**t. Find m such that p(m) = 0.
2/11
Let n(y) be the first derivative of y**3/15 + 9*y**2/10 - 22*y/5 + 136. Determine u so that n(u) = 0.
-11, 2
Let i(t) = t**3 - 12*t**2 + 33*t - 16. Let w be i(3). Let j(f) be the first derivative of 625*f + 25*f**3 - 10 + 5/4*f**4 + 375/2*f**w. Factor j(r).
5*(r + 5)**3
Let s = -91 - -34. Let u = s - -61. Factor 2/5*f**2 + 0 - 2/5*f**u + 0*f - 2/5*f**3 + 2/5*f**5.
2*f**2*(f - 1)**2*(f + 1)/5
Let q(t) = -3*t**2 + 23*t + 14. Let p(v) = -v**2 + 8*v + 5. Suppose -11 = 5*i + l - 95, -3*l = -2*i + 37. Let o(u) = i*p(u) - 6*q(u). Find w such that o(w) = 0.
1
Let h(j) be the third derivative of j**6/780 + 31*j**5/390 + 287*j**4/156 + 833*j**3/39 + 589*j**2. Factor h(x).
2*(x + 7)**2*(x + 17)/13
Factor 105*a - 20*a**3 + 35*a**3 - 120*a**2 - 10*a**3 + 230.
5*(a - 23)*(a - 2)*(a + 1)
What is n in -5/4*n + 1/4*n**2 + 3/2 = 0?
2, 3
Let z be (-237)/(-1106)*(-4)/((-96)/14). Find q such that -1/2 + 0*q + z*q**3 + 3/8*q**2 = 0.
-2, 1
Let i = -4644 + 23117/5. Let z = i + 21. Suppose -8/5*x**3 - 2*x**2 + 0 - z*x = 0. What is x?
-1, -1/4, 0
Let r(n) be the first derivative of 6/5*n**3 + 72/5*n - 1 + 9/20*n**4 - 42/5*n**2 - 3/25*n**5. Solve r(f) = 0.
-3, 2
Let a = -18 + 19. Let d(u) = u**4 + u**3. Let n(c) = 9*c**4 - 3*c**3 + 3*c**2 + 9*c - 6. Let x(y) = a*n(y) - 6*d(y). Determine g so that x(g) = 0.
-1, 1, 2
Let v(h) be the first derivative of -1/21*h**6 + 5 + 2/35*h**5 + 5/14*h**4 - 2/21*h**3 - 8/7*h**2 - 8/7*h. Solve v(s) = 0.
-1, 2
Let t be (-27)/(-45)*(-2)/(-3). Find q such that 4/5*q**3 + 8/5*q**2 - t*q - 4/5*q**4 - 4/5 - 2/5*q**5 = 0.
-2, -1, 1
Let y = 24641 + -73913/3. Determine r, given that 4 - y*r + 2/3*r**2 = 0.
2, 3
Let c(l) be the first derivative of l**6/900 - 7*l**5/300 - 2*l**4/15 + 4*l**3 + 28. Let m(x) be the third derivative of c(x). Let m(r) = 0. What is r?
-1, 8
Let p(r) be the first derivative of -6 - 2*r + 1/10*r**5 + 0*r**2 - 1/4*r**4 + 1/6*r**3. Let h(m) be the first derivative of p(m). Factor h(s).
s*(s - 1)*(2*s - 1)
Let v(t) be the third derivative of -7*t**5/120 + 89*t**4/48 + 13*t**3/6 + 8*t**2 + 2. Determine d so that v(d) = 0.
-2/7, 13
Let r be (-40)/25*(-4 + 77/28). Factor w + 1/5*w**3 + 2/5 + 4/5*w**r.
(w + 1)**2*(w + 2)/5
Let i be 37/(-74) - (2 + 13/(-5)). Let o(f) be the second derivative of f**3 + i*f**5 - 9*f**2 + 5/6*f**4 + f + 0. Factor o(x).
2*(x - 1)*(x + 3)**2
Let c(g) = -9*g**5 - 12*g**4 - 13*g**3. Let f(d) = -8*d**5 - 12*d**4 - 12*d**3. Let r be (2 - 5)*4/(-3). Let i(t) = r*c(t) - 5*f(t). Factor i(o).
4*o**3*(o + 1)*(o + 2)
Let p be ((-2)/8)/((-15)/300). Let c(o) be the third derivative of 0*o**3 + 1/30*o**6 + 1/12*o**4 - 1/210*o**7 - 1/12*o**p + 5*o**2 + 0*o + 0. Factor c(f).
-f*(f - 2)*(f - 1)**2
Let f(a) be the first derivative of a**5/60 - a**4/12 + 17*a**2/2 + 1. Let k(z) be the second derivative of f(z). Factor k(j).
j*(j - 2)
Let k(h) be the first derivative of -1/9*h**6 - 4/3*h - 4/9*h**3 + 5/3*h**2 + 7 - 2/3*h**4 + 8/15*h**5. Determine d, given that k(d) = 0.
-1, 1, 2
Factor 2/5*t**2 + 1/10*t**3 + 7/5 - 19/10*t.
(t - 2)*(t - 1)*(t + 7)/10
Let h(f) be the first derivative of -441*f**4/4 - 406*f**3 + 321*f**2/2 + 18*f - 797. Determine q, given that h(q) = 0.
-3, -1/21, 2/7
Let s(t) = 8*t - 213. Let r be s(27). Let l(q) be the second derivative of -q**2 - q**r - 7*q - 1/2*q**4 + 0 - 1/10*q**5. Solve l(z) = 0.
-1
Let k be 14 + (-238)/21 - -1. Suppose -17/3*o**4 - k*o**2 + 7*o**3 + 0 + 5/3*o**5 + 2/3*o = 0. Calculate o.
0, 2/5, 1
Factor -3*o**2 - 8 - 15 + 2*o**2 + 801*o - 777*o.
-(o - 23)*(o - 1)
Suppose p + 0*p + 3 = -c, -2*c = 5*p. Let g be 8*c/110*-1. Factor -2/11 - 2/11*j**2 + g*j.
-2*(j - 1)**2/11
Suppose 264 = -7*a + 51*a. Let d(n) be the first derivative of -4*n + 1 + 1/3*n**a + 8/3*n**3 - 4/5*n**5 + n**2 - n**4. Find i such that d(i) = 0.
-1, 1, 2
Let l be 36/3978*13 + 290/13