*c**2. Factor m(v).
(v - 1)**2*(v + 2)*(v + 3)
Suppose 0 = 2*g + g - 6. Suppose 460*f = 454*f + 36. Factor 35*z**2 - f*z + 12 - 3*z - 38*z**g + 0.
-3*(z - 1)*(z + 4)
Let g(s) = 2*s**3 - 28*s**2 + 82*s + 167. Let k(p) = -2*p + 1. Let j(m) = -2*g(m) - 50*k(m). Determine a, given that j(a) = 0.
-2, 4, 12
Let o(f) be the third derivative of f**5/24 - 1205*f**4/48 + 100*f**3 - 4673*f**2. Solve o(p) = 0 for p.
1, 240
Let -9929/2*n**3 - 8*n**5 + 1611*n + 2219/2*n**2 + 248 + 2004*n**4 = 0. What is n?
-1/4, 1, 2, 248
Let j be 70/21*(-462)/(-28). Suppose -j*n + 75*n = 40. Determine y, given that 9/2*y**n + 8 + 1/2*y**3 + 12*y = 0.
-4, -1
Let g(n) be the second derivative of -1/210*n**5 + 0 + 0*n**3 + 13/2*n**2 + 15*n - 1/42*n**4. Let u(r) be the first derivative of g(r). Factor u(v).
-2*v*(v + 2)/7
Suppose -2027 = 2*t - 5*z, -7*z + 3*z = 3*t + 3075. Let b = t + 1023. Suppose 2*s + 0 + 2/3*s**b - 8/3*s**3 = 0. Calculate s.
-3/4, 0, 1
Let a(m) = -7*m**3 - 12*m**2 + m + 58. Suppose 17*g + 52 = 4*g. Let x(o) = -48*o**3 - 84*o**2 + 9*o + 405. Let p(t) = g*x(t) + 27*a(t). Let p(r) = 0. What is r?
-3, 2
Let d(m) = -m**4 - 43*m**3 + 267*m**2 + 288*m + 7. Let n(r) = -r**4 - 43*r**3 + 264*r**2 + 288*r + 6. Let w(s) = -6*d(s) + 7*n(s). Factor w(a).
-a*(a - 6)*(a + 1)*(a + 48)
Let o(v) = -v**3 + v + 1. Let d(i) = 5*i**4 - 5*i**3 - 20*i**2 + 5*i + 10. Let q = -228 - -233. Suppose 2*n + 0 = 2. Let h(z) = n*d(z) + q*o(z). Factor h(j).
5*(j - 3)*(j - 1)*(j + 1)**2
Let k(t) be the second derivative of t**6/30 - 17*t**5/20 + 49*t**4/12 + 19*t**3/2 - 117*t**2 - 794*t + 2. Determine c, given that k(c) = 0.
-2, 3, 13
Let m(x) be the second derivative of 47*x - 11/3*x**3 - 5/3*x**4 + 0 + 0*x**2 - 7/40*x**5 + 1/60*x**6. Solve m(l) = 0 for l.
-2, 0, 11
Let -38/9*n - 2/9*n**2 - 20 = 0. Calculate n.
-10, -9
Suppose -4*f = -5*u + 17 + 7, -4*u + f + 28 = 0. Let v(n) be the first derivative of 6*n**2 + u*n + 27 + 4/3*n**3. Factor v(i).
4*(i + 1)*(i + 2)
Let l(c) be the third derivative of -c**5/90 + 49*c**4/36 + 50*c**3/9 + 141*c**2 - 6*c. Factor l(p).
-2*(p - 50)*(p + 1)/3
Let r(l) be the first derivative of 10*l**2 + l**4 - 229*l + 261*l + 50 + 13 + 14*l**2 + 8*l**3. Factor r(c).
4*(c + 2)**3
Let v(p) be the first derivative of -19*p**3/18 + 163*p**2/12 - 24*p - 5661. Factor v(w).
-(w - 1)*(19*w - 144)/6
Let s be (360/(-48))/((-3)/4). Suppose 315 = -k + s*k. Factor 8 - k*m**3 - 66*m**2 + 11*m + 14*m - 18*m + 5*m.
-(m + 2)*(5*m - 2)*(7*m + 2)
Suppose 0 = -2*w + 3*v - 5, 3*w - 13 = -4*v + 5. Solve -7*u + 10*u**w + 0 - 5*u**2 - 53*u + 55 = 0.
1, 11
Let a(s) = -s**2 + 15*s - 53. Let j be a(8). Solve r**4 - 6*r**3 - 6057 + 0*r**j + 5*r**2 + 6057 = 0 for r.
0, 1, 5
Let k = -407 - -417. Let q be 22/k - (-6 + 279/45). Solve -1/10*c**q + 0 + 3/5*c = 0 for c.
0, 6
Let x(p) be the third derivative of p**5/180 - 140*p**4/9 + 2338*p**2. Factor x(t).
t*(t - 1120)/3
Let g(v) = -28*v**4 + 1682*v**3 - 2176*v**2 - 2794*v + 1100. Let d(w) = w**4 + 3*w**3 + 2*w + 2. Let h(c) = 4*d(c) + g(c). Let h(z) = 0. Calculate z.
-1, 1/3, 2, 277/4
Let h(z) = 3*z**4 - 112*z**3 - z**2 + 708*z + 1015. Let j(t) = t**4 - 35*t**3 - 2*t**2 + 236*t + 338. Let c(b) = 2*h(b) - 7*j(b). Factor c(p).
-(p - 21)*(p - 4)*(p + 2)**2
Let o = 663 - 661. Solve 60 + 981*q**o - 5*q**3 - 966*q**2 + 103*q - 23*q = 0.
-2, -1, 6
Factor 6075/7 + 3/7*r**2 + 270/7*r.
3*(r + 45)**2/7
Let z = 24966 - 24966. Factor -3/4*d**2 - 3/4*d**3 - 1/4*d - 1/4*d**4 + z.
-d*(d + 1)**3/4
Factor -136/5*b - 2/5*b**2 + 56.
-2*(b - 2)*(b + 70)/5
Factor -783*f**2 + 147119 - 4*f**3 - 92380*f - 445*f**2 + 141181.
-4*(f - 3)*(f + 155)**2
Let r(d) be the first derivative of d**4/18 - 7*d**3/9 - 8*d**2/3 - 89*d - 220. Let s(x) be the first derivative of r(x). Factor s(h).
2*(h - 8)*(h + 1)/3
Let y(c) be the first derivative of 49 - 616/27*c**3 - 47/9*c**4 + 376/9*c**2 + 2/3*c**6 - 224/9*c + 16/3*c**5. Find r such that y(r) = 0.
-7, -2, 2/3, 1
Factor -2/5*t**2 + 258/5*t - 508/5.
-2*(t - 127)*(t - 2)/5
Let i be (50/((-10000)/60))/(3/(-15)). Let -9*y**3 + 0 + 12*y - 15/2*y**4 + 6*y**2 - i*y**5 = 0. What is y?
-2, 0, 1
What is w in -8/3 + 7/3*w**4 + 46/3*w**2 - 11*w**3 - 4*w = 0?
-2/7, 1, 2
Let l(j) = -20*j**2 + 208*j - 473. Let u be l(7). Factor -9/2*b + 0 - 6*b**2 - 3/2*b**u.
-3*b*(b + 1)*(b + 3)/2
Let w(d) be the second derivative of -d**4/54 + 326*d**3/27 - 325*d**2/9 + d + 89. Determine t, given that w(t) = 0.
1, 325
Let h(q) = -37*q - 308 + 13683*q**2 - 4*q - 13684*q**2. Let a be h(-10). Let 2/11*j**a + 8/11*j + 8/11 = 0. Calculate j.
-2
Let v = -591 + 593. Let o(n) be the first derivative of 9/8*n**v - 3/4*n + n**3 - 10. Factor o(d).
3*(d + 1)*(4*d - 1)/4
Let g(y) be the third derivative of -169*y**8/1680 - 299*y**7/105 - 16813*y**6/600 - 7103*y**5/75 + 499*y**4/6 - 80*y**3/3 + 2505*y**2. Solve g(w) = 0 for w.
-8, -5, 2/13
Let l(k) be the first derivative of -2*k**6/15 + k**5 + k**4 - 26*k**3/3 - 20*k**2 - 240*k + 10. Let j(t) be the first derivative of l(t). Factor j(c).
-4*(c - 5)*(c - 2)*(c + 1)**2
Let l(d) = d**3 - 391*d**2 + 13412*d + 78. Let j be l(38). Factor -15/4 - 1/4*b**j + 4*b.
-(b - 15)*(b - 1)/4
Let m be 1/(4/(-46)) + 3/(-6). Let s = 28 - m. Factor 16*g**2 + 3*g**4 + 3*g - s*g**2 - 3*g**3 + 21*g**2.
3*g*(g - 1)**2*(g + 1)
Let w(m) be the second derivative of -m**5/200 + 43*m**4/60 - 1849*m**3/60 + 95*m + 2. Find a such that w(a) = 0.
0, 43
Let v = -9 + 15. Suppose 10 = v*p - 4*p. Factor -p*o**2 + 4*o**3 - 2*o**2 - 8*o**2 - 19*o**3 - 5*o - 5*o**4.
-5*o*(o + 1)**3
Let b(c) = -c**3 + c**2 + c + 6. Let n(q) = 14*q**3 - 410*q**2 + 666*q + 204. Suppose 37*s - 62 = 12. Let j(u) = s*b(u) - n(u). Factor j(a).
-4*(a - 24)*(a - 2)*(4*a + 1)
Let m(x) be the second derivative of x**7/14 - 3*x**6/5 - 9*x**5/10 + 11*x**4 - 51*x**3/2 + 27*x**2 - 7182*x. Determine z so that m(z) = 0.
-3, 1, 6
Suppose -a + 7 = 3*p - 12, 2*p - 7 = 5*a. Suppose -4*w = 2*b, -1 + 5 = -4*w. Determine v, given that -p*v**2 - 1102*v + 3*v**3 + 1100*v - v**3 + 4 + b*v**4 = 0.
-2, -1, 1
Let f(g) be the third derivative of -g**6/780 - 619*g**5/390 - 23870*g**4/39 + 96100*g**3/39 - 346*g**2. Factor f(v).
-2*(v - 1)*(v + 310)**2/13
Suppose -41*t + 474*t - 1612 = 30*t. Solve 771/2*c**2 - 360*c - 78*c**3 + 96 - 81/2*c**t - 3*c**5 = 0 for c.
-8, 1/2, 1
Let j(w) be the second derivative of 5/9*w**3 + 0 - 3*w**2 - 1/72*w**4 + 226*w. Let j(m) = 0. What is m?
2, 18
Suppose -53 = -19*f - 43*f + 195. Let c(v) be the second derivative of -3/40*v**5 - v**3 + 0 + 1/2*v**f + 17*v + 0*v**2. Factor c(n).
-3*n*(n - 2)**2/2
Let f(z) be the second derivative of -z**4/4 + 5*z**3/2 + 21*z**2 + 1536*z. Determine q so that f(q) = 0.
-2, 7
Let q(h) = -2*h**2 + 6*h + 3. Let u be q(5). Let j(i) = i**2 + 12*i - 85. Let w be j(u). Factor w - 1/4*p**4 + 1/4*p**2 - 1/4*p + 1/4*p**3.
-p*(p - 1)**2*(p + 1)/4
Suppose -17476 = -5*s + 4*c, 3*s = 2*s - 2*c + 3484. Let g be (10/8 - s/720) + 4. Solve 2/5*q**2 + 0 + 0*q + 6/5*q**3 + g*q**5 + 6/5*q**4 = 0.
-1, 0
Suppose -16*d + 21*d = 7*u + 69, 3*u = 2*d - 29. Find q, given that -4/23 - 6/23*q - 30/23*q**3 + 32/23*q**2 + 8/23*q**d = 0.
-1/4, 1, 2
Let v be ((30/7)/((40/28)/(-10)))/(-4). Let k(h) be the first derivative of -5*h + 5 + 20/3*h**3 - v*h**2. Solve k(y) = 0.
-1/4, 1
Let i = 149714/21819 - 14/3117. Find t, given that 20/7*t**3 + i*t**2 - 20/7*t + 2/7*t**4 - 50/7 = 0.
-5, -1, 1
Let h(w) be the first derivative of w**4/18 + 382*w**3/27 + 379*w**2/9 + 42*w - 1911. Determine o, given that h(o) = 0.
-189, -1
Let n = 529806/5 + -105961. Factor n*p**2 + 9/5*p + 8/5.
(p + 1)*(p + 8)/5
Let y(a) = -90*a**2 + 19680*a - 1075876. Let p(g) = -405*g**2 + 88560*g - 4841440. Let u(d) = -9*p(d) + 40*y(d). Factor u(i).
5*(3*i - 328)**2
Let y(o) be the third derivative of -6*o - 7/480*o**6 + 0 + 1/80*o**5 + 1/168*o**7 - 10*o**2 + 0*o**4 + 0*o**3 - 1/1344*o**8. Factor y(x).
-x**2*(x - 3)*(x - 1)**2/4
Factor -78*z + z**2 + 34 + 120*z - 61*z.
(z - 17)*(z - 2)
Suppose -3*n = -5*r + 14, 0 = -0*n - n - 2*r + 10. Let s be (5 - 8)/((-45)/12*n). Determine c, given that -2/5*c**2 + 4/5 + s*c = 0.
-1, 2
Factor 16755 + 5419*s**2 - 26784*s + 3998*s**2 + 4*s**4 - 417*s**2 + 9921 - 1024*s**3.
4*(s - 247)*(s - 3)**3
Let f be 12 - (-4)/((-8)/2). Suppose -v + f*v - 6*v = 0. Let -7*d + 3*d**2 + 5*d**3 - 4*d*