661 - -380681/3806610. Solve -4/5*w + p*w**2 + 7/10 = 0 for w.
1, 7
Suppose -17*k = -31 + 8 - 11. Let q(m) be the first derivative of 4/9*m**3 - 8/3*m**k + 4*m - 21. Factor q(r).
4*(r - 3)*(r - 1)/3
Let z(t) be the first derivative of -7*t**4/4 + 43*t**3/6 + 53*t**2/4 - 2*t + 4767. What is q in z(q) = 0?
-1, 1/14, 4
Let n be (-1 + -46)/(-16 - -17). Let k(i) = -2*i**2 - 92*i + 94. Let r be k(n). Factor -2/7*j**2 + 0 + r*j.
-2*j**2/7
Let q(f) be the first derivative of 0*f**3 + 0*f**2 - 30 + 0*f + 6/5*f**5 - f**4 - 1/3*f**6. Factor q(n).
-2*n**3*(n - 2)*(n - 1)
Let u(b) be the third derivative of -b**7/1155 - 9*b**6/110 - 34*b**5/11 - 2050*b**4/33 - 8000*b**3/11 - 2*b**2 + 2*b - 792. Solve u(g) = 0.
-24, -10
Suppose 3*c + 10 = c, s - 4*c = 335. Determine i, given that 22*i**3 + s*i**4 - 321*i**4 - 25*i**3 + 3*i**5 + 6*i**2 = 0.
-1, 0, 1, 2
Let r(m) = -m**3 + 30*m**2 - 144*m - 2. Let o be r(6). Let u be ((-16)/32 + 0)/(o/8). Factor 0*d + 0 - 5*d**u + 35/2*d**3.
5*d**2*(7*d - 2)/2
Let o(t) be the third derivative of -5625/4*t**3 + 0 - 75/8*t**4 + 0*t + 269*t**2 - 1/40*t**5. Factor o(k).
-3*(k + 75)**2/2
Let w(j) be the third derivative of 4*j + 1/60*j**5 + 1/8*j**4 - 13*j**2 + 0*j**3 + 0. Determine t so that w(t) = 0.
-3, 0
Let r = 135 + -128. Find m such that -6*m**2 + 27 + 8*m - 4*m**3 + m**4 - r - 12 + m**4 = 0.
-1, 2
Solve u**2 - 388*u - 188 - 279 + 78 = 0 for u.
-1, 389
Let k(x) be the second derivative of x**4/4 + 31*x**3/6 - 11*x**2 - 1958*x. Factor k(p).
(p + 11)*(3*p - 2)
Let v(m) be the third derivative of -m**7/315 - 167*m**6/180 - 163*m**5/15 - 485*m**4/9 - 1288*m**3/9 - m**2 + 4622. Factor v(b).
-2*(b + 2)**3*(b + 161)/3
Factor -34/3*y**2 + 64/9 - 1628/9*y.
-2*(y + 16)*(51*y - 2)/9
Let d(m) = -m**2 + 75*m + 40. Let g(v) = -75*v - 39. Let p(l) = l**2 + 24*l + 2. Let o be p(0). Let a(x) = o*d(x) + 3*g(x). Factor a(i).
-(i + 37)*(2*i + 1)
Let a(h) = 8*h - 143. Let b(o) = -23*o + 427. Let n(f) = 7*a(f) + 2*b(f). Let g be n(15). Factor 12/5*d**g - 4/5*d**4 - 4/5*d**5 + 4*d**2 + 8/5*d + 0.
-4*d*(d - 2)*(d + 1)**3/5
Let m be 186 + 6*(-8)/(-6). Factor -m + 21*a**2 + 34*a + 3*a**2 + 184.
2*(3*a + 5)*(4*a - 1)
Suppose 4*g = -x - 101, 80 = -3*g - 5*x - 0*x. Let m be (21/(-35))/(20/g). Find u, given that 3/4*u - 3/4 + 3/4*u**2 - m*u**3 = 0.
-1, 1
Let p = 228729 + -228721. Factor -24/7 - 26/7*f**2 - 6/7*f**3 + p*f.
-2*(f - 1)*(f + 6)*(3*f - 2)/7
Let d = 2425 + -3618. Let l = -1191 - d. Let -l*r + 0 + 1/3*r**3 + 5/3*r**2 = 0. Calculate r.
-6, 0, 1
Let i(w) be the first derivative of -w**5/15 - 2*w**4/3 + w**3/3 + 11*w**2/3 - 16*w/3 - 4589. Factor i(d).
-(d - 1)**2*(d + 2)*(d + 8)/3
Suppose 3*y - 15 = 3*g, 5*g + 16 = 3*y - 1. What is k in 24*k**2 - 10*k + 3*k**5 - 2*k - 9*k**3 - 6*k**4 + 3*k**y - 3*k**4 = 0?
-2, 0, 1, 2
Let s(p) be the second derivative of -p**4/3 - 54*p**3 + 504*p**2 + 8*p + 48. Factor s(y).
-4*(y - 3)*(y + 84)
Let f(g) be the first derivative of 3*g**4/4 - 25*g**3/2 + 12*g**2 - 34*g - 28. Let r(a) be the first derivative of f(a). Suppose r(n) = 0. What is n?
1/3, 8
Let y be 512/14 - 60/105. Let j(d) = -d**2 + 31*d - 391. Let u(q) = -q + 1. Let s(p) = y*u(p) - 4*j(p). Solve s(r) = 0.
20
Let q(r) be the first derivative of 19*r**6/15 + 53*r**5/20 - r**4/2 - 19*r**3/6 + r**2 - 257*r - 144. Let g(h) be the first derivative of q(h). Solve g(t) = 0.
-1, 2/19, 1/2
Suppose -21*n**2 + 39*n**2 + 8*n**2 + 0*n**3 + 24*n + 2*n**3 = 0. What is n?
-12, -1, 0
Let m(k) be the first derivative of k**6/40 + k**5/15 + k**4/24 + 11*k**2/2 + 8. Let h(x) be the second derivative of m(x). Factor h(a).
a*(a + 1)*(3*a + 1)
Let s(f) be the first derivative of -f**9/1764 + f**8/1470 + 3*f**7/490 - 2*f**5/105 + 27*f**3 - 108. Let y(u) be the third derivative of s(u). Solve y(d) = 0.
-1, 0, 2/3, 2
Let c(w) = -3*w**2 + 19*w + 7. Let l be c(7). Let q = l + 10. Find z, given that -82 + 16*z - 5*z**q + 92 - z = 0.
-1, 2
Let w be (-10078)/(-5) + (-19 - (-679)/35). Let k be (4/(-42))/((-216)/w). Factor k*m**2 - 2/3*m - 2/9*m**3 + 0.
-2*m*(m - 3)*(m - 1)/9
Let o(z) be the first derivative of -125/2*z**2 + 25/3*z**3 - 3*z - 5/12*z**4 - 1. Let w(h) be the first derivative of o(h). Let w(a) = 0. Calculate a.
5
Let k(t) = 130*t**3 - 170*t**2 + 630*t + 834. Let j(z) = -54*z**3 + 68*z**2 - 252*z - 334. Let l(f) = -12*j(f) - 5*k(f). Let l(b) = 0. Calculate b.
-1, 9
Let t(u) be the second derivative of 0*u**4 + 1/480*u**6 + 0 + 1/6*u**3 - 2*u - 1/80*u**5 + 10*u**2. Let f(x) be the first derivative of t(x). Factor f(p).
(p - 2)**2*(p + 1)/4
Let w = 204 + -186. Let -5*m**2 + 38*m + 4*m**2 + 3 - 22*m - w*m = 0. What is m?
-3, 1
Suppose -124400*j - 50 = -124425*j. Factor -3*c + 0 + 1/2*c**j.
c*(c - 6)/2
Let d(k) = 112*k + 2138. Let h be d(-19). Let z(y) be the first derivative of -y**2 - 4*y - h + 2/3*y**3. Find j such that z(j) = 0.
-1, 2
Find t, given that 22881*t**3 + 5360*t**2 + 320 - 14748*t**3 - 14838*t**3 + 12780*t + 395*t**4 = 0.
-1, -2/79, 2, 16
Let d(u) be the third derivative of -u**5/210 + 2921*u**4/42 - 8532241*u**3/21 + 18*u**2 - 13*u + 2. Factor d(z).
-2*(z - 2921)**2/7
Let k = -97908/77 + 34666/33. Let q = -662/3 - k. Determine s so that -8/21*s + q + 2/21*s**2 = 0.
2
Suppose 4*d + 3*r - 4 + 6 = 0, -3*r + 6 = 0. Let i(s) = -13*s - 2. Let a be i(d). Factor u**2 - 21 + 43 + u - a.
(u - 1)*(u + 2)
Let z(b) = b**3 + 5*b**2 - 286*b - 2246. Let i be z(-9). Determine a so that 1/4*a**2 + 0 + 1/8*a**3 + 0*a - 1/8*a**i = 0.
-1, 0, 2
Let q(u) be the third derivative of 287*u**2 - 1/6*u**6 - 2/105*u**7 - 64/3*u**3 + 0*u + 2/5*u**5 + 16/3*u**4 + 0. What is a in q(a) = 0?
-4, 1, 2
Let x(i) be the second derivative of -1/114*i**4 + 12/19*i**2 - 11/57*i**3 + 51*i + 0. Determine c, given that x(c) = 0.
-12, 1
Suppose 23*m - 37*m + 28 = 0. Let -26*b**2 + 1024*b - 25*b**m - 54*b**3 - 13*b**2 + 55*b**3 = 0. Calculate b.
0, 32
Let i = -85568 - -427843/5. Solve 9/5*o**3 - 3/5*o**5 - i*o**4 + 0 - 6/5*o + 3/5*o**2 = 0 for o.
-2, -1, 0, 1
Let q = 10 + -19. Let h(v) = 19*v**3 + 11*v**2 - 70*v + 31. Let z(j) = -1472 - 9*j**3 - j**2 - 5*j**2 + 1456 + 35*j. Let l(c) = q*z(c) - 4*h(c). Factor l(k).
5*(k - 1)**2*(k + 4)
Let -18*c**5 - 27*c**5 + 188*c**4 - 555*c**3 - 60*c - 172*c**2 + 552*c**2 + 23*c**4 + 69*c**4 = 0. Calculate c.
0, 2/9, 1, 2, 3
Let z = 3729430/358599 + -2/1792995. Suppose 0 + z*c**2 + 28/5*c - 4/5*c**4 + 4*c**3 = 0. What is c?
-1, 0, 7
Let -174/7*h**3 + 0*h + 48*h**2 + 3/7*h**4 + 0 = 0. What is h?
0, 2, 56
Let p be ((-2)/(-90))/((-46)/(-24) - 1). Let w = p + 4117/330. Factor w*h - 15*h**2 + 5/2.
-5*(h - 1)*(6*h + 1)/2
Suppose -358 = 5*p - 2*d - 73, 0 = 2*p + 5*d + 114. Let l be (-6)/(-8) + p/(-4). Solve 25*b**2 + 17*b - 35*b + 28*b - l*b**3 = 0 for b.
-1/3, 0, 2
Let b = 525833 + -2629149/5. Suppose 64/5*l + 9/5*l**4 + 48/5*l**3 + 88/5*l**2 + b = 0. Calculate l.
-2, -2/3
Let m be -2*(82/4 + 2). Let a = m + 49. Find y such that 4*y**4 - y**5 + 9*y**5 - 7*y**4 + 7*y**a - 4*y**3 = 0.
-1, 0, 1/2
Let z(w) = -7*w**4 - 19*w**3 - 92*w**2 - 98*w - 3. Let v(k) = -2*k**4 - 2*k**2 + 2*k - 1. Let f(d) = -3*v(d) + z(d). Factor f(s).
-s*(s + 2)*(s + 4)*(s + 13)
Let f(g) be the first derivative of -g**4/22 + 8*g**3/33 - 4*g**2/11 + 4389. Factor f(a).
-2*a*(a - 2)**2/11
Find b, given that -918/7 + 75/7*b + 3/7*b**2 = 0.
-34, 9
Let j(o) = 3*o**2 - 316*o + 1883. Let n be j(99). Factor 4*q**3 + 16*q + 66/5*q**n + 2/5*q**4 + 32/5.
2*(q + 1)**2*(q + 4)**2/5
Let z = 180 + -1256/7. Let g be 4/((-16)/6)*((-18)/3 - (-244)/42). Factor g*k**2 + 2/7 + z*k.
2*(k + 1)**2/7
Let t(h) be the second derivative of h**4/54 - 3668*h**3/27 + 3363556*h**2/9 + 8*h - 85. Factor t(a).
2*(a - 1834)**2/9
Let a be (-3)/(-9)*(-627)/(-1045) - (-31)/20. Factor 13/4*c**3 - 9/2*c + a*c**4 - 3/4*c**2 + 0 + 1/4*c**5.
c*(c - 1)*(c + 2)*(c + 3)**2/4
Determine r so that 0 - 488/19*r - 2/19*r**2 = 0.
-244, 0
Suppose -1 + 1 = -2*y. Suppose y*n - 1 = -3*n - b, -3*b = 3*n - 3. Find z, given that -6*z**4 + 13*z**2 + n*z - 7*z**2 - 3*z + 3*z**5 = 0.
-1, 0, 1
Factor 208/15 - 38/15*w**3 - 328/15*w + 2/15*w**4 + 12*w**2.
2*(w - 13)*(w - 2)**3/15
Let j(v) be the second derivative of -v**7/126 + 146*v**6/5 - 431649*v**5/10 + 31510377*v**4 - 20702317689*v**3/2 + 2*v + 176. Factor j(z).
-z*(z - 657)**4/3
Factor 133*u - 16*u**2 - 216 - 5*u