 = 0. What is w?
-40, -3
Factor 0 - 4/3*r**4 - 10/3*r**3 + 28/3*r**2 - 5*r + 1/3*r**5.
r*(r - 5)*(r - 1)**2*(r + 3)/3
Let u(v) be the second derivative of -1/5*v**5 + 28 + 22/3*v**3 - 24*v**2 - v + 2/3*v**4. Find r such that u(r) = 0.
-3, 1, 4
Solve -38*d - 3*d**3 + 7*d**3 - 6*d**3 + 46*d - 656 + 0*d**3 + 164*d**2 = 0.
-2, 2, 82
Solve -2/5*d**2 - 189728/5 + 1232/5*d = 0 for d.
308
Let g(m) = 7*m**2 + 1893*m + 1910. Let k(v) = -3*v**2 + v - 4. Let o(c) = -2*g(c) - 6*k(c). What is r in o(r) = 0?
-1, 949
Let l(b) be the first derivative of -15 - 12*b - 2/9*b**3 + 19/3*b**2. Factor l(y).
-2*(y - 18)*(y - 1)/3
Let y(i) = -4*i**2 + 4*i - 5. Let v be y(1). Let m be 3 + (-80)/24 - v/12. Factor m*a**2 + 1/3*a + 1/4.
(a + 1)*(a + 3)/12
Let j be -103 - (2 + -2) - 5. Let u be j/26 - -4 - 750/(-312). Let 27/2 - 3/4*p**3 - 3*p**2 + u*p = 0. What is p?
-3, 2
Suppose 6*b + 12 = 12. What is n in -44*n + 7 + b + 1 - 8*n**2 - 16*n**2 = 0?
-2, 1/6
Let q(x) be the first derivative of 3/8*x**2 + 37 + 3/4*x**4 + 0*x - x**3. Let q(k) = 0. What is k?
0, 1/2
Let t(g) = 1875*g**2 + 6272*g + 5292. Let o(m) = 1875*m**2 + 6265*m + 5292. Let h(d) = 4*o(d) - 5*t(d). Factor h(q).
-3*(25*q + 42)**2
Let p = 315 - 313. Suppose 40 + 5*a**2 - 5*a**2 - 24*a + 5*a**p - 21*a = 0. Calculate a.
1, 8
Suppose 12*w - 33*w + 840 = 0. Factor 27*m**2 + 5*m**4 - 14*m + w - 86*m + 63*m**2 - 35*m**3.
5*(m - 2)**3*(m - 1)
Factor 46/21*m - 44/21 - 2/21*m**2.
-2*(m - 22)*(m - 1)/21
Let a(y) be the third derivative of 2*y**7/105 + 31*y**6/6 + 307*y**5/15 + 51*y**4/2 + 2*y**2 + 1658*y + 2. Factor a(z).
4*z*(z + 1)**2*(z + 153)
Let w(i) be the first derivative of 0*i + 0*i**2 - 5*i**4 - 73 + 20/3*i**3 + i**5. Let w(o) = 0. Calculate o.
0, 2
Factor -266/3 - 2/3*i**2 + 532/3*i**3 + 268/3*i**4 - 533/3*i + 1/3*i**5.
(i - 1)*(i + 1)**3*(i + 266)/3
Let g be (-6 - (-171)/76)*(-11)/(264/16). Determine o, given that -1/6 - g*o**2 + 3/2*o + 7/6*o**3 = 0.
1/7, 1
Let j(v) be the second derivative of -v**6/10 - 1169*v**5/20 - 25285*v**4/2 - 1090050*v**3 + 1098500*v**2 - 23*v + 5. Factor j(n).
-(n + 130)**3*(3*n - 1)
Let s be -1 + (4 - (-5 + (-1036)/(-135))). Let o = s + 1/135. Factor 0*x**2 + 0 + 0*x + 1/6*x**4 - o*x**3 + 1/6*x**5.
x**3*(x - 1)*(x + 2)/6
Factor 13*r**3 + 3 + 12*r**3 - 8 + 35*r + 45*r**2 + 5*r**4 + 15.
5*(r + 1)**3*(r + 2)
Let r(f) be the second derivative of -f**5/5 - 3*f**4 + 8*f**3 + 40*f**2 - 493*f + 1. Factor r(w).
-4*(w - 2)*(w + 1)*(w + 10)
Suppose -5*t - 324 = -579. Factor 27*j**3 + j + 26*j**3 - 3*j**2 - t*j**3.
j*(j - 1)*(2*j - 1)
Let w(t) = 821*t + 4927. Let c be w(-6). Suppose 4 = -v + 3*v - 5*n, 3*v + 4*n = 6. Factor -c - 1/2*s**3 + s**v + 1/2*s.
-(s - 2)*(s - 1)*(s + 1)/2
Let d(r) = 3*r**2 + 12*r + 13. Suppose -5*z = 10, 6*v = 7*v - z - 3. Let y(x) = -1. Let s(h) = v*y(h) + d(h). Factor s(j).
3*(j + 2)**2
Let v = 2/3483 - -6896/121905. Let s(x) be the first derivative of 0*x**3 - 1/14*x**4 + 13 - v*x**5 + 0*x + 0*x**2. Find q, given that s(q) = 0.
-1, 0
Let a be 296/64 - 6/(-16). Suppose a = 16*o + 5. What is q in o*q**4 + 0 - 4/17*q**3 + 0*q**2 + 2/17*q + 2/17*q**5 = 0?
-1, 0, 1
Let l(u) = -3*u**3 + 3*u**2 + 24*u. Let c(n) be the first derivative of -3*n**4/4 + n**3 + 23*n**2/2 - 46. Let w(q) = -6*c(q) + 5*l(q). Factor w(v).
3*v*(v - 3)*(v + 2)
Let 13468*q**2 + 1444*q**3 + 1496*q**3 - 44*q**4 - 42513*q**2 + 8712 - 21239*q**2 + 38676*q = 0. What is q?
-2/11, 1, 33
Let m(q) be the third derivative of -q**7/8820 - q**6/315 - q**5/28 - 161*q**4/24 + 209*q**2. Let l(t) be the second derivative of m(t). Factor l(k).
-2*(k + 3)*(k + 5)/7
Let p be 3/36 - 497/(-84). Suppose 124*g**3 + 36*g**2 - 118*g**2 - 223*g**2 + p*g**3 + 100*g - 10*g**4 + 85*g**3 = 0. What is g?
0, 1/2, 1, 20
Let w be -20 + (108/30 - (-2)/5). Let s(n) = -4*n**2 - 268*n + 224. Let k(o) = o**2 + 53*o - 45. Let b(v) = w*k(v) - 3*s(v). Determine z so that b(z) = 0.
-12, 1
Suppose 145 + 340*v**2 - 462*v**3 - 80*v**2 + 14*v**5 + 95 + 4*v**4 + 952*v = 0. Calculate v.
-6, -1, -2/7, 2, 5
Determine k so that -509232 + 2468/3*k**2 - 2/3*k**3 - 252968*k = 0.
-2, 618
Let j(r) be the second derivative of 3*r**5/20 - 137*r**4 - 549*r**3/2 + 368*r - 3. What is u in j(u) = 0?
-1, 0, 549
Determine g, given that -1/6 + 3/2*g**3 - 19/6*g**2 + 11/6*g = 0.
1/9, 1
Let r(z) be the second derivative of 1/70*z**5 + 1/6*z**4 + 0 + 8/7*z**2 + 2/3*z**3 - 45*z. Factor r(j).
2*(j + 1)*(j + 2)*(j + 4)/7
Let a be 18/((-1080)/(-490))*16/7. Determine z so that a*z - 14/3*z**3 - 12*z**2 - 16/3 + 10/3*z**4 = 0.
-2, 2/5, 1, 2
Let y(u) be the third derivative of u**8/63 + 466*u**7/315 - 209*u**6/45 + 121*u**5/45 + 10*u**4/3 + 528*u**2 + 2*u. Find o such that y(o) = 0.
-60, -1/4, 0, 1
Suppose 6*i + 3 = 21. Find v, given that -7*v**i - 5*v - 45*v - 3*v**3 - 50*v**2 - 75*v + 5*v**3 = 0.
-5, 0
Let f(z) be the first derivative of -2*z**3/39 + 396*z**2/13 - 78408*z/13 + 1154. Suppose f(x) = 0. What is x?
198
Let u(h) = 25*h + 1575. Let w be u(-63). Suppose 4*s - 21 = -3*s. Factor 2*o + w - 3/2*o**s + 2*o**2 + 1/2*o**5 - o**4.
o*(o - 2)**2*(o + 1)**2/2
Let u(y) be the second derivative of -128/5*y**2 + 32/15*y**3 - 1/15*y**4 - 10 + 2*y. Solve u(j) = 0 for j.
8
Let s(x) = 26*x**2 + 732*x + 1435. Let g(j) = -7*j**2 + j + 5. Let n(q) = 3*g(q) + s(q). Factor n(v).
5*(v + 2)*(v + 145)
Suppose s + 13*s = 33*s. Let h be (-3)/6 - (-3)/2. Factor 5*o - 9*o**2 + s - 10*o - o - h - 4*o**3.
-(o + 1)**2*(4*o + 1)
Let b be 18*((-2)/(336/2152) - -13). Factor 240/7*z**2 + 0 + b*z + 486/7*z**4 + 702/7*z**3.
6*z*(z + 1)*(9*z + 2)**2/7
Let z(a) = -15*a**3 - 699*a**2 + 2987*a - 2970. Let q(g) = 8*g**3 + 348*g**2 - 1494*g + 1484. Let s(m) = 11*q(m) + 6*z(m). Determine f, given that s(f) = 0.
-187, 2
Let b(t) be the third derivative of -t**6/150 - 169*t**5/300 - 11*t**4/8 - t**2 + 526*t. Factor b(d).
-d*(d + 1)*(4*d + 165)/5
Let p(d) be the second derivative of -3*d**6/20 + 179*d**5/20 + 827*d**4/24 + 136*d**3/3 + 21*d**2 + 8485*d. Determine l so that p(l) = 0.
-1, -2/9, 42
Let p(h) be the third derivative of -13/180*h**6 - 1/126*h**8 - 2/3*h**3 + 0 - 1/10*h**5 - 4*h**2 + 17/36*h**4 - 9*h + 1/21*h**7. Suppose p(w) = 0. Calculate w.
-1, 3/4, 1, 2
Let f be ((-672)/(-108))/((-420)/(-135) + -2). Suppose x**3 + 22/5*x**2 + f*x + 8/5 = 0. Calculate x.
-2, -2/5
Let g(m) be the first derivative of -98*m - 10*m**3 - 1/2*m**4 - 63*m**2 - 40. Factor g(i).
-2*(i + 1)*(i + 7)**2
Let -789*u**2 + 11023*u**2 - 3818*u + 1360*u + 9*u**3 - 3414*u + 89*u**3 + 840 = 0. What is u?
-105, 2/7
Let y(w) be the first derivative of -w**4 - 1112*w**3/3 - 38642*w**2 + 6080. Suppose y(u) = 0. What is u?
-139, 0
Let i be -5 + 1 - ((-128)/28)/((-144)/(-168)). Solve 0*m**2 + i*m**4 + 4/9*m**5 + 8/9*m**3 + 0 + 0*m = 0.
-2, -1, 0
Find f, given that -9/2*f**5 - 1152*f + 129/2*f**4 - 356*f**3 + 512 + 936*f**2 = 0.
1, 8/3, 4
Let u be 44 + 504/((-288)/24). Suppose 15 = 2*w + 3*w. Solve 30 - 3/5*m**w - 27*m + 36/5*m**u = 0.
2, 5
Suppose -54*w - 96 = -58*w. Let r be (4/(-36))/(w/(-54)). Find s such that 1/2 - r*s**3 + 1/4*s - 1/2*s**2 = 0.
-2, -1, 1
Let j = -38370 - -38379. Let 1/2*q**4 + j*q**2 - 10*q + 4 - 7/2*q**3 = 0. What is q?
1, 2
Let d(a) be the second derivative of a**4/54 + 8*a**3 - 436*a**2/9 + 4620*a. Factor d(n).
2*(n - 2)*(n + 218)/9
Factor -1/4*c**3 + 387/4 + 513/4*c + 125/4*c**2.
-(c - 129)*(c + 1)*(c + 3)/4
Let g(i) be the first derivative of i**3/9 + 1826*i**2/3 + 3334276*i/3 - 1409. Suppose g(v) = 0. What is v?
-1826
Suppose 482*y = 513*y - 124. Let p(v) = v - 2. Let n be p(4). Factor -8*i + 5*i**n - 16*i**4 - 33*i**2 - 36*i**3 - 8*i**4 + 4*i**4 - y*i**5.
-4*i*(i + 1)**3*(i + 2)
Let d(w) = 256*w + 1284. Let k be d(-5). Let o(b) be the first derivative of -k*b**3 + 4/5*b**5 - 16*b + 20 - 2*b**4 + 16*b**2. Solve o(f) = 0.
-2, 1, 2
Suppose -y + 5 = 3. Suppose 4*g + 2*c - 8 = 0, -14*g - 2*c = -13*g + 1. Factor -22*i**y - 10*i**2 + 5 + i**g + 17*i**2 + 9*i**3.
5*(i - 1)**2*(2*i + 1)
Factor 243 + 207/7*h**2 + 3/7*h**3 + 1161/7*h.
3*(h + 3)**2*(h + 63)/7
Let i be (2/24)/((-157)/(-4396)). Let g(q) be the third derivative of -i*q**4 - 1/5*q**5 + 10/3*q**3 + q**2 + 0 + 0*q. Factor g(n).
-4*(n + 5)*(3*n - 1)
Let c(p) be the third derivative of -p**5/3 + 503*p**4/6 + 404*p**3/3 + 2301*p**2. Solve c(s) = 0.
-2/5, 101
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