51*s**2 + 48*s**2 + 230 - 206*s**2 = 0.
-2, 23
Let o = -25344 + 25344. Determine w so that o*w + 2/11*w**4 + 0 + 0*w**2 - 4/11*w**3 + 2/11*w**5 = 0.
-2, 0, 1
Let z(q) be the first derivative of -q**3/9 + 1495*q**2/3 - 2235025*q/3 + 5735. Factor z(l).
-(l - 1495)**2/3
Factor 34840/9*h**3 + 2/9*h**5 + 524/9*h**4 + 67600/9*h**2 + 0 + 0*h.
2*h**2*(h + 2)*(h + 130)**2/9
Solve -7498683/2 - 3/2*j**2 - 4743*j = 0.
-1581
Let n = 160760/19293 - -5/6431. Solve -n*q**2 + 59/6*q**4 + 28/3*q + 14*q**5 - 3/2 - 70/3*q**3 = 0.
-9/7, -1, 1/4, 1/3, 1
Let x(j) be the third derivative of -j**7/120 - j**6/40 - j**5/60 - 16*j**3 - 198*j**2. Let k(p) be the first derivative of x(p). Factor k(d).
-d*(d + 1)*(7*d + 2)
Let g(t) be the first derivative of t**4/48 - 223*t**3/4 - 259. Factor g(c).
c**2*(c - 2007)/12
Let f be (-988)/(10 + 36/(-66) + (-2488)/198 - -2). Solve 468/5*c**3 + f*c - 12/5*c**4 - 4791/5*c**2 - 1083/5 = 0 for c.
1/2, 19
Suppose 0 = 3*l + 4*s + 8, 28*l - 5*s + 11 = 148. Suppose 13/4*r**2 + 0 - 3/2*r + 1/4*r**5 - 1/4*r**l - 7/4*r**3 = 0. What is r?
-3, 0, 1, 2
Let v(u) be the second derivative of u**8/336 - 4*u**7/315 + u**6/60 - 11*u**4/3 + 30*u. Let w(g) be the third derivative of v(g). Let w(h) = 0. Calculate h.
0, 3/5, 1
Let z(i) be the first derivative of -140/3*i**3 + 186 - 5/2*i**2 + 140*i + 5/4*i**4. Suppose z(f) = 0. What is f?
-1, 1, 28
Let z be (3 - (-121)/(-11)) + 985. Let r = 5867/6 - z. Factor 1/6*i**5 + 0 + 1/2*i**3 + 0*i - 3/2*i**2 + r*i**4.
i**2*(i - 1)*(i + 3)**2/6
Factor -1227*v - 1202*v - 6*v**3 + 3563*v - 1200*v - v**4 + 49*v**2.
-v*(v - 3)*(v - 2)*(v + 11)
Suppose 0 = -w + 4*k - 225, -w - 3*k - 2*k = 198. Let d = w - -1493/7. Factor 2/7 + 2/7*j - 2/7*j**2 - d*j**3.
-2*(j - 1)*(j + 1)**2/7
Suppose 6 = 2*t - 2*k + k, -3*t = 5*k + 4. Factor -10092/5 - 3/5*x**t + 348/5*x.
-3*(x - 58)**2/5
Let g be (-195)/78 + 5/(-2) + 1. Let i(f) = 7*f**2 - 21*f - 25. Let a(c) = -3*c**2 + 10*c + 12. Let o(k) = g*i(k) - 9*a(k). Factor o(z).
-(z + 2)*(z + 4)
Let k be (-1047)/(-698) - ((3/(-6))/(-1) - 0). Let j(o) be the first derivative of 2*o - k - 2*o**2 + 2/3*o**3. Suppose j(d) = 0. What is d?
1
Let y(c) = -2*c - 18. Let s be y(-9). Let j be s/(0 + 2 + -1) - -3. Factor -4*t**2 - 5*t**4 - 5*t**5 + 3*t**5 - j*t**4 - 10*t**3.
-2*t**2*(t + 1)**2*(t + 2)
Let z be 4*12/18*5/(250 + 0). Let d(i) be the second derivative of -12*i - 1/225*i**6 + 8/15*i**3 + 0 + z*i**5 - 11/45*i**4 - 3/5*i**2. Factor d(w).
-2*(w - 3)**2*(w - 1)**2/15
Let m(i) be the first derivative of -i**4/4 - 10*i**3/3 - 9*i**2/2 + 9385. Suppose m(w) = 0. What is w?
-9, -1, 0
Let k be (-11)/(-22) + 10/4. Let s be (-3)/((-5)/(-15)*6/(-8)). Suppose -36*a + s*a**2 + 2 - 2 - 178*a**3 + 198*a**k + 4*a**4 = 0. What is a?
-3, 0, 1
Let a(d) = 29*d**5 + 58*d**4 - 538*d**3 + 2704*d**2 - 5638*d + 4090. Let r(x) = -5*x**5 - 3*x**4 + x**3 + x + 1. Let l(g) = -a(g) - 6*r(g). Factor l(c).
(c - 16)**2*(c - 4)*(c - 2)**2
Let p(t) be the third derivative of -t**5/20 - 101*t**4/8 + 103*t**3 - 1474*t**2. Factor p(w).
-3*(w - 2)*(w + 103)
Factor 8/15*y - 2*y**2 + 2/5.
-2*(3*y + 1)*(5*y - 3)/15
Let c(k) = 1881*k**5 - 1860*k**4 + 5*k**3 - 13. Let n(g) = -1411*g**5 + 1395*g**4 - 4*g**3 + 10. Let a(x) = 10*c(x) + 13*n(x). Find y such that a(y) = 0.
-2/467, 0, 1
Let w(o) be the third derivative of 13*o**2 + 4/3*o**5 + 10/3*o**3 + 85/24*o**4 + 0*o + 0 + 1/8*o**6. Find m such that w(m) = 0.
-4, -1, -1/3
Let i(t) = 427*t + 64050. Let o be i(-150). Factor -2/3 - 1/3*a**3 + o*a**2 + a.
-(a - 1)**2*(a + 2)/3
Factor -52*v**4 - 53*v**3 - 4*v**5 - 562*v**2 - 451*v**2 + 873*v**3 - 1287*v**2.
-4*v**2*(v - 5)**2*(v + 23)
Let c = 203 + -201. Determine u, given that -471*u**3 + 484*u**4 + 16 + 852*u**c - 436*u**3 - 208*u - 237*u**3 = 0.
2/11, 1
Let l be 0/33*(-31)/(-713). Factor -16/7*o + 6/7*o**3 + 12/7*o**2 + l - 2/7*o**4.
-2*o*(o - 4)*(o - 1)*(o + 2)/7
Find z, given that 2*z + 1/6*z**4 - 29/6*z**2 + 14/3 - 2*z**3 = 0.
-2, -1, 1, 14
Let v = 5 + -3. Let o(u) = -14*u**2 - 161*u + 87. Let n be o(-12). Suppose -n*l**2 + l**4 + 4*l**3 - 2*l + 3*l**v - 2*l**3 - 1 = 0. What is l?
-1, 1
Let t(h) be the first derivative of 200/3*h**3 + 0*h**2 + 115 + 0*h - 5/4*h**4. Factor t(l).
-5*l**2*(l - 40)
Let x(v) = 5163*v - 20652. Let g be x(4). Factor 0 - 14/3*z**5 - 8/15*z**4 + 8/15*z**3 + 0*z + g*z**2.
-2*z**3*(5*z + 2)*(7*z - 2)/15
Factor 0 + 2/9*h**2 - 1300/9*h.
2*h*(h - 650)/9
Let n = 738 - 735. Factor 47*q**3 + 20*q**4 - 108*q**3 - 5*q**5 + 61*q**n.
-5*q**4*(q - 4)
Suppose 67 = 8*s + 43. Let c(o) be the second derivative of 16*o + 0 - 1/6*o**4 - o**2 + 2/3*o**s. Let c(t) = 0. Calculate t.
1
Let p(t) be the third derivative of t**7/4200 + t**6/450 - t**5/600 - t**4/30 - 47*t**3/6 - 20*t**2. Let d(s) be the first derivative of p(s). Factor d(l).
(l - 1)*(l + 1)*(l + 4)/5
Find i such that 106*i**3 + 12728*i**5 - 12720*i**5 - 73*i**4 - 42*i - i**4 + 146*i**2 = 0.
-1, 0, 1/4, 3, 7
Let k(z) = 5000*z**3 - 4504*z**2 + 1346*z - 139. Suppose 20*p - 18 = 2*p. Let y(w) = -w**2 - w - 1. Let j(v) = p*k(v) - 4*y(v). Factor j(q).
5*(10*q - 3)**3
Factor -1800/7 - 3/7*k**2 + 30*k.
-3*(k - 60)*(k - 10)/7
Let p(a) be the third derivative of -a**6/180 + a**5/12 - 9*a**3 - 147*a**2. Let s(x) be the first derivative of p(x). Factor s(g).
-2*g*(g - 5)
Factor 104 + 76/3*w**2 - 1/6*w**3 + 310/3*w.
-(w - 156)*(w + 2)**2/6
Let u(r) be the second derivative of 1/294*r**7 + 2*r + 1/210*r**6 + 5/42*r**3 - 3/70*r**5 + 4 - 3/14*r**2 + 1/42*r**4. Factor u(t).
(t - 1)**3*(t + 1)*(t + 3)/7
Let g(t) be the third derivative of -t**7/280 + t**6/120 + t**5/4 + t**4 - 127*t**3/6 - 169*t**2. Let l(v) be the first derivative of g(v). Factor l(r).
-3*(r - 4)*(r + 1)*(r + 2)
Let w(d) be the first derivative of 15/2*d**2 - 44 + 24/5*d**5 + 1/2*d**6 + 16*d**3 + 0*d + 27/2*d**4. Factor w(a).
3*a*(a + 1)**3*(a + 5)
Let s be 6/(32 + 25 + -24). What is p in 6/11*p + 0*p**2 - 4/11 - s*p**3 = 0?
-2, 1
Let t(a) be the first derivative of 4*a**3/3 - 86*a**2 + 760*a + 1996. Suppose t(r) = 0. What is r?
5, 38
Let f(v) be the first derivative of -2*v**5/35 + 45*v**4/14 + 28*v**3 + 604*v**2/7 + 816*v/7 + 439. What is h in f(h) = 0?
-2, 51
Let c(v) be the first derivative of -v**5/10 - 203*v**4/8 - 101*v**3/3 + 15. What is i in c(i) = 0?
-202, -1, 0
Let p(d) be the second derivative of -13*d + 0*d**5 - 1/54*d**4 - 9/2*d**3 + 0 + 0*d**2 + 1/810*d**6. Let w(a) be the second derivative of p(a). Factor w(m).
4*(m - 1)*(m + 1)/9
Let t(h) be the first derivative of h**5/10 + 5*h**4/8 + 2*h**3/3 + 2319. Factor t(m).
m**2*(m + 1)*(m + 4)/2
Let h(o) be the third derivative of 7*o**5/300 - o**4/20 - 8*o**3/15 + 332*o**2. Let h(g) = 0. What is g?
-8/7, 2
Let z(d) be the first derivative of d**6/2 - 929*d**5/5 + 47581*d**4/2 - 1049360*d**3 - 3904576*d**2 - 2249728*d + 3258. Factor z(y).
(y - 104)**3*(y + 2)*(3*y + 1)
Let -1957*s**4 - 19206*s**3 + 51 - 1310*s**4 + 29 + 4 - 2844*s + 25233*s**2 = 0. What is s?
-7, 2/33, 1
Let h = 175 + 60. Solve -824*x**3 - 170*x - 946*x**2 + 96*x**4 + 78*x - 40 - h*x + 196*x**5 - 17*x - 82*x**4 = 0 for x.
-1, -2/7, 5/2
Let l(x) = -x**2 - x. Let s(g) = -4*g**2 - 4*g. Let q(d) = 5*d**2 + 5*d. Let h(i) = 3*q(i) + 4*s(i). Let u(p) = 3*h(p) - 6*l(p). Factor u(a).
3*a*(a + 1)
Let a(n) = 2*n**2 + 1176*n + 162458. Let m(v) = -2*v**2 - 1167*v - 162456. Let t(j) = 3*a(j) + 4*m(j). What is o in t(o) = 0?
-285
Let u = -1/31599 + 63203/157995. Suppose 3*h = -x + 15, -6*x + 20 = -x + 4*h. Solve 0*p**3 + x*p + 2/5*p**4 + u - 4/5*p**2 = 0.
-1, 1
Let o(j) = j**3 - 7*j**2 + 3*j - 1. Let q be o(7). Suppose -3*i = -46 - q. Let p**2 + i*p + 25*p - 52*p - 6 = 0. Calculate p.
-1, 6
Determine n, given that -2/9*n**4 + 38/9*n**3 + 176/9 - 58/3*n**2 - 38/9*n = 0.
-1, 1, 8, 11
Determine w, given that 5/6*w**2 - 30 + 25/6*w = 0.
-9, 4
Let q = 95945 + -95943. Factor 4/5*u**3 + 12/5*u**q - 8*u + 0.
4*u*(u - 2)*(u + 5)/5
Let z = 2744385712/3658202175 - -2/14691575. Let o = z + -18/83. Factor -2/15*u**2 - 8/15 - o*u.
-2*(u + 2)**2/15
Let s(i) be the first derivative of -i**6/360 - i**5/30 + 5*i**4/24 + 74*i**3/3 - 128. Let t(w) be the third derivative of s(w). Factor t(a).
-(a - 1)*(a + 5)
Let q(s) be the first derivative of -24*s**5/5 - 75*s**4/4 + 69*s**3 - 93*s**2/2 - 15*s - 2493. What is u in q(u) = 0