p**3 - 191/2*p + 9*p**2 = 0.
-8, -3/5, 5
Let x(h) be the second derivative of -h**4/4 + 49*h**3 - 291*h**2/2 + 5*h + 138. Factor x(q).
-3*(q - 97)*(q - 1)
Let -5/3*m**3 + 8001125/3 - 4215*m**2 - 2662825*m = 0. Calculate m.
-1265, 1
Let i(b) be the first derivative of 7*b**4/24 - 215*b**3/18 + 347*b**2/6 + 36*b + 4601. Suppose i(w) = 0. What is w?
-2/7, 4, 27
Let s(o) = -o**2 - 6*o + 20. Let p be s(-8). Suppose 13*k = 15*k - p. Let -2/3*m**2 + 4/3 - 2/3*m**4 + 2*m**3 - k*m = 0. What is m?
-1, 1, 2
Factor 170*m**4 + 170*m**2 + 325*m**3 - 103 - 10*m**2 + 5*m**5 + 103.
5*m**2*(m + 1)**2*(m + 32)
Suppose -k + 9 = 5*q - 2, 3*q - 3*k - 3 = 0. Suppose 4*p - 240 = -q*p. Suppose -j**5 + 90*j - 80*j**3 - p*j**4 - 90*j - 4*j**5 = 0. Calculate j.
-4, 0
Let s = -160/1071 - -30862/1071. Suppose s*t - 1849/3 - 1/3*t**2 = 0. What is t?
43
What is q in 1398*q**2 + 192 - 15*q**3 + 120*q + 3*q**4 - 2904*q**2 + 1416*q**2 = 0?
-4, -1, 2, 8
Factor 10/3*c**2 + 230/3 + 32*c.
2*(c + 5)*(5*c + 23)/3
Let q = -411 + 441. Let j be (-18)/27*(3 + q/(-8)). Suppose 3*a - j*a**2 + 0 = 0. Calculate a.
0, 6
Let w(z) = -z + 11. Let l(r) = 2*r**2 + 6*r - 44. Let h(a) = -l(a) + 6*w(a). Factor h(p).
-2*(p - 5)*(p + 11)
Factor 77*d**3 + 2346*d**2 + d**4 + 3738*d**2 + 13*d**3 + 66*d**3.
d**2*(d + 78)**2
Let k(i) = 2*i**2 - 20*i - 169. Let n(f) be the first derivative of f**3/3 - 11*f**2 - 169*f + 70. Let h(g) = -2*k(g) + 3*n(g). Solve h(t) = 0 for t.
-13
Let r be -23 - (-45583)/1975 - (-88)/150. Let g be (9/(-6))/((-9)/4). Factor -g*s - r + 1/2*s**2 - 1/6*s**4 + 1/3*s**3.
-(s - 2)**2*(s + 1)**2/6
Suppose -35*p = -27*p - 11200. Let h be (-6)/4 - p/(-784). Factor 6/7 - h*d**2 + 4/7*d.
-2*(d - 3)*(d + 1)/7
Let h(w) be the first derivative of 5/16*w**4 - 55/8*w**2 + 45/2*w - 15 - 10/3*w**3. Factor h(i).
5*(i - 9)*(i - 1)*(i + 2)/4
Let c(a) be the second derivative of -a**6/6 - 5*a**5 - 545*a**4/12 - 135*a**3 - 180*a**2 + a + 31. Factor c(l).
-5*(l + 1)**2*(l + 6)*(l + 12)
Factor 24968*x**2 - 2644*x**2 - 4580*x + 800 + 2096*x**2 - 2214*x - 2026*x - 605*x**3.
-5*(x - 40)*(11*x - 2)**2
Let g = 4885113/20 + -244198. Let w = g - 229/4. What is z in 0 - w*z**2 + 2/5*z = 0?
0, 1
Let a(q) be the first derivative of -4*q**3/21 - 24*q**2 - 656*q/7 + 1026. Determine j, given that a(j) = 0.
-82, -2
Let m(z) be the second derivative of 0*z**2 + 0 + 1/54*z**4 - 5/3*z**3 + 270*z. Factor m(q).
2*q*(q - 45)/9
Factor k**3 + 38/3*k - 19/3*k**2 - 8.
(k - 3)*(k - 2)*(3*k - 4)/3
Let g(l) = -115 + 4*l**2 - 26*l - 3*l**2 + 192. Let w be g(23). Find t such that -12*t**3 + 11*t**4 + w - 10*t**2 + 12*t - 14*t**4 + 4 + t**2 = 0.
-2, -1, 1
Let m(r) be the first derivative of 2*r**3/33 + 8*r**2/11 - 768*r/11 - 2825. Factor m(c).
2*(c - 16)*(c + 24)/11
Suppose -696 = 4*j - 126*a + 122*a, -4 = 2*a. Let c be (40/(-30))/(j/24). Find x such that 14/11*x - 16/11 + c*x**2 = 0.
-8, 1
Suppose 3*j = -y - 1, 24 = -3*y - j + 29. Find l, given that 2*l**y - 14*l - 9*l + 3*l**2 - 12*l + 30 = 0.
1, 6
Let a(q) = 2*q**3 + 9*q**2 - 4*q + 4. Let n be a(-5). Let l be (-1 - -2) + -3 + 6 + n. Let 0*d**2 + 3/2*d - 3/2*d**l + 0 = 0. Calculate d.
-1, 0, 1
Let r(i) be the third derivative of 10240/3*i**3 + 0*i - 80/3*i**4 + 0 - 13*i**2 + 1/12*i**5. Determine h so that r(h) = 0.
64
Let q = 97392/20537 - 28/1867. Suppose 30/11*c + q + 2/11*c**2 = 0. Calculate c.
-13, -2
Let m(w) = -w - 5. Let v be m(-25). Factor -y**4 + 36*y + 0*y**4 - 88 + 3*y**3 - v - 2*y**4 - 9*y**3 + 33*y**2.
-3*(y - 2)**2*(y + 3)**2
Let k = -27 - -30. Let -6 + 80*t - 154*t**2 - 4 + k - 1 - 242*t**3 = 0. Calculate t.
-1, 2/11
Factor 1504*r**4 + 16*r**5 - 58706*r**3 - 38*r**5 + 20*r**5 - 224046*r**3.
-2*r**3*(r - 376)**2
Let t = -20 + 24. Let d be 2/t*37*(-12 + 14). Factor -592*s**2 + 12 + d*s - s - 15*s**3 + 601*s**2.
-3*(s - 2)*(s + 1)*(5*s + 2)
Let o = 1085/8 - 16267/120. Let l(y) be the second derivative of o*y**3 + 1/50*y**5 - 1/15*y**4 + 0 + 0*y**2 - 9*y. Find j, given that l(j) = 0.
0, 1
Factor -1/2*d**3 + 75/2*d - 37*d**2 + 0.
-d*(d - 1)*(d + 75)/2
Let y(w) be the third derivative of w + 1/15*w**6 + 8/3*w**3 + 1/5*w**5 + 13*w**2 - 4/3*w**4 + 0 - 2/105*w**7. Find k, given that y(k) = 0.
-2, 1, 2
Let y be (54 + -1)*2 + -8. Let a be 3164/y + (-2)/14. Find b such that 3/7*b**3 - 375/7 + a*b - 45/7*b**2 = 0.
5
Let q(f) be the third derivative of -f**7/2100 - 11*f**6/600 - 97*f**5/600 + 11*f**4/10 - 12*f**3/5 - f**2 - 414. Factor q(l).
-(l - 1)**2*(l + 12)**2/10
Suppose 0 = -642*o + 639*o + 1503. Let b = o - 498. Factor -4/5*n**2 + 4/5*n**4 - 2/5*n**5 + 2/5*n + 0 + 0*n**b.
-2*n*(n - 1)**3*(n + 1)/5
Let r = -17479/13 + 1347. Suppose 3*g + 2*g + 62 = 36*g. Find q such that -2*q**g - 8/13 + r*q**3 - 40/13*q + 8/13*q**5 + 34/13*q**4 = 0.
-2, -1, -1/4, 1
Let s = 71401 - 71398. Find g, given that 8/5 - 2*g**2 + 2/5*g**4 - 6/5*g**s + 6/5*g = 0.
-1, 1, 4
Let l(y) be the second derivative of -y**4/16 + 7*y**3/2 + 45*y**2/2 + y - 40. Factor l(b).
-3*(b - 30)*(b + 2)/4
Factor -157*y**3 + 63*y**3 - 5*y**4 - 60*y**2 - 40*y + 64*y**3.
-5*y*(y + 2)**3
Let g(u) be the second derivative of -u**4/51 + 7*u**3/17 - 19*u**2/17 - 61*u + 2. Factor g(c).
-2*(c - 1)*(2*c - 19)/17
Let c be ((-75)/24)/((-145)/1450). Factor -25/4*t**3 + 5/4*t**5 + 50*t - c*t**2 - 20 + 25/4*t**4.
5*(t - 1)**3*(t + 4)**2/4
Let i be 18810/(-117) + (-12)/52. Let k be ((-69)/i)/(18/28). Factor -k + 2/3*f**4 - 8/3*f**2 + 7/3*f + 2/3*f**3 - 1/3*f**5.
-(f - 1)**4*(f + 2)/3
Let b(j) = -j**4 - j**3 + j**2 + j - 3. Suppose -5*t - 24 = 3*h, -2*h + 4 = 10. Let i(m) = m**4 + m**3 - m**2 - m + 5. Let s(p) = t*i(p) - 5*b(p). Factor s(l).
2*l*(l - 1)*(l + 1)**2
Let x = -800 + 800. Let w(q) be the first derivative of 1/15*q**6 + x*q**3 - 20 + 0*q**5 - 1/5*q**4 + 0*q + 1/5*q**2. Factor w(g).
2*g*(g - 1)**2*(g + 1)**2/5
Let c(k) be the first derivative of -56/33*k**3 + 91 - 2/55*k**5 + 9/22*k**4 + 36/11*k**2 - 32/11*k. Solve c(n) = 0.
1, 2, 4
Let p(z) be the first derivative of 2*z**6/15 - 12*z**5/25 - 3*z**4 - 68*z**3/15 - 12*z**2/5 - 100. Factor p(d).
4*d*(d - 6)*(d + 1)**3/5
Let b be (0*(-3)/30)/((-4)/(-2)). Let r(q) be the second derivative of b - 1/8*q**3 + 1/16*q**4 + 0*q**2 + 25*q. Let r(m) = 0. Calculate m.
0, 1
Factor 0*q**2 + 3/7*q**4 + 0 - 5/7*q**3 + 0*q.
q**3*(3*q - 5)/7
Let l(k) = k**3 + 55*k**2 - 115*k - 53. Let q be l(-57). Let u(j) be the second derivative of -12*j**2 + 5/3*j**q + 0 - 11*j - 26/3*j**3. Factor u(h).
4*(h - 3)*(5*h + 2)
Let w(i) be the second derivative of 0 - 62/3*i**3 + 0*i**2 - 30*i - 1/3*i**4. Factor w(a).
-4*a*(a + 31)
Let d(p) be the first derivative of -p**6/6 + 47*p**5/5 - 45*p**4/4 - 47*p**3/3 + 23*p**2 + 574. Suppose d(m) = 0. What is m?
-1, 0, 1, 46
Let b(d) be the third derivative of d**8/336 + 29*d**7/210 + 29*d**6/20 + 43*d**5/30 - 815*d**4/24 + 175*d**3/2 - 3700*d**2. Determine o, given that b(o) = 0.
-21, -5, 1
Suppose 4*y + 97*k - 29 = 90*k, 4*k = -4*y + 20. Solve 200/19 - 360/19*a + 122/19*a**y + 36/19*a**3 + 2/19*a**4 = 0.
-10, 1
Let c(g) be the second derivative of g**5/200 + 17*g**4/120 + 13*g**3/15 - 3990*g. Factor c(n).
n*(n + 4)*(n + 13)/10
Let u(s) be the second derivative of -4*s**3 + 3/5*s**5 - 1/28*s**7 + 0*s**4 + 0*s**6 + 0*s**2 + 0 + 29*s. Factor u(b).
-3*b*(b - 2)**2*(b + 2)**2/2
Let a(l) = -2*l**2 - 37*l + 24. Let p be a(-19). Suppose -p*u = 2*y + 21, 2*y + 2*u + 12 = 3*y. Factor 1/4*q**y - q + 3/4.
(q - 3)*(q - 1)/4
Let w(l) be the third derivative of -l**7/105 - 47*l**6/30 - 1801*l**5/30 + 1598*l**4 - 13872*l**3 + 4*l**2 + 60*l - 4. Factor w(a).
-2*(a - 4)**2*(a + 51)**2
Let r = -50 - -201/4. Let s be 159/12 + 0 + (40/(-2) - -7). Determine i so that s*i**3 + 0 + 0*i**2 - r*i = 0.
-1, 0, 1
Let l(b) = b**3 - 65*b**2 + 4*b. Let n be l(0). Determine w so that 4/5*w**2 + n + 12/5*w = 0.
-3, 0
Suppose 1395*l + 260 = 1525*l. Factor -2/7*i + 9/7*i**l + 0 - i**3.
-i*(i - 1)*(7*i - 2)/7
Let r(t) be the third derivative of 1/40*t**6 - 2*t**4 + 3/20*t**5 + 0 + 6*t**3 + 8*t**2 + t. Find s, given that r(s) = 0.
-6, 1, 2
Let n(i) be the third derivative of i**7/42 - 5*i**6/6 + 13*i**5/3 + 100*i**4 + 480*i**3 + 4*i**2 + 110. Factor n(x).
5*(x - 12)**2*(x + 2)**2
Let v(z) be the second derivative of 3*z**5/20 + 81*z**4 + 17496*z**3 + 1889568*z**2 + z + 133. Factor v(k).
3*(k + 108)**3
S