00, 1
Let o(k) = -2*k + 26. Let b be o(6). Determine a so that -4089 + b*a**4 + 4089 - 14*a**3 - 30*a**2 - 2*a**5 = 0.
-1, 0, 3, 5
Let s(w) be the second derivative of -28 - 2*w + 2/5*w**5 + 2*w**4 + 3*w**3 + 0*w**2. Solve s(n) = 0 for n.
-3/2, 0
Let h be (-2)/33*-6 + 1552/19206. Find o such that h*o**2 - 4/9 - 2/9*o**5 + 8/9*o**3 - 2/3*o + 0*o**4 = 0.
-1, 1, 2
Let u = 389789 - 389757. Factor 8*q**2 - u*q + 1/4*q**4 + 7/2*q**3 + 0.
q*(q - 2)*(q + 8)**2/4
Let t(m) = -7*m + 204. Let n be t(27). Factor -27*g**2 - 14*g**2 - 54*g - 69 + n + 23*g**2 - 2*g**3.
-2*(g + 3)**3
Let i = 181 - 325. Let u be (-55)/(-90) - (-64)/i. Suppose u*a**3 + 0*a + 1/6*a**2 + 0 = 0. What is a?
-1, 0
Let b = 186890288/1309 + -1570326/11. Let u = 386/17 - b. Factor -u*l + 6/7*l**2 - 32/7.
2*(l - 8)*(3*l + 2)/7
Let v(p) = 3794*p - 49313. Let d be v(13). Factor 1/3*z**3 + 3*z**2 + d + 9*z.
(z + 3)**3/3
Let p = -10147 - -30443/3. Let g(n) be the second derivative of 7/3*n**2 + 0 + p*n**3 - 1/18*n**4 - 25*n. Determine x, given that g(x) = 0.
-1, 7
Let y(g) be the first derivative of -9/2*g**2 + 7/2*g**4 - 8/3*g**3 + 6/5*g**5 + 2*g - 198 - 5/6*g**6. Let y(w) = 0. Calculate w.
-1, 1/5, 1, 2
Let a = 739 + -660. Suppose 0 = 29*c - a - 8. Determine q so that -3/2 + 63/8*q**2 - 15/4*q**4 - 33/8*q**c + 3/2*q = 0.
-2, -1/2, 2/5, 1
Let t(j) = -4*j**2 - 36*j - 64. Let g(l) = -8*l**2 - 73*l - 128. Let k(b) = 2*b**2 + 7*b + 15. Let z be k(-2). Let d(i) = z*t(i) - 4*g(i). Factor d(s).
-4*(s + 4)**2
Suppose 3*s - 7*s + 8 = 0. Find q such that -s*q**4 - 14*q**3 - 34*q**2 - 409*q + 0*q**3 - 12 + 375*q = 0.
-3, -2, -1
Let b be (2556/(-16))/((-99)/(-12) - 8). Let v = b - -644. Factor -5/4*z**2 + v*z + 0.
-5*z*(z - 4)/4
Factor 109/4*l + 27 + 1/4*l**2.
(l + 1)*(l + 108)/4
Suppose c - 4 = 1, -78 = -3*q - 3*c. Let f(g) = -4*g**2 + 86*g - 42. Let s be f(q). Factor 2/5*p + 0 - 2/5*p**3 + s*p**2.
-2*p*(p - 1)*(p + 1)/5
Suppose -30*g = 16*g - 1196. Suppose -59 + 7 = -g*c. Let -48/5 + 24/5*u - 3/5*u**c = 0. What is u?
4
Let v(i) = 4*i**3 - i**2. Let p be v(1). Suppose -u**3 - u + 5*u**p + 3*u**2 - 3 + 0*u**3 - 3*u**3 = 0. What is u?
-3, -1, 1
Factor -228/5*d + 0 - 3/5*d**2.
-3*d*(d + 76)/5
Let q(y) = -67*y + 741. Let j be q(11). Let u be (39 + -4)/(2 - 0). Find g, given that u*g**j + 6*g**5 + 4 - 25/2*g**2 + 15*g - 30*g**3 = 0.
-4, -2/3, -1/4, 1
Let s(b) be the second derivative of -b**5/4 - 80*b**4 - 7350*b**3 + 96040*b**2 + 154*b. Solve s(g) = 0.
-98, 4
Let b(k) be the first derivative of 1/120*k**6 - 16 + 0*k**3 + 0*k + 1/30*k**5 + 1/24*k**4 - 5/2*k**2. Let t(c) be the second derivative of b(c). Factor t(g).
g*(g + 1)**2
What is j in 1230 - 50723 + 12317 - 17499 - 810*j - 3*j**2 = 0?
-135
Let i(s) be the first derivative of s**6/18 + s**5/5 - s**4/3 - 548. Factor i(j).
j**3*(j - 1)*(j + 4)/3
Let n be 4/(-2) + 6 + -4. Suppose 4*d = 3*w - 22, n*w + 2 = -5*w - 3*d. Factor c**w + 3*c**2 - 9*c**2.
-5*c**2
Let d(r) be the second derivative of -1/5*r**6 + 132*r + 2*r**3 + 0*r**2 + 5/4*r**4 + 0 - 21/20*r**5. Factor d(p).
-3*p*(p - 1)*(p + 4)*(2*p + 1)
Factor -6668/7*b - 444/7*b**2 - 120/7.
-4*(b + 15)*(111*b + 2)/7
Let w be 8/(-36)*837/(-62). Let -15/4*f**2 + w + 3/4*f**4 - 9/4*f + 9/4*f**3 = 0. Calculate f.
-4, -1, 1
Let x(l) be the second derivative of -1/15*l**5 + 0 - 23/9*l**4 + 16/3*l**3 + 0*l**2 - 47*l. Factor x(v).
-4*v*(v - 1)*(v + 24)/3
Let i(x) be the first derivative of -x**4 - 4*x**3 + 18*x**2 + 108*x - 3918. Suppose i(m) = 0. Calculate m.
-3, 3
Determine v, given that -2028 + 1/4*v**3 + 1417/4*v - 37/2*v**2 = 0.
13, 48
Let y = -7487 + 7487. Let 4/3*k + 1/3*k**4 + y + 0*k**2 - k**3 = 0. What is k?
-1, 0, 2
Let d(t) be the second derivative of -t**5/5 + 157*t**4/3 + 1946*t**3/3 + 1630*t**2 + 7*t + 3. Factor d(c).
-4*(c - 163)*(c + 1)*(c + 5)
Let l be (37/((-999)/6))/((-14)/12). Let u(a) be the first derivative of 16/7*a - 6/7*a**2 - l*a**3 - 16. Determine m, given that u(m) = 0.
-4, 1
Factor -40*w**3 + 69*w**2 + 19*w**2 - 15475020*w**4 + 15475018*w**4.
-2*w**2*(w - 2)*(w + 22)
Let q(l) be the second derivative of 11264/3*l**3 + 157*l + 288*l**4 + 0 + 2/15*l**6 + 16384*l**2 + 10*l**5. Factor q(p).
4*(p + 2)*(p + 16)**3
Factor -174/7*t**4 - 345/7*t**3 + 6/7*t**2 + 0 + 0*t.
-3*t**2*(t + 2)*(58*t - 1)/7
Factor 0 - 224/3*j**2 + 20/3*j + 649/3*j**3 - 121/3*j**4.
-j*(j - 5)*(11*j - 2)**2/3
Factor -1/2*v**3 - 21/2*v - 6*v**2 + 49.
-(v - 2)*(v + 7)**2/2
Suppose -t = 5*j + 2, -4*t - 1 = 2*j - 11. Factor 401 - 401 + 2*g + g**3 - t*g**2.
g*(g - 2)*(g - 1)
Factor -8/7*f**2 + 2/7*f**4 - 10/7*f**3 + 88/7*f - 96/7.
2*(f - 4)*(f - 2)**2*(f + 3)/7
Factor 1 + 15*m**2 + 12*m + 564577*m**3 - 1 - 564574*m**3.
3*m*(m + 1)*(m + 4)
Let j(v) be the second derivative of 2/5*v**5 - 4*v**2 - 4/15*v**6 + 0 - 2/3*v**3 - 2/21*v**7 + 252*v + 4/3*v**4. Suppose j(q) = 0. What is q?
-2, -1, 1
Let z(w) = w**3 - 8*w**2 + 13*w - 37. Let q be z(7). Factor 10 + q - 10*o**2 + 5*o**4 + 6 - 16.
5*(o - 1)**2*(o + 1)**2
Suppose -6*s = -4*s - d + 1724, 5*s + 4328 = -2*d. Let m = s + 870. Suppose -6*h + m + 3/2*h**2 = 0. Calculate h.
2
Let l(g) be the first derivative of -g**4/54 + 4*g**2/9 + 41*g - 2. Let f(w) be the first derivative of l(w). Factor f(n).
-2*(n - 2)*(n + 2)/9
Let b = -54 + 60. Let d be b + -1 + 12/(-4). Let d*o**2 - 8*o - 9 + 0 + 9 = 0. What is o?
0, 4
Let z(h) be the first derivative of h**5/30 + h**4/6 + h**3/18 - h**2/2 - 1460. What is b in z(b) = 0?
-3, -2, 0, 1
Let m be 4574/(-57175)*(2 - 1 - 26). What is g in -13/5*g**m + 0 - 92/5*g**3 + 2/5*g - 77/5*g**4 = 0?
-1, -2/7, 0, 1/11
Let y(m) be the second derivative of -3/4*m**5 - 2 + 0*m**3 + 1/6*m**6 + 28*m + 0*m**2 + 5/6*m**4. Suppose y(f) = 0. What is f?
0, 1, 2
Let r(f) be the first derivative of 0*f**5 + 1/17*f**2 + 0*f + 58 + 0*f**3 - 1/17*f**4 + 1/51*f**6. Solve r(l) = 0 for l.
-1, 0, 1
Let m(l) = l**4 - l**3 + 3*l**2 - 2*l. Let r(g) = 3*g**4 - 83*g**3 - 291*g**2 - 291*g - 100. Let z(d) = 2*m(d) + r(d). Let z(k) = 0. What is k?
-1, 20
Let i(p) be the first derivative of 5/3*p**3 - 1/4*p**2 + 43 + 0*p. What is h in i(h) = 0?
0, 1/10
Let c = 18181 + -18179. Let w(a) be the third derivative of 30*a**c + 0*a - 7/90*a**5 + 1/36*a**4 - 1/180*a**6 + 1/315*a**7 + 2/3*a**3 + 0. Solve w(h) = 0.
-2, -1, 1, 3
Let c(f) = 65*f**3 - 220*f**2 - 45*f + 45. Let j(b) = 73 - 4*b**2 + 14*b**2 + 2*b - 75 - 3*b**3. Let u(m) = 2*c(m) + 45*j(m). Determine k, given that u(k) = 0.
0, 2
Suppose -2*z - 1 = d, 2*d + 0*d = -2*z + 4. Factor -383*l**3 + 393*l**3 + 9*l**2 + 15*l**4 + d*l**5 - 9*l**2.
5*l**3*(l + 1)*(l + 2)
Factor -3532/5*y**3 - 4/5*y**4 - 20120180*y + 41075800 - 207444*y**2.
-4*(y - 2)*(y + 295)**3/5
Let a be -3 - (905/(-6) - (-10)/(-60)). Suppose 5*p - 2*j = -4*j + a, 5*j = 5*p - 155. Factor 23*u + u + 2*u**3 + 17*u**2 + p*u + 54 + u**2.
2*(u + 3)**3
Suppose 105*b - 23*b = -259*b + 682. Factor -6/5*f + 1/5*f**3 + 3/5*f**b - 8/5.
(f - 2)*(f + 1)*(f + 4)/5
Suppose 1194852*z - 1633932 + 4*z**5 + 9764*z**3 + 465648*z + 59716*z**3 - 571320*z**2 - 1020*z**4 = 0. Calculate z.
3, 123
Let a(y) be the second derivative of y**4/66 - 70*y**3/3 + 13475*y**2 + 3*y + 80. Solve a(w) = 0 for w.
385
Let k(i) = -7*i**3 - 82*i**2 - 144*i + 8. Let f(d) = -d**2 - 4*d + 2. Let j(b) = 4*f(b) - k(b). Factor j(a).
a*(a + 2)*(7*a + 64)
Let i(x) be the first derivative of 16/3*x**3 - 38*x**2 - 34 + 48*x. Suppose i(j) = 0. Calculate j.
3/4, 4
Let j(g) be the third derivative of 3/40*g**6 + 0*g**3 - 7/20*g**5 + 0 + 109*g**2 + 0*g - 3/4*g**4. Factor j(q).
3*q*(q - 3)*(3*q + 2)
Factor 3/2*a + 1/4*a**2 + 5/4.
(a + 1)*(a + 5)/4
Let b(m) be the first derivative of -1/6*m**3 - m + 1/8*m**4 - 11/12*m**2 - 115 + 1/30*m**5. Factor b(d).
(d - 2)*(d + 1)**2*(d + 3)/6
Let a(j) be the first derivative of j**3 + 15/2*j**2 + 0*j - 15/4*j**4 - 3/5*j**5 + 55. Determine c so that a(c) = 0.
-5, -1, 0, 1
Suppose -23*f + 719 = 190. Suppose -11*u - f + 45 = 0. Find k such that -28/5*k - 32/5*k**u + 0 - 4/5*k**3 = 0.
-7, -1, 0
Solve -490*b**2 - 39/2*b**4 - 231*b**3 + 0 + 4116*b - 1/2*b**5 = 0.
-14, 0, 3
Let m be (-3)/320*84/(-63). Let x(q) be the third derivative of 4*q**2 + m*q**6 + 0*q**3 + 0 - 3/40*q**5 + 0*q - 5/8*q**4. Factor x(c).
3*c*(c - 5)*(c + 2)/2
Let p be 26/8 + (-212)/(-742) + 13/28. Let s(z) be the third derivative