m + 4)**2
Let k(g) be the first derivative of 2*g**5/5 - 137*g**4/2 - 1160*g**3 - 7088*g**2 - 19072*g - 3415. Factor k(c).
2*(c - 149)*(c + 4)**3
Let n be 527/93 + (-5 - -2). Determine t, given that -2/3*t**3 - n*t**2 + 4 - 2/3*t = 0.
-3, -2, 1
Let n(i) be the third derivative of -i**5/60 - 9*i**4/8 - i**2 + 376*i. Factor n(a).
-a*(a + 27)
Determine u, given that 36/5*u**4 + 2/5*u**5 - 1792/5*u - 336/5*u**2 + 152/5*u**3 + 3072/5 = 0.
-8, -6, 2
Let c(q) be the third derivative of q**6/72 - q**5/8 - 35*q**4/6 - 9*q**3/2 + 94*q**2. Let a(u) be the first derivative of c(u). Factor a(d).
5*(d - 7)*(d + 4)
Find s such that -16*s**4 + 25*s**3 + 351423*s**5 - 10*s - 351438*s**5 + 25*s**2 - 9*s**4 = 0.
-2, -1, 0, 1/3, 1
Factor -30*i**2 + 79*i + i**3 + 40*i + 9535 - 9385.
(i - 25)*(i - 6)*(i + 1)
Suppose 34 - 54 = 2*l. Let f be (-25)/l*(-2 + 106). Factor f*s + 245*s - 516*s + s**2.
s*(s - 11)
Let n(j) be the first derivative of j**3/9 - 23*j**2/2 + 1190*j/3 - 4522. Let n(h) = 0. Calculate h.
34, 35
Suppose 303*v + 2460 = 342*v + 2*l, 4*l + 328 = 4*v. Factor -10*u**2 - 512/5 + v*u.
-2*(5*u - 16)**2/5
Let t(b) be the second derivative of -b**6/6 + 13*b**5/4 - 15*b**4/2 - 130*b**3/3 + 220*b**2 + 2*b + 295. Determine a so that t(a) = 0.
-2, 2, 11
Let s = 252 - 306. Let f be (195/(-260))/(s/16). Factor 0 + f*w + 1/9*w**2.
w*(w + 2)/9
Let w(n) be the first derivative of 39 - 13/2*n**2 - 12*n + 4/3*n**3. Factor w(f).
(f - 4)*(4*f + 3)
Suppose -4*b = -5*k - 150, 24*k = 19*k - 10. Let f(z) be the second derivative of 0 + 1/12*z**4 + b*z - z**3 + 4*z**2. Factor f(n).
(n - 4)*(n - 2)
Let t(q) be the third derivative of -81*q**2 + 11/84*q**4 + 0*q**3 + 0 - 11/420*q**6 - 1/210*q**5 + 0*q + 1/735*q**7. Suppose t(c) = 0. What is c?
-1, 0, 1, 11
Let c be 2/1 - (-2 - -2 - 4). What is j in -6*j**2 + j + 2*j + c*j + 3 + 12*j**2 = 0?
-1, -1/2
Suppose -3000 - 240*w**2 - 1400*w - 1/2*w**4 - 18*w**3 = 0. Calculate w.
-10, -6
Let i = 12437 + -5634. Determine q so that -7019*q**3 + i*q**3 - 30*q**4 + 288*q**2 + 84*q**4 - 128*q = 0.
0, 4/3
Factor 1836*u**2 + 2*u**4 + 1405*u**2 + 362*u - 1865*u**2 + 1006*u + 350*u**3.
2*u*(u + 2)**2*(u + 171)
Let m be ((-1)/(-2))/((-2)/192). Let x be (6/m*4)/((-2)/500). Determine w so that 8*w - 40*w**4 - 13*w - 190*w**2 - 40 + 5*w**5 + x*w**3 + 17*w + 128*w = 0.
1, 2
Suppose 0*l + 2*l + 507 = 5*u, 197 = 2*u + 5*l. Factor -480*x + 2880 + u*x**4 + 92*x**3 + 28*x**3 - 106*x**4 - 700*x**2.
-5*(x - 12)**2*(x - 2)*(x + 2)
Let 4/3*o**2 + 1784/3*o + 198916/3 = 0. Calculate o.
-223
Let i = 1079/11720 - 5/293. Let z(s) be the third derivative of -2/5*s**3 + 7/100*s**5 + 0 - i*s**4 + 0*s + 3*s**2. What is d in z(d) = 0?
-4/7, 1
Solve 8/25*f - 66/5 + 2/25*f**2 = 0 for f.
-15, 11
Let i be ((-8)/(-40))/(4/10 + 90/(-240)) - 8. Determine z, given that 0 + 4/17*z**2 + 26/17*z**4 + i*z - 30/17*z**3 = 0.
0, 2/13, 1
Suppose -4*y - 5035 + 4995 = -3*c, -5*y + 138 = 8*c. Find s such that -7/3*s**4 + 7/3*s**y + s - 1/3*s**3 - 2/3*s**5 + 0 = 0.
-3, -1, -1/2, 0, 1
Let l = 26 + -9. Let q be 4/(-22) - l/((-1309)/168). Factor -6*j**2 - 4*j - 3*j**4 - 5*j**4 - 6*j**3 + q*j + 6*j**4.
-2*j*(j + 1)**3
Determine g, given that 8/5 + 2268/5*g**2 - 2276/5*g = 0.
2/567, 1
Let u be -1*(4 + (-11 - -4)). Let o(m) = m**3 - 2*m**2 - 3*m + 3. Let d be o(u). Factor 8*h - 13 - 4*h**2 - 2*h**4 + 0*h**2 + 19 - 12*h**d + 4*h**3.
-2*(h - 1)*(h + 1)**2*(h + 3)
Let j = -74 + 91. Suppose -j*a = -13*a - 48. What is s in -4 + a - 9*s**2 + 7*s**2 = 0?
-2, 2
Let p be ((-326370)/1104)/(-55) + (0 - 5). Find f such that 15/8*f + 3/2*f**4 + 0 - 9/4*f**3 + p*f**5 - 3/2*f**2 = 0.
-5, -1, 0, 1
Let o be (-2 - 10)*(-126)/72. Let s be ((-7)/o)/((-25)/15). Solve -s*x**3 + 1/5*x**4 - 1/5*x**2 + 0 + 0*x + 1/5*x**5 = 0.
-1, 0, 1
Let h(d) be the first derivative of -d**6/80 - 3*d**5/40 + d**3 - 159*d**2/2 - 156. Let g(u) be the second derivative of h(u). Factor g(s).
-3*(s - 1)*(s + 2)**2/2
Let b(k) be the first derivative of 1/50*k**5 + 9*k + 0*k**2 - 5 - 2/15*k**3 + 1/30*k**4. Let w(m) be the first derivative of b(m). Factor w(g).
2*g*(g - 1)*(g + 2)/5
Suppose -14*g = 138 - 194. Let u(d) be the second derivative of 14*d + 2/9*d**g + 0*d**2 + 1/12*d**5 + 1/6*d**3 + 0. Factor u(y).
y*(y + 1)*(5*y + 3)/3
Let u(m) = 71*m + 1078. Let b be u(-15). Let x(d) be the first derivative of 0*d**2 - 1/5*d**5 + 3/4*d**4 - 2/3*d**3 + 0*d - b. Factor x(v).
-v**2*(v - 2)*(v - 1)
Let a = -463555 - -463557. Factor -16562/3*v**a - 8/3 - 728/3*v.
-2*(91*v + 2)**2/3
Let l(g) = -3*g**3 - 2*g**2 + 224*g + 225. Let k be l(-1). Let r(h) be the third derivative of 32/3*h**3 - 7/15*h**5 - 9*h**4 + 0*h - 14*h**k + 0. Factor r(t).
-4*(t + 8)*(7*t - 2)
Let o(u) = 91*u**2 + 257*u - 5356. Let s(k) = 862*k**2 + 2314*k - 48202. Let l(p) = -19*o(p) + 2*s(p). Find h, given that l(h) = 0.
-67, 16
Let i = 11656/7 - 104890/63. Let w(g) be the first derivative of -27 - 2*g + i*g**3 - 2/3*g**2. Determine q so that w(q) = 0.
-1, 3
Suppose -o + m - 8 = 0, 7*m - 4*m - 3 = 0. Let h be (18/(-10) - -2)/(o/(-28)). Determine i so that -1/5 + h*i**3 - 3/5*i + 0*i**2 = 0.
-1/2, 1
Let j(a) = -6*a**2 + 27*a - 46. Let x be (5/4)/((-72)/(-864)). Let u(p) = -p**2 - p - 3. Let m(g) = x*u(g) - 3*j(g). Determine q so that m(q) = 0.
1, 31
Let g = -901 + 880. Let l = 111/5 + g. Factor l*x**4 + 0*x + 0 - 2/5*x**3 - 4/5*x**2.
2*x**2*(x - 1)*(3*x + 2)/5
Find u such that 1616/9*u**2 + 704/3*u + 100/3*u**3 - 1792/9 + 14/9*u**4 = 0.
-14, -4, 4/7
Let u(m) = -4*m**2 + 2*m. Let q be u(1). Let k(n) = 2*n**2 - 128*n - 120. Let t(f) = 64*f + 60. Let h(p) = q*k(p) - 5*t(p). Determine i, given that h(i) = 0.
-15, -1
Factor 44/9*y + 20/3*y**2 - 260/3 + 4/9*y**3.
4*(y - 3)*(y + 5)*(y + 13)/9
Let z = 5427 - 2335. Factor 1491*u - z*u - 3*u**2 + 1511*u.
-3*u*(u + 30)
Let n(y) be the first derivative of -9*y**6/4 - 315*y**5/2 - 15429*y**4/8 - 16743*y**3/2 - 12060*y**2 - 7050*y - 2193. Find i such that n(i) = 0.
-47, -5, -2/3
Let l(y) be the second derivative of y**5/20 - y**4/6 - y**3/3 + y**2/2 - 11*y. Let j be l(3). Factor -4*s**2 - 5*s**2 - 16*s**4 - j*s + 0*s + s**2 + 28*s**3.
-4*s*(s - 1)**2*(4*s + 1)
Let u = 4/13961 - -586262/349025. Let p(s) be the first derivative of -u*s**5 - 8/15*s**3 + 0*s - 11 + 0*s**2 - 2*s**4. Factor p(n).
-2*n**2*(3*n + 2)*(7*n + 2)/5
Let d = -2773/504 + 557/56. Factor 0 + 2/9*b**3 - d*b**2 + 200/9*b.
2*b*(b - 10)**2/9
Let o(p) be the second derivative of 7*p**4/9 + 220*p**3/9 - 64*p**2/3 - 70*p - 8. Factor o(d).
4*(d + 16)*(7*d - 2)/3
Let n be (-1 - -16)*(5/(-5))/(-1). Solve -11*b**5 + 50*b**4 - 4*b - n*b**5 + 40*b**2 + 21*b**5 - 85*b**3 + 4*b = 0.
0, 1, 8
Let m(p) = -p**2 - 7*p + 146. Let y be m(9). Factor 10391 - y*o**3 - 41*o - 10499 - 24*o**2 - 49*o.
-2*(o + 3)**2*(o + 6)
Determine i, given that 81/4*i**2 + 6 + 165/2*i = 0.
-4, -2/27
Let t(c) = -7*c**2 - 16*c + 111. Let f(x) = 29*x**2 + 64*x - 445. Let w(u) = -6*f(u) - 25*t(u). Find j, given that w(j) = 0.
-21, 5
Let t be ((-325)/50)/((-1170)/60). What is k in -25/3*k + 0 - 10/3*k**2 - t*k**3 = 0?
-5, 0
Let s(c) = 29*c + 16*c**4 + 16*c + 45*c**2 + 5*c**3 - 15*c**4. Let l(x) = -x**4 - 4*x**3 - 46*x**2 - 45*x. Let g(a) = 6*l(a) + 7*s(a). Factor g(q).
q*(q + 3)**2*(q + 5)
Let n(p) be the first derivative of -1/10*p**5 + 5/3*p**3 - 12*p + 5*p**2 - 5/8*p**4 + 31. What is c in n(c) = 0?
-6, -2, 1, 2
Let d(z) = -3*z**2 + 297*z - 3*z**2 + 48*z - 88*z - 2651. Let m(o) = -9*o**2 + 385*o - 3976. Let r(n) = -7*d(n) + 5*m(n). Solve r(i) = 0.
21
Factor -14 - 10*h - 2/7*h**3 + 26/7*h**2.
-2*(h - 7)**2*(h + 1)/7
Let n = 38 - 41. Let i be n/(-2)*(-7 - -9). Let 0*s**2 - 947 + s**2 + s + 946 - s**i = 0. What is s?
-1, 1
Let n(x) be the third derivative of -x**6/72 + x**5 - 265*x**4/24 + 310*x**3/9 - 10090*x**2. Factor n(b).
-5*(b - 31)*(b - 4)*(b - 1)/3
Factor 0 - 3/2*f**2 - 243/2*f.
-3*f*(f + 81)/2
Let m(y) be the first derivative of -y**5/4 - 25*y**4/16 - 5*y**3/2 + 3466. Find d, given that m(d) = 0.
-3, -2, 0
Suppose 180*w**3 + 55*w + 57052*w**4 - 122*w**2 + 5*w**5 - 34*w**2 - 57122*w**4 - 14*w**2 = 0. Calculate w.
0, 1, 11
Let d(w) = 5*w**4 - 12*w**3 - 6*w**2 + 37*w - 21. Let m(h) = 6*h**4 - 12*h**3 - 6*h**2 + 36*h - 20. Let v(l) = -4*d(l) + 3*m(l). What is y in v(y) = 0?
-2, 1, 6
Let l(w) be the second derivative of -