= 0.
-3, -1, 0
Let m = 1729 + -1444. Suppose m*p = 294*p. Factor 4/5*l**5 + p*l + l**3 - 1/5*l**2 - 8/5*l**4 + 0.
l**2*(l - 1)*(2*l - 1)**2/5
Let a(j) = -j**3 - 15*j**2 + j + 15. Suppose 59 = 40*o + 659. Let t be a(o). Solve 0 - 1/3*g**4 + t*g**2 - g**3 + 4/3*g = 0.
-2, 0, 1
Suppose -78 = -5*j + 12. Factor -24 - 7*n**2 + 9*n**2 - j*n - 30 + 10.
2*(n - 11)*(n + 2)
Let h(q) be the first derivative of -q**6/69 + 8*q**5/115 + 37*q**4/46 - 80*q**3/69 + 336. Suppose h(u) = 0. What is u?
-5, 0, 1, 8
Let q(m) be the first derivative of -m**6/2 - 108*m**5 - 5799*m**4 + 33120*m**3 - 50784*m**2 + 574. Factor q(d).
-3*d*(d - 2)**2*(d + 92)**2
Let m be 87/1044 - 14/(-48). Let z(i) be the first derivative of m*i**2 + 1/12*i**3 + 9 - i. Factor z(y).
(y - 1)*(y + 4)/4
Let n(d) be the first derivative of 2/7*d**2 - 125 + 6/7*d - 2/21*d**3. Suppose n(u) = 0. What is u?
-1, 3
Let y(n) be the first derivative of n**4/12 - 11*n**3/6 + 14*n**2 + 137*n + 202. Let b(c) be the first derivative of y(c). Let b(o) = 0. What is o?
4, 7
Let j(f) = -30*f**3 - 575*f**2 + 18365*f + 543965. Let m(u) = -u**3 + 4*u**2 - u - 1. Let t(h) = j(h) - 35*m(h). Find s, given that t(s) = 0.
-17, 80
Let o = -24779 - -24781. Let j(w) be the first derivative of 2/3*w - 2 + 1/6*w**o + 19/12*w**4 - 5/3*w**3 - 7/15*w**5. Let j(t) = 0. What is t?
-2/7, 1
Factor 275*b**2 + 14*b**4 + 266*b**2 + 2*b**5 - 595*b**2 - 108*b + 18*b**3.
2*b*(b - 2)*(b + 3)**3
Factor -34/5*g**2 + 2/5*g**3 + 62/5*g - 6.
2*(g - 15)*(g - 1)**2/5
Factor -95 - 9/2*y + 1/2*y**2.
(y - 19)*(y + 10)/2
What is z in -309/4*z + 155/2 - 1/4*z**2 = 0?
-310, 1
Let k be 3 - -1*(-3)/3. Suppose -5*f - z + 85 = 0, 0 = -3*f + k*z - 6*z + 34. Determine y so that -f*y + 10*y + 6*y + 4*y**2 - 3*y**2 = 0.
0, 2
Let 18465655*y - 4*y**3 - 18464923*y + 3342*y**4 - 5867*y**3 + 1824*y**2 - 27*y**5 = 0. What is y?
-2/9, 0, 1, 122
Let g(w) be the second derivative of w**8/1120 + w**7/140 + w**6/80 - 34*w**3/3 - 271*w. Let v(m) be the second derivative of g(m). Factor v(j).
3*j**2*(j + 1)*(j + 3)/2
Suppose 2*r + r - 21 = 0. Suppose 16 = 2*c - 4*q, 4*c = -r*q + 11*q + 20. Suppose 3*h**c + 3/4*h**3 + 15/4*h + 3/2 = 0. What is h?
-2, -1
Let s(a) = -a + 1. Let n be s(-1). Let q be 279/135 - (-20)/(-300). Determine w, given that -24*w - 333*w**q - 72 + 660*w**n - 329*w**2 = 0.
-6
Let p(q) be the third derivative of -q**5/60 - q**4/24 + 10*q**3/3 - 2*q**2 - 816*q. Factor p(o).
-(o - 4)*(o + 5)
Suppose -2*d + 289 = 3*b, -15*d + 16*d - 97 = -b. Suppose -b*n - 5 = -96*n. Determine w, given that 10/3*w**4 - 5/3 + 5*w**3 - 5/3*w**2 - n*w = 0.
-1, -1/2, 1
Let m(y) be the second derivative of -7/4*y**4 + 0*y**2 + 0 + 0*y**5 + 1/10*y**6 - 3*y**3 + 88*y. Suppose m(x) = 0. What is x?
-2, -1, 0, 3
Let z(l) be the third derivative of -85*l**2 + 0 + 1/210*l**5 + 0*l + 11/84*l**4 - 4/7*l**3. Determine r so that z(r) = 0.
-12, 1
Let y = 226554 + -1132466/5. Solve -4/5*s**2 - 5776/5 + y*s = 0 for s.
38
Factor -165*f - 29*f**2 + 27*f**2 - 42*f - 31*f.
-2*f*(f + 119)
Let l(w) be the third derivative of -52 + 17/3*w**4 - 578/3*w**3 - w**2 - 1/15*w**5 + 0*w. Find k such that l(k) = 0.
17
Let q = -273535/11 + 24867. Solve -2/11 - q*b**2 - 4/11*b = 0 for b.
-1
Let x(h) be the first derivative of -58 - 4/33*h**3 + 0*h**2 + 0*h - 1/22*h**4. Let x(w) = 0. Calculate w.
-2, 0
Let g = -138 + 139. Factor 9*b**2 - 5 + g - 5*b - 2 + 2*b.
3*(b - 1)*(3*b + 2)
Suppose -29 = 2*z - 11. Let k be (2 - 4)/(3/z). What is s in -25*s - 15*s**2 - 22*s**4 + k + 85*s**3 - 6 - 28*s**4 + 5 = 0?
-1/2, 1/5, 1
Suppose 0 = -95*v - 2984 + 3269. Find c, given that v*c**4 + 3/2*c**3 - 3/2*c**5 + 0*c - 3*c**2 + 0 = 0.
-1, 0, 1, 2
Suppose 0 = -3*z + 34*r - 29*r + 55, z - 4*r = 30. Let f(x) be the second derivative of z*x**2 + 0 + 45*x + 5/12*x**4 - 10/3*x**3. Factor f(g).
5*(g - 2)**2
Suppose 0 = -34*k + 58*k - 576. Let y(v) be the first derivative of 1/3*v**3 - v - 3/4*v**2 - k + 3/8*v**4. Find t, given that y(t) = 0.
-1, -2/3, 1
Suppose -94 = 7*w - 108. Let c(n) = -7*n**3 - 25*n**2 + 160*n - 180. Let l(m) = -8*m**3 - 25*m**2 + 160*m - 180. Let b(y) = w*l(y) - 3*c(y). Factor b(q).
5*(q - 2)**2*(q + 9)
Let a(n) be the second derivative of -n**5/40 + n**4/8 + 3*n**3/2 + 1388*n. Factor a(s).
-s*(s - 6)*(s + 3)/2
Suppose -2*w + 2*c = -w - 4, 3*w - 1 = -5*c. Factor -8*k**4 - 4*k**5 - 13*k**2 + 26*k + 37*k + 29*k - 24 - 115*k**w + 72*k**3.
-4*(k - 1)**4*(k + 6)
Let o be (4 + -4)*6*5/(-60). Let j(g) be the third derivative of -1/10*g**5 - 18*g**2 + 0*g + o*g**4 + 1/70*g**7 + 1/2*g**3 + 0 + 0*g**6. Factor j(q).
3*(q - 1)**2*(q + 1)**2
Let n = 981 - 980. Let t be (-7*n)/(9/((-252)/91)). Determine a so that -t - 66/13*a + 10/13*a**2 = 0.
-2/5, 7
Let d(k) be the third derivative of k**8/84 + 2932*k**7/105 + 538753*k**6/30 + 357704*k**5/5 + 89304*k**4 - 505*k**2. Factor d(f).
4*f*(f + 1)**2*(f + 732)**2
Suppose -20 - 8 = -2*l. Let a be (-2)/l*(-8 - -4). Find y, given that 2/7*y**2 - a*y + 0 = 0.
0, 2
Let y = 886 + -884. Suppose 206*j = 178*j + 84. Suppose 0*w - 8/11*w**y + 2/11*w**j + 0 = 0. What is w?
0, 4
Let y(m) be the first derivative of -2*m**3/57 - 30*m**2/19 + 62*m/19 - 145. Determine t, given that y(t) = 0.
-31, 1
Let j(n) = -6*n**2 - 2944*n + 1083480. Let t(s) = 4*s**2 + 2944*s - 1083458. Let h(q) = 3*j(q) + 4*t(q). Let h(l) = 0. What is l?
736
Let s(t) be the first derivative of t**4/32 + t**3/4 - 15*t**2/16 + 256*t - 114. Let r(i) be the first derivative of s(i). Factor r(b).
3*(b - 1)*(b + 5)/8
Let z(g) be the second derivative of -g**6/15 + 4078*g**5/45 - 6031*g**4/18 + 1306*g**3/3 - 1808*g**2/9 - g - 553. Suppose z(p) = 0. Calculate p.
2/9, 1, 904
Determine o so that 224/9 - 10/3*o + 1/9*o**2 = 0.
14, 16
Suppose 3/2*j**2 - 300 - 1/2*j**4 + 449*j - 150*j**3 = 0. What is j?
-300, -2, 1
Let h(r) = 1270*r + 17782. Let i be h(-14). Factor -1/4*y**4 + 3/4 + 11/4*y + 7/2*y**i - 1/4*y**5 + 3/2*y**3.
-(y - 3)*(y + 1)**4/4
Let -87*r**2 - 30*r**4 - 80*r**2 - 2*r**5 + 167*r**2 = 0. What is r?
-15, 0
Let z(v) be the first derivative of v**4/8 + 5*v**3/6 - 14*v**2 - 30*v - 3010. What is d in z(d) = 0?
-10, -1, 6
Determine g, given that 290/13*g**3 + 60/13 - 586/13*g**2 + 22/13*g**4 + 214/13*g = 0.
-15, -2/11, 1
Let f(i) be the first derivative of i**3/3 + 76*i**2 + 5776*i + 1959. Solve f(a) = 0 for a.
-76
Let t(w) be the first derivative of 2/45*w**5 + 10/9*w**3 + 76 + 7/18*w**4 + 8/9*w + 13/9*w**2. Factor t(o).
2*(o + 1)**3*(o + 4)/9
Let z(j) be the third derivative of 0 + 48*j**2 + 0*j + 0*j**5 - 1/1260*j**6 - 2/63*j**3 + 1/84*j**4. Factor z(l).
-2*(l - 1)**2*(l + 2)/21
Let f(i) be the first derivative of -111*i**4/4 - 326*i**3/3 - 114*i**2 - 40*i + 3737. Determine v so that f(v) = 0.
-2, -2/3, -10/37
Let x = -27 - -30. Let h = -19 + 19. Factor 5*b - 20*b**x + 4*b + 29*b**3 + h*b - 6 + 24*b**2.
3*(b + 1)*(b + 2)*(3*b - 1)
Let f(j) = -4*j**3 + 94*j + 3. Let q(a) = -a**3 + a**2 + 2*a + 1. Let h(u) = -2*f(u) + 6*q(u). Factor h(g).
2*g*(g - 8)*(g + 11)
Suppose -32*y - 2061 - 2419 = 0. Let s be (-1424)/y + (-28)/49. Factor -24/5*c**2 - 32/5 + 4/5*c**3 + s*c.
4*(c - 2)**3/5
Factor 721*i + 965*i - 3*i**2 + 4427933 - 4664816.
-3*(i - 281)**2
Let r(q) = q**3 - 95*q**2 - 702*q - 1221. Let x be r(102). What is c in -1/7*c**x - 18/7 + 3/7*c + 4/7*c**2 = 0?
-2, 3
Determine j so that -1262/11*j + 2/11*j**2 - 1264/11 = 0.
-1, 632
Factor 1000/13*a + 998/13 + 2/13*a**2.
2*(a + 1)*(a + 499)/13
Suppose 0 = -349*h + 347*h + 28. Let -41*z**4 + 30*z - 36 - 6*z**3 + h*z**2 + 10*z**4 + 13*z**4 + 16*z**4 = 0. What is z?
-3, 1, 2
Factor -13467 - 5162*q**2 + 109*q**4 + 4350*q**3 - 22847*q + q**5 + 40*q**4 - 16*q**4.
(q - 3)*(q + 1)**2*(q + 67)**2
Let w be 4/14 - 63/49. Let p be w + (-39)/(-6) + (6 - 11). Factor o - p - 1/2*o**2.
-(o - 1)**2/2
Suppose -2*x + 1 = 3*o, 1001 = 4*o + 1005. What is n in 0 + 1/6*n**x + 4/3*n = 0?
-8, 0
Let 243/5*j**4 - 2052/5*j**3 - 48 + 2064/5*j - 3984/5*j**2 = 0. Calculate j.
-2, 2/9, 10
Let f = -119 + 121. Suppose -12*k**3 + 24*k**5 - 77*k - 4*k**4 + 8*k**f + 101*k - 4 - 36*k**3 = 0. What is k?
-1, 1/6, 1
Factor 58/7*q**2 + 440/7*q + 2/7*q**3 + 384/7.
2*(q + 1)*(q + 12)*(q + 16)/7
Factor w**4 - 17*w**3 + 86*w**2 - 28*w**2 + 12*w**2 - 680*w + 680*w.
w**2*(w - 10)*(w - 7)
Determine m so that -20*m - 15/2*m**2 + 22 