 2
Let t be (1*5)/(21 + -1 - 29559/1503). Factor -5/2*o + 5/2*o**3 - 15 + t*o**2.
5*(o - 1)*(o + 1)*(o + 6)/2
Let v(w) be the third derivative of -1/120*w**5 - 7/48*w**4 + 18*w**2 + 0*w + 0 - w**3. Factor v(p).
-(p + 3)*(p + 4)/2
Let f be -51*11/5049 - 386/(-18). Let f*l + 112/3 + 4/3*l**2 = 0. Calculate l.
-14, -2
Let o(b) = 72*b - 4100. Let c be o(57). Let s(k) be the third derivative of 0 - 1/75*k**5 - 15*k**2 + 0*k**3 + 0*k**c + 0*k. Factor s(r).
-4*r**2/5
Let w(p) = -188*p**2 + 793*p + 9. Let m(n) = 21*n**2 + n - 1. Let f(o) = -45*m(o) - 5*w(o). Suppose f(d) = 0. What is d?
-802, 0
Let u(s) be the third derivative of -s**6/360 - 97*s**5/180 - 100*s**4/3 - 128*s**3 - 289*s**2. Factor u(n).
-(n + 1)*(n + 48)**2/3
Let l = -21603 - -21603. Let t(k) be the second derivative of 1/20*k**4 + k**3 - 33/10*k**2 + l + 41*k. Determine f, given that t(f) = 0.
-11, 1
Let v(i) be the second derivative of -3/4*i**3 + 2*i**2 + 1/24*i**4 + 11 + 7*i. Suppose v(r) = 0. Calculate r.
1, 8
Suppose 0 = s + 5*h - 41, -2*s + 4*h + 85 = 3. Suppose s + 4 = 3*w. Suppose w + 2*g**2 - 11 + 4*g - g**2 = 0. Calculate g.
-2
Let q = 723596/7 - 103370. Factor -48/7*j + q*j**4 + 0 + 72/7*j**2 - 36/7*j**3.
6*j*(j - 2)**3/7
Solve -41*q**4 + 83/2*q**3 + 0 + 74*q**2 - 45/2*q**5 + 14*q = 0 for q.
-2, -1, -2/9, 0, 7/5
Let a(j) be the first derivative of 4*j**3/3 + 274*j**2 + 544*j - 1134. Let a(b) = 0. What is b?
-136, -1
Suppose -163*f - 30 = -173*f. Factor 110*s**3 - 1112*s + 4936*s**2 + 250*s**5 + 3368*s + 658*s**f - 1950*s**4 + 320 + 1652*s**3.
2*(s - 5)*(s - 4)*(5*s + 2)**3
Let f(b) be the second derivative of -b**6/135 - b**5/90 + 11*b**4/54 + b**3/3 - 2*b**2 - 54*b + 18. Let f(a) = 0. Calculate a.
-3, -2, 1, 3
Let u(r) be the second derivative of r**6/330 + 11*r**5/20 + 79*r**4/44 - 11*r**3/6 - 119*r**2/11 + 1747*r. Solve u(y) = 0.
-119, -2, -1, 1
Suppose 3*r = 3*h - 3, -3*h - 3*r + 0*r = -21. Factor 0*b**2 - 3/2*b**h + 24 + 6*b**3 - 24*b.
-3*(b - 2)**3*(b + 2)/2
Find d such that -128*d + 7125*d**2 + 4*d**4 - 14219*d**2 - 48*d**3 + 7238*d**2 = 0.
0, 2, 8
Factor 0 - 2352/5*j**3 + 0*j - 2/5*j**5 - 594/5*j**4 - 2344/5*j**2.
-2*j**2*(j + 2)**2*(j + 293)/5
Let x(m) be the first derivative of 1/3*m**3 - 15/7*m**2 - 18 + 8/7*m. Find l such that x(l) = 0.
2/7, 4
Let w(p) be the first derivative of 2*p**5/5 - 16*p**4 + 168*p**3 + 128*p**2 - 2048*p + 1007. Find z, given that w(z) = 0.
-2, 2, 16
Let r(y) be the third derivative of -y**8/48 - 32*y**7/105 - 107*y**6/120 - 5*y**5/6 - 236*y**2 - 2. Factor r(v).
-v**2*(v + 1)**2*(7*v + 50)
Let a = -1159 + 1122. Let q be (5/30)/(1 + a/44). Let 2/21*h**5 - 16/21 + 4/7*h**4 + 4/21*h**2 + q*h**3 - 8/7*h = 0. Calculate h.
-2, -1, 1
Suppose -o = -14 + 34. Let q = o - -22. Factor 2*r**3 + r**3 - 10*r + 4*r**3 - 2*r**3 - 5*r**q.
5*r*(r - 2)*(r + 1)
Let n(j) be the third derivative of -1/2*j**7 - 73/10*j**5 + 0*j + 12*j**3 + 13/2*j**4 + 111/40*j**6 + 22 + 1/28*j**8 + j**2. Factor n(i).
3*(i - 3)*(i - 2)**3*(4*i + 1)
Let r(s) be the second derivative of s**5/28 + s**4/42 - 35*s**3/6 - 7*s**2 + 99*s. Factor r(m).
(m - 7)*(m + 7)*(5*m + 2)/7
Let a(x) be the third derivative of x**6/540 - 1361*x**5/270 + 115940*x**4/27 - 462400*x**3/27 + 751*x**2. Determine d so that a(d) = 0.
1, 680
Find x, given that 243/5 + 648/5*x**2 + 288/5*x**3 + 648/5*x + 48/5*x**4 = 0.
-3/2
Suppose 61 = 4*d - 3*b, 4*d + 3*b + 20 = 63. Suppose 9*j - d*j = 16*j. Suppose j*z**2 - 2/11*z**3 - 4/11 + 6/11*z = 0. What is z?
-2, 1
Let r(l) be the third derivative of -3/8*l**4 - l**3 + 0 - 1/20*l**5 + 2*l**2 + 8*l. Factor r(p).
-3*(p + 1)*(p + 2)
Let y = -156120 + 156122. Determine j, given that 0 + 1/4*j**5 - j**3 + 1/2*j**y + 3/4*j - 1/2*j**4 = 0.
-1, 0, 1, 3
Suppose -1114 + 1418 = 75*p + p. Suppose w - 14 = -3*n + 45, 5*w - 5*n = 235. Factor -80*z**p - 290/3*z**3 - w*z**2 - 24*z**5 - 10*z - 2/3.
-2*(z + 1)**3*(6*z + 1)**2/3
Let k(c) be the third derivative of -1/270*c**5 + 53*c**2 - 4/27*c**4 + 17/27*c**3 + 0*c + 0. Factor k(v).
-2*(v - 1)*(v + 17)/9
Let h(k) be the second derivative of k**5/20 - 5*k**4/2 + 50*k**3 - 500*k**2 + k + 258. Find v such that h(v) = 0.
10
Let z(v) be the first derivative of -2*v**3/27 + 169*v**2/9 + 76*v - 4506. Find s such that z(s) = 0.
-2, 171
Let n(d) = -2*d**3 - 3*d**2 - 3*d. Let x be n(-1). Factor -x*m**2 + 29 + 33*m - 59 - m**2.
-3*(m - 10)*(m - 1)
Let u be (-450)/(-135)*9/15. Let v(z) be the second derivative of -72/7*z**4 + 144/7*z**3 + 96/35*z**5 - 162/7*z**u - 32/105*z**6 - 14*z + 0. Factor v(a).
-4*(2*a - 3)**4/7
Let 1584*p - 11/2*p**4 - 73*p**3 + 1/2*p**5 + 0 + 672*p**2 = 0. What is p?
-11, -2, 0, 12
Let v(p) = 2*p**3 + p**2 - 4*p + 3. Let k be v(1). Let z = 2/303 + 295/1212. Factor -4 - z*u**k - 2*u.
-(u + 4)**2/4
Let t = -17943 - -17945. Let a(y) be the first derivative of -14 + 3/16*y**t - 9/4*y + 1/8*y**3. Suppose a(j) = 0. What is j?
-3, 2
Let j(x) be the third derivative of -x**7/840 - x**6/10 - 119*x**5/40 - 289*x**4/12 + 14*x**3 - 39*x**2. Let g(h) be the first derivative of j(h). Factor g(l).
-(l + 2)*(l + 17)**2
Solve -5*x - 112 - 40*x - 19*x + 0*x - 4*x**2 = 0.
-14, -2
Let h(k) be the second derivative of k**7/126 + 29*k**6/135 - 4*k**5/15 + 27*k**3 - 11*k. Let f(v) be the second derivative of h(v). Factor f(q).
4*q*(q + 12)*(5*q - 2)/3
Let v(p) = -5613*p**3 + 1771*p**2 - 123*p + 5. Let w(a) = -2806*a**3 + 893*a**2 - 61*a + 3. Let l(f) = 6*v(f) - 10*w(f). Factor l(c).
-2*c*(53*c - 8)**2
Let d(i) be the second derivative of -23/6*i**3 - 5/12*i**4 - i - 5*i**2 - 2 + 1/10*i**5. Factor d(t).
(t - 5)*(t + 2)*(2*t + 1)
Let n be (-1599)/3852 - (-7)/21. Let j = 18/107 - n. Factor -1/2*z - 3/4 + j*z**2.
(z - 3)*(z + 1)/4
Let u(x) be the first derivative of -5*x**3/3 + 1435*x**2/2 + 143. Suppose u(g) = 0. What is g?
0, 287
Let q(b) be the first derivative of -9/4*b**2 - b**3 + 28 - 1/8*b**4 - 2*b. Factor q(t).
-(t + 1)**2*(t + 4)/2
Let l be ((-46)/(-4))/(1/2). Let b = l - 19. Determine x so that -5*x**4 + 0*x**b - 8*x**3 + 9*x**4 = 0.
0, 2
Let j(s) be the first derivative of -9*s**4/13 - 166*s**3/39 - 112*s**2/13 - 94*s/13 + 7452. Factor j(o).
-2*(o + 1)**2*(18*o + 47)/13
Let h be -4 + 5 + 3 + -1*1. Suppose 3*m + 50 = o + 3*o, -17 = -o + h*m. Factor 6*r**2 + 0*r - 12 + o*r**2 - 4*r - r**2.
4*(r - 1)*(4*r + 3)
Let h(w) be the first derivative of -w**6/120 + 2*w**5/15 - 17*w**4/24 + 5*w**3/3 + 79*w**2/2 + 145. Let b(z) be the second derivative of h(z). Factor b(q).
-(q - 5)*(q - 2)*(q - 1)
Let w(y) be the second derivative of -13/18*y**4 + 17/3*y**3 - 21*y**2 + 1/30*y**5 + 4 - 22*y. What is v in w(v) = 0?
3, 7
Let h be (-6)/32 - ((-6)/(-45))/((-10)/15). Let p(k) be the second derivative of -9*k + h*k**5 + 0*k**4 + 0 + 13/240*k**6 + 0*k**3 + 0*k**2. Factor p(s).
s**3*(13*s + 2)/8
Let u(l) be the first derivative of 4*l**3/9 - 1270*l**2/3 - 5096*l/3 - 3352. Factor u(f).
4*(f - 637)*(f + 2)/3
Suppose -2*r + 6*r - 2*g = 30, 2*g - 20 = -r. Suppose -4*o + 5*c = o - r, o - 4*c = -1. Factor 0 + 16/15*q**2 + 2/15*q**o + 32/15*q.
2*q*(q + 4)**2/15
Let g(r) = -7189060*r**3 - 2123193*r**2 - 208998*r - 6865. Let u(h) = h**3 - 7*h + 2. Let p(i) = 2*g(i) + 6*u(i). Factor p(o).
-2*(193*o + 19)**3
Let s = 47 - 43. Suppose -s*p + 232 = 54*p. Let -9/8*o**5 + 3 + 45/8*o**3 + 3/4*o**p - 15/4*o**2 - 9/2*o = 0. What is o?
-2, -1, 2/3, 1, 2
Suppose 1672/13*y**2 - 240/13*y - 2884/13*y**3 - 98/13*y**4 + 0 = 0. What is y?
-30, 0, 2/7
Let b = 340 + -244. What is t in 15*t**2 + 25*t + b - 19*t**2 - 30*t - 87*t = 0?
-24, 1
Let z(p) be the third derivative of 23/216*p**4 + 0*p - 11/27*p**3 + 0 - 1/540*p**5 + 177*p**2. Factor z(y).
-(y - 22)*(y - 1)/9
Solve -1/2*o**3 - 4 + 8*o + 1/4*o**4 - 15/4*o**2 = 0 for o.
-4, 1, 4
Let m(q) = 5*q**4 - q**3 + q**2 - q - 1. Let c(s) = -133*s**4 + 25*s**3 - 101*s**2 - 67*s + 195. Let u(r) = -2*c(r) - 54*m(r). Let u(n) = 0. What is n?
-4, -3, 1, 7
Let n(z) be the first derivative of 14*z**2 - 168*z - 166. Let h be n(6). Factor 1/3*y + 1/3*y**2 + h.
y*(y + 1)/3
Determine u so that 82 - 29 - 69*u - u**2 + 20*u - 323 - 44*u = 0.
-90, -3
Solve 32000/3 - 14/3*x**5 - 15724/3*x**3 + 90640/3*x**2 + 46400*x + 274*x**4 = 0.
-1, -2/7, 20
Let i be -4*(-9)/108*33. Let m be i + (-60)/42 + -5. Factor 16/7*x**2 + 2/7*x**4 - 2*x**3 + 0 + m*x.
2*x*(x - 4