
Let c = 14097 - 14095. Let l(t) be the first derivative of 5/28*t**4 + c - 1/35*t**5 + 0*t - 1/3*t**3 + 3/14*t**2. Factor l(s).
-s*(s - 3)*(s - 1)**2/7
Let s(w) be the second derivative of -17*w**5/4 + 31*w**4/36 + 104*w**3/9 + 8*w**2/3 + 25*w + 2. Let s(v) = 0. Calculate v.
-4/5, -4/51, 1
Let m(k) be the first derivative of -2/3*k**3 + 1/2*k**2 - 1/4*k**4 + 2*k - 136. Factor m(q).
-(q - 1)*(q + 1)*(q + 2)
Determine q, given that -420 + q**3 - 572*q + 738*q - 198 + 247*q + 824*q - 620*q**2 = 0.
1, 618
Let h(a) = -a**2 + 22. Let n(j) = j**2 + 6620*j - 2191352. Let t(x) = -6*h(x) - n(x). Factor t(i).
5*(i - 662)**2
Let c(o) be the second derivative of -o**6/15 + o**5/15 + 13*o**4/18 - 8*o**3/9 - 4*o**2/3 - 1796*o + 2. Suppose c(k) = 0. Calculate k.
-2, -1/3, 1, 2
Let w(b) = -b**4 - b**3 - b**2 + b + 2. Let i(l) = l**4 + 27*l**3 - 124*l**2 + 234*l - 156. Let c(r) = i(r) + 2*w(r). Determine h, given that c(h) = 0.
2, 19
Let u(o) be the third derivative of o**5/20 - 227*o**4/4 + 453*o**3/2 + 404*o**2 + 3*o. Factor u(a).
3*(a - 453)*(a - 1)
Let v(m) = 8003251*m**2 + 11330*m - 2. Let u(g) = 40016260*g**2 + 56657*g - 13. Let b(z) = 2*u(z) - 11*v(z). Solve b(f) = 0 for f.
-2/2829
Let h(c) be the third derivative of 1/14*c**4 + 0*c + 0 + 73*c**2 + 1/210*c**5 - 1/3*c**3. Find n, given that h(n) = 0.
-7, 1
Factor 22/9*w**2 + 32/9 + 52/9*w + 2/9*w**3.
2*(w + 1)*(w + 2)*(w + 8)/9
Let u(k) be the first derivative of -2*k**5/5 - 23*k**4/2 - 104*k**3 - 252*k**2 + 864*k - 3834. Determine y so that u(y) = 0.
-12, -6, 1
Let r be -28*(-3)/(-36)*-5. Let j(c) be the second derivative of 2*c + r*c**4 + 44/3*c**3 + 5/2*c**5 + 0 + 8*c**2. Factor j(u).
2*(u + 2)*(5*u + 2)**2
Suppose -s**3 - 13990 - 586*s**2 + 3455*s - 46671*s - s**3 - 28642 = 0. Calculate s.
-146, -1
Let w be -2 + (8/68 - (-313608)/(-510)). Let m = w - -617. Factor 1/5 - 1/5*v**2 + 1/5*v - m*v**3.
-(v - 1)*(v + 1)**2/5
Let d(f) = -100*f**2 + 34*f + 145. Let a be d(-4). Let i = a + 1593. Factor 1/4 + m**i - m.
(2*m - 1)**2/4
Let o(t) be the first derivative of 0*t**3 - 1/150*t**6 + 1/75*t**5 - 2 + 0*t + 21/2*t**2 + 1/15*t**4. Let p(v) be the second derivative of o(v). Factor p(z).
-4*z*(z - 2)*(z + 1)/5
Let u be (4 - (0 - -2)) + 27. Factor -3*j + u - 27 + 0*j**3 + j**3 + 0*j.
(j - 1)**2*(j + 2)
Suppose -6330 - 11340 = -30*m. Find i, given that m*i - 103*i**3 - 15 - 200*i**2 + 23*i**3 - 474*i = 0.
-3, 1/4
Let d = 3/850 - -62041/2550. Let u = d - 508/21. Factor 0 + u*j**3 + 2/7*j**2 + 0*j.
j**2*(j + 2)/7
Let l = 149 - 150. Let g(q) = 6*q**2 + 2. Let s(b) = b**2 - b + 1. Let t(x) = l*g(x) + 2*s(x). Factor t(o).
-2*o*(2*o + 1)
Let j(h) be the first derivative of -2*h**3/9 + 41*h**2 - 240*h - 6513. Factor j(l).
-2*(l - 120)*(l - 3)/3
Let f = -1 - 1. Let c be 220/30 + f/(-3). Let -c*k**3 - 23*k**2 + 5*k**2 - k**4 - 4 + 31 = 0. Calculate k.
-3, 1
Let u(b) = 53*b + 38. Let m be u(-11). Let q = 547 + m. Suppose -10/3*j**2 - 2/9*j**4 + 0 - 14/9*j**3 - q*j = 0. What is j?
-3, -1, 0
Suppose -526 = -20*r - 67*r - 91. Let m(l) be the third derivative of 1/735*l**7 + 0*l + 1/140*l**6 + 0*l**3 - 1/21*l**4 + 0 - 12*l**2 + 0*l**r. Factor m(d).
2*d*(d - 1)*(d + 2)**2/7
Suppose 0 = 2236*k - 2448*k + 424. Factor 4/9 - o + 2/9*o**k.
(o - 4)*(2*o - 1)/9
Let f(x) be the first derivative of -4*x**5 + 2617*x**4 - 4184*x**3/3 + 7790. Find s, given that f(s) = 0.
0, 2/5, 523
Let u be -30 + (-1790)/(-80) + 3 + 1 + 4. Find t such that 3/2*t + 15/8*t**2 + 0 + u*t**3 = 0.
-4, -1, 0
Suppose -338 + 93 = -113*r + 94. Factor 0*b + 22/15*b**r - 4/15*b**4 - 2/3*b**2 + 0.
-2*b**2*(b - 5)*(2*b - 1)/15
Suppose -72*p - 2*p = 90*p. Let z(l) be the second derivative of 1/5*l**5 + 19*l - 2/63*l**7 + 0*l**3 + 0*l**2 + p*l**6 + 0 - 2/9*l**4. Factor z(b).
-4*b**2*(b - 1)**2*(b + 2)/3
Let k = -98 + 95. Let b be (-407)/(-222) - ((-7)/k - 2). Factor -9*g + 15/2 + b*g**2.
3*(g - 5)*(g - 1)/2
Let u(x) = x**2 + 95*x + 854. Let s(m) = -m**2 - 45*m - 426. Let l(v) = -10*s(v) - 6*u(v). Factor l(j).
4*(j - 36)*(j + 6)
Let m be (9 - -75)/7*4/72. What is v in -2/3*v - 1/6*v**2 - m = 0?
-2
Let l(x) = -x**2 + x + 4. Let r be l(-1). Factor 79*a**4 + r*a**3 + 3*a**3 - 43*a**4 - 20*a - 41*a**4 + 20*a**2.
-5*a*(a - 2)*(a - 1)*(a + 2)
Let n(z) be the first derivative of 17*z**7/1680 + z**6/360 + 8*z**3/3 - 3*z**2/2 - 1. Let g(k) be the third derivative of n(k). Let g(q) = 0. What is q?
-2/17, 0
Suppose 144 = -3*v - 3*v. Let m(l) = 15*l**3 + 45*l**2 + 102*l - 24. Let r(u) = -3*u**3 - 9*u**2 - 21*u + 5. Let y(t) = v*r(t) - 5*m(t). Factor y(x).
-3*x*(x + 1)*(x + 2)
Let o be 98/147 + 4287/(-6417). Let l = o + 5707/2139. Factor -50/3*m + 28*m**2 + l - 6*m**3.
-2*(m - 4)*(3*m - 1)**2/3
Let v(c) be the third derivative of -1/5*c**3 + 0 + 0*c + 1/15*c**4 - 1/150*c**5 - 75*c**2. Let v(q) = 0. What is q?
1, 3
Let z(y) be the second derivative of -y**9/25200 - y**8/5600 + y**7/1400 + y**4/3 + 2*y**2 - 4*y - 3. Let h(t) be the third derivative of z(t). Factor h(w).
-3*w**2*(w - 1)*(w + 3)/5
Factor -91 - 1/4*h**2 - 41/4*h.
-(h + 13)*(h + 28)/4
Let u = 702 + -903. Let f be u/(-134)*(-8)/(-18). Let f + 0*a - 2/3*a**2 = 0. Calculate a.
-1, 1
Let t(u) be the first derivative of -u**4/4 + 619*u**3/3 - 4100. Factor t(y).
-y**2*(y - 619)
Determine d, given that 1/8 + 69*d + 9522*d**2 = 0.
-1/276
Let g(z) be the first derivative of 5*z**6/24 - z**5/4 + 1011. Factor g(r).
5*r**4*(r - 1)/4
Let p be (-2)/(((-4845)/(-102))/(-19)). Determine z so that -p*z + 0 - 2/5*z**2 = 0.
-2, 0
What is h in 20*h**2 + 0 + 27/4*h**3 - 69*h + 1/4*h**4 = 0?
-23, -6, 0, 2
Find y such that 165*y - 10*y**4 - 179*y**2 + 5 - 2*y**5 + 66*y**3 - 10 + 11*y**3 + 3*y**4 - 49 = 0.
-9, 1, 3/2, 2
Let p(v) be the third derivative of 1225/39*v**3 - 35/78*v**4 + 320*v**2 + 0*v + 0 + 1/390*v**5. Factor p(r).
2*(r - 35)**2/13
Let m = 4553 + -22763/5. Let a(d) be the second derivative of -13*d + 0 - 1/12*d**4 + 2/5*d**3 - m*d**2. Determine v so that a(v) = 0.
2/5, 2
Let j(f) = -2*f**2 + 102*f - 540. Let g be j(6). Let u(n) be the first derivative of g*n**2 + 15 + 1/4*n**3 - 3*n. Factor u(b).
3*(b - 2)*(b + 2)/4
Suppose 0 = -3*y + 142 - 91. Find i, given that 52*i + 39*i**2 - 72*i**2 + 30*i**2 - y = 0.
1/3, 17
Let r(u) be the first derivative of -114*u**3/5 + 35*u**2 - 8*u/5 - 1913. Solve r(j) = 0 for j.
4/171, 1
Let p(l) be the second derivative of -30*l**2 - 8/3*l**3 - 6 + 1/9*l**4 - 7*l. Factor p(m).
4*(m - 15)*(m + 3)/3
Let m(l) be the third derivative of 0*l**3 - 1/72*l**6 - 1/2*l**5 + 5*l + 0 + l**2 - 45/8*l**4. Factor m(y).
-5*y*(y + 9)**2/3
Suppose 3*v = 2*l + 8, -5*v - l = -7 - 2. What is o in v*o**2 + 19 - 19*o + 31*o - 19 = 0?
-6, 0
Let y(t) be the second derivative of 8*t**3/3 - 539*t**2/2 + 207*t. Let b be y(34). What is k in -2/3*k**4 + 4/9*k**3 + 2/9*k**b + 2/9 + 4/9*k**2 - 2/3*k = 0?
-1, 1
Let b(d) be the second derivative of 29*d**3 - 2523/2*d**2 - 1/4*d**4 - 6*d - 8. Suppose b(v) = 0. Calculate v.
29
Let a(j) be the third derivative of -j**8/4032 + 11*j**7/504 - 121*j**6/144 - j**5/20 + j**3/3 - 75*j**2. Let r(t) be the third derivative of a(t). Factor r(i).
-5*(i - 11)**2
Let z be -13 - (24/240 + 21/(-10)). Let l be ((-144)/(-132))/((-14)/z). Let -4/7*w**2 - 4/7*w**4 + l*w**3 + 1/7*w**5 + 0 + 1/7*w = 0. What is w?
0, 1
Let v(r) be the second derivative of r**6/660 - 13*r**5/660 + r**4/11 - 5*r**3/2 - r. Let i(w) be the second derivative of v(w). Suppose i(a) = 0. What is a?
4/3, 3
Let u = -1 + 3. Suppose -4*b = 93*b - 194. Factor 2*i**2 - i**2 - i**b - i**u.
-i**2
Let l be (8/12 - (-230)/96) + 9259/(-148144). Factor -9 + 21/2*g - 3*g**l + 3/2*g**2.
-3*(g - 1)*(g + 2)*(2*g - 3)/2
Suppose 2*b + 12*u = -140, 4*b = -27*u + 29*u + 32. Factor 2*y - 12/5 - 2/5*y**b.
-2*(y - 3)*(y - 2)/5
Factor -342 - 12*a**2 - 187*a + 1053*a + 921*a - 416*a.
-3*(a - 114)*(4*a - 1)
Let u(j) be the second derivative of -148225*j**4 + 770*j**3 - 3*j**2/2 - 6446*j. What is x in u(x) = 0?
1/770
Let o(i) = -1. Let x(h) = 3*h - 18. Let v(n) = -9*o(n) + x(n). Let j be v(4). What is b in 4*b - 4*b**j - 164 + 164 = 0?
-1, 0, 1
Let b(p) = 14*p**2 - 5*p - 10. Let q be b(-1). Let s(t) be the second derivative of -1/108*t**4 - 8/27*t**3 - q*t + 0 - 32/9*t**2. Solve s(r) = 0 for r.
-8
Let x be (1/(-36))/((-98)/147). Let s(q) be the third derivat