
Let k(t) be the third derivative of t**7/2940 - t**5/140 - t**4/42 - 7*t**3/3 - t**2. Let n(f) be the first derivative of k(f). Suppose n(m) = 0. Calculate m.
-1, 2
Suppose 247*s - 887 = 101. Determine m so that 6/7*m**s + 1/7*m**5 + 16/7*m - 24/7*m**2 + 0 + 1/7*m**3 = 0.
-4, 0, 1
Let i be -3*(-32)/24 + -4. Let g(c) be the second derivative of -2/21*c**4 + 2/7*c**2 + 0*c**3 + 4*c + 0 + i*c**5 + 2/105*c**6. Determine j so that g(j) = 0.
-1, 1
Let i(y) be the second derivative of -y**5/330 - y**4/66 + y**3/11 + y**2 + 5*y. Let m(o) be the first derivative of i(o). Factor m(b).
-2*(b - 1)*(b + 3)/11
Let h = -57 - -68. Let z(m) be the first derivative of 12/5*m**3 + 11/5*m**4 + 7/5*m**2 - h + 1/5*m**6 + 2/5*m + 26/25*m**5. Factor z(d).
2*(d + 1)**4*(3*d + 1)/5
Let b = 373/282 + 1/94. Let n(z) be the second derivative of 0 + 2/5*z**5 + z**4 + z**2 + b*z**3 - 8*z + 1/15*z**6. Factor n(m).
2*(m + 1)**4
Suppose 0 = -5*w - 28 + 103. Suppose s**2 + w + 40*s - 6*s**2 - 4*s**2 - 6*s**2 = 0. Calculate s.
-1/3, 3
Let h(k) be the third derivative of 0*k**3 + 0 + 0*k**5 - 1/112*k**8 - 1/8*k**4 - 8*k**2 + 0*k + 0*k**7 + 1/20*k**6. Factor h(p).
-3*p*(p - 1)**2*(p + 1)**2
Let g = -24240/7 - -3463. Solve 1/7*t**3 - 2/7*t + g*t**2 + 0 = 0.
-2, 0, 1
Let k(s) be the first derivative of -s**6/540 - s**5/180 + s**4/18 + 2*s**3 - 9. Let r(g) be the third derivative of k(g). Factor r(o).
-2*(o - 1)*(o + 2)/3
Let p be ((-18)/(-4))/((-120)/20)*-8. Suppose -37 + 25 = -p*o. Factor -12*r**3 - 6 + 3/2*r**5 + 21/2*r + 3*r**o + 3*r**4.
3*(r - 1)**3*(r + 1)*(r + 4)/2
Let c(w) = w + 2. Suppose -2*l - 20 = 4*k - 6*l, 3*k = 5*l - 25. Let r be c(k). Factor d + d + d**2 - 5*d - 2*d**r.
-d*(d + 3)
Let a(b) be the first derivative of -b**5/5 - b**4 - 2*b**3 - 2*b**2 - b + 197. Find i such that a(i) = 0.
-1
Let x(d) be the first derivative of -d**4/20 + 32*d**3/5 - 1536*d**2/5 + 32768*d/5 - 147. Factor x(h).
-(h - 32)**3/5
Suppose 0 = -w - s - 1, 3*s = -50 + 47. Suppose -2*r + w*r**2 + 3/2*r**3 - 1/2*r**4 + 0 = 0. What is r?
-1, 0, 2
Suppose 5*x = v + 37, 5*x + 3*v - 33 = 2*v. Solve x*g + 3*g**2 - 18*g + 8*g = 0 for g.
0, 1
Suppose 4 + 8 = 2*t. Let x(o) = -o**3 - o**2 + o. Let i(z) = -9*z**3 + 9*z - 6. Let m(k) = t*x(k) - i(k). Solve m(s) = 0 for s.
-1, 1, 2
Let d(m) be the second derivative of m**4/10 - 9*m**3/5 - 6*m**2 - 162*m. Factor d(g).
6*(g - 10)*(g + 1)/5
Suppose 18/5*v**3 + 4/5*v**4 + 0*v**2 - 6/5*v**5 - 8/5*v + 0 = 0. Calculate v.
-1, 0, 2/3, 2
Suppose -v + o = 2 + 6, 0 = 3*v + o + 16. Let i be v*5/(-10) + 6/(-2). Factor 0 - 1/3*u**3 + 1/3*u + i*u**2.
-u*(u - 1)*(u + 1)/3
Let x = -330 + 661/2. Let g(y) be the second derivative of -4*y + 0 - 3*y**2 + x*y**3 + 1/4*y**4. Suppose g(q) = 0. What is q?
-2, 1
Let i(v) be the second derivative of -v**4/6 + 4*v**3/3 - 4*v**2 - 96*v - 2. Factor i(p).
-2*(p - 2)**2
Factor -8 - 44/3*a - 16/3*a**2 + 4/3*a**3.
4*(a - 6)*(a + 1)**2/3
Let k(v) be the first derivative of 1/3*v**3 + 2*v**2 + 22 - 5*v. Solve k(y) = 0 for y.
-5, 1
Let z(c) be the third derivative of c**11/332640 - c**10/75600 + c**9/60480 + c**5/60 + 9*c**2. Let r(f) be the third derivative of z(f). Factor r(d).
d**3*(d - 1)**2
Let m be ((-65)/(-15) - 4)*-15 - -21. Suppose m*t - 17 = 15. Factor 0*d**t - 2/9*d**3 + 0 + 0*d.
-2*d**3/9
Suppose 40 = 5*r + 5*k, -5*k = 47*r - 51*r - 22. Factor -32/13*b + 0 + 16/13*b**r - 2/13*b**3.
-2*b*(b - 4)**2/13
Let s(u) be the third derivative of -u**10/287280 + u**8/31920 - u**6/6840 - u**4/3 + 17*u**2. Let z(q) be the second derivative of s(q). Factor z(h).
-2*h*(h - 1)**2*(h + 1)**2/19
Solve 1935*u**2 + 3840 + 153*u**3 - 34*u**3 + 0*u**3 + 5*u**4 + 61*u**3 + 5600*u = 0.
-16, -3, -1
Suppose -3*a + 13 - 7 = 0. Suppose 3*s = -15, -w - 14 = 6*s - a*s. Let r(m) = -2*m**2 + 6*m. Let p(t) = t**2 - 5*t. Let z(i) = w*p(i) + 5*r(i). Factor z(k).
-4*k**2
Let u(b) = -195*b**2 - 200*b - 3. Let h(n) = 2340*n**2 + 2400*n + 35. Let t(p) = 2*h(p) + 25*u(p). Suppose t(g) = 0. Calculate g.
-1, -1/39
Let z = -1291/2 + 3875/6. Factor 0 + 2/3*w**2 + 1/3*w + z*w**3.
w*(w + 1)**2/3
Let x(v) be the third derivative of 0*v**4 + 0*v**5 + 0 + 0*v**3 + 0*v - 1/70*v**7 - 1/20*v**6 - 3*v**2. Find z, given that x(z) = 0.
-2, 0
Let k = 1970 - 1970. Determine m, given that 3/4*m - 3/4*m**3 + 0*m**2 + k = 0.
-1, 0, 1
Suppose 4*u + 24 = 6*n, -3*u + 5*u = n. Find t such that -2/11*t**4 - 4/11*t**u - 8/11 + 8/11*t + 6/11*t**2 = 0.
-2, 1
Let v(b) = -4*b**2 - 8*b + 2. Let c(j) be the third derivative of -j**3/6 - 4*j**2. Let n(f) = -6*c(f) - v(f). Determine z, given that n(z) = 0.
-1
Factor 1/6*t**2 + 11/2 + 7/3*t.
(t + 3)*(t + 11)/6
Let w(f) = f**3 - f**2 - f + 4. Let g be w(0). Suppose g*z + 3 = 31. Factor 6*l + 5*l**2 + z*l**2 - 10*l**2.
2*l*(l + 3)
Let g(s) be the third derivative of -11*s**6/48 - 29*s**5/16 - 35*s**4/8 + 5*s**3/6 + 355*s**2. Suppose g(n) = 0. What is n?
-2, 1/22
Let k(f) be the second derivative of -f**6/105 + 2*f**5/35 - 5*f**4/42 + 2*f**3/21 + 13*f - 2. What is r in k(r) = 0?
0, 1, 2
Factor -32/7*l**3 + 0 - 2/7*l**4 + 0*l + 34/7*l**2.
-2*l**2*(l - 1)*(l + 17)/7
Factor -896 - 7*m**2 - 5870*m + 6254*m + 0*m**3 - 17*m**2 - 4*m**3.
-4*(m - 4)**2*(m + 14)
Let t(z) = 9*z**2 + 337*z + 1747. Let p(q) = 3*q**2 + 114*q + 582. Let w(i) = 17*p(i) - 6*t(i). Let w(f) = 0. Calculate f.
-14
Determine z, given that -26/7*z**2 - 8/7*z - 30/7*z**3 - 2*z**4 - 2/7*z**5 + 0 = 0.
-4, -1, 0
Let z(b) be the second derivative of -1/21*b**4 + 2/7*b**2 + 11/70*b**5 - 9*b + 0 - 11/21*b**3. Factor z(a).
2*(a - 1)*(a + 1)*(11*a - 2)/7
Let k(o) be the third derivative of -o**6/60 - o**5/3 - 3*o**4/4 - 49*o**2 - 3*o. What is f in k(f) = 0?
-9, -1, 0
Let r(h) = -h**3 + 0*h**3 - 11*h**2 - 8*h - 10 + 19*h. Let k be r(-12). Factor -8*w + 12 - 10*w**2 + 0 + 12*w**2 - 6*w**k.
-4*(w - 1)*(w + 3)
Suppose 44*p - 42*p = 8. Let n(f) be the first derivative of -1/10*f**5 + 2 - 1/3*f**3 + 3/8*f**p + 0*f**2 + 0*f. Suppose n(s) = 0. What is s?
0, 1, 2
Let f(z) = -z**3 - 16*z**2 - 38*z + 17. Let r be f(-13). Suppose -17*b + 15*b + r = 0. Factor 1/3*k**3 - 2/3*k + 1/3*k**b + 0.
k*(k - 1)*(k + 2)/3
Let n(v) = v**3 - 3*v**2 + 3. Let s be n(3). Factor 0 - 2/3*j**s + 0*j**2 + 8/3*j.
-2*j*(j - 2)*(j + 2)/3
What is x in -27*x - 44*x**2 - 37*x**2 - 39*x**2 + 121*x**2 = 0?
0, 27
Let u(h) = h**2 - h - 1. Let s(c) = -4*c**2 + 4*c + 6. Let p(a) = a**2 - 16*a - 1. Let i be p(16). Let v(z) = i*s(z) - 6*u(z). Find l such that v(l) = 0.
0, 1
Let s(h) be the first derivative of -3 - 1/15*h**3 - 3/20*h**4 + 3/10*h**2 + 0*h + 1/25*h**5. Find q such that s(q) = 0.
-1, 0, 1, 3
Let s(l) = -2*l**2 + 5. Let y(x) = 28*x**2 - 1016*x - 64596. Let d(n) = 16*s(n) + y(n). Factor d(r).
-4*(r + 127)**2
Let -115*j**2 + 435/2*j + 45/2*j**3 - 5/4*j**4 - 495/4 = 0. What is j?
1, 3, 11
Let h = -66159/80 + 827. Let n(m) be the second derivative of 1/56*m**7 + 1/48*m**4 + 0 - 1/24*m**6 + 0*m**2 - m + 0*m**3 + h*m**5. Factor n(q).
q**2*(q - 1)**2*(3*q + 1)/4
Suppose -3*u + 0 = 3. Let k be (5 + (-4 - u))*(-2)/(-7). Factor 4/7*c - 1/7*c**2 - k.
-(c - 2)**2/7
What is z in -3/7*z**2 + 0*z + 0 = 0?
0
Let q = -3839 + 3839. Factor -1/5*w**4 + q*w**2 + 1/5*w**3 + 0 + 0*w.
-w**3*(w - 1)/5
Let v(m) be the first derivative of m**6/9 + 4*m**5/5 - 64*m**3/9 - 405. Factor v(a).
2*a**2*(a - 2)*(a + 4)**2/3
What is t in 240 - 3*t**3 - t**3 - 36*t + 24*t**2 - 224 = 0?
1, 4
Let a(o) be the third derivative of -o**6/150 + 4*o**5/75 - o**4/10 - 22*o**2 - 2. Factor a(s).
-4*s*(s - 3)*(s - 1)/5
Let a(r) be the third derivative of 1/32*r**4 + 1/60*r**5 + 0*r + 0 + 34*r**2 - 1/24*r**3. Factor a(h).
(h + 1)*(4*h - 1)/4
Let s(n) be the first derivative of n**5/15 + 23*n**4/4 + 529*n**3/3 + 12167*n**2/6 - 228. Solve s(a) = 0 for a.
-23, 0
Let u(o) be the third derivative of o**5/15 - 17*o**4/6 + 32*o**3/3 + 9*o**2 - 16. Factor u(p).
4*(p - 16)*(p - 1)
Suppose -9 = -2*q - 3*c, 16*q - 19*q + 12 = 3*c. Factor -3*l**q + 7/3*l**2 + 2/3*l + 0.
-l*(l - 1)*(9*l + 2)/3
Factor -7/6*q - 1/3*q**2 - 2/3 + 1/6*q**3.
(q - 4)*(q + 1)**2/6
Factor -114/7*y + 3/7*y**2 + 1083/7.
3*(y - 19)**2/7
Let j = 16 - 10. Let s = 218 - 206. Solve -3*q**2 + 90*q + s - 90*q - j*q**2 + 3*q**3 = 0.
-1, 2
Let j(v) be the second derivative of 0*v**2 + 0 - 1/36*v**4 + 4/9*v**3 + 24*v. Suppose j(l) = 0. 