t**2/7 + 48*t/7 - 2. Factor z(j).
-3*(j - 2)**3*(j + 2)/7
Let t(b) be the first derivative of 0*b + 25/3*b**3 - 5/4*b**4 - 15*b**2 - 26. Factor t(m).
-5*m*(m - 3)*(m - 2)
Let b(d) = -15*d**3 + 147*d**2 + 242*d + 95. Let a(c) = 2*c**3 - c**2 - c - 1. Let m(p) = -5*a(p) - b(p). Find z, given that m(z) = 0.
-1, -3/5, 30
Suppose -163*u + 325 = -164. Let -62/3*q**2 + 10/3*q**u - 6 + 34*q = 0. What is q?
1/5, 3
Let z(k) = -k**4 - 5*k**3 + k**2 + k. Let a(f) be the third derivative of -f**6/120 + 7*f**2. Let j(s) = 4*a(s) - z(s). Let j(h) = 0. Calculate h.
-1, 0, 1
Let p be (-14)/21 + 1 + 1/(-6). Let w(q) be the first derivative of 0*q + 1/8*q**2 + 1/16*q**4 - 4 - p*q**3. Let w(b) = 0. Calculate b.
0, 1
Let b(r) be the second derivative of -r**6/75 + r**5/25 + 11*r**4/30 - 4*r**3/5 - 36*r**2/5 + 5*r - 2. Determine l so that b(l) = 0.
-2, 3
Let m(v) = -v + 23. Let h be m(13). Let k = -7 + h. Let -k*y**2 + 6*y**2 - 6*y**2 + 3*y**4 = 0. Calculate y.
-1, 0, 1
Let g(j) be the third derivative of 11/45*j**5 + 121/540*j**6 + 0 + 1/9*j**4 + 1/3*j**3 + 5*j**2 + 0*j. Let d(y) be the first derivative of g(y). Factor d(p).
2*(11*p + 2)**2/3
Factor 39/7*u**2 + 0*u + 3/7*u**4 + 0 + 6*u**3.
3*u**2*(u + 1)*(u + 13)/7
Let p be 1/(-3) - 22/(-6). Let h be (-48)/6 + 336/36. Determine s, given that p*s**3 + 14/3*s**2 + h*s + 0 = 0.
-1, -2/5, 0
Let 1/9*l**2 + 8/9*l + 4/3 = 0. What is l?
-6, -2
Let a be (0 - (-3)/(-2))/(-16 + 13) + 7. Factor 0*t**4 + 5/2*t**5 + a*t + 5 - 10*t**3 - 5*t**2.
5*(t - 2)*(t - 1)*(t + 1)**3/2
Let 2/5*j**3 + 0 - 2/5*j + 0*j**2 = 0. Calculate j.
-1, 0, 1
Let u(b) be the first derivative of -68*b**2 - 16*b - 275/2*b**4 - 140*b**3 + 7 - 50*b**5. Factor u(m).
-2*(m + 1)*(5*m + 2)**3
Factor 0 - 1/3*x**3 + 38/3*x + 17/3*x**2.
-x*(x - 19)*(x + 2)/3
Let h(n) be the first derivative of -5*n**4/8 + 5*n**3/2 - 5*n**2/2 - 49. Factor h(g).
-5*g*(g - 2)*(g - 1)/2
Let h(s) be the third derivative of -s**8/840 + 4*s**7/175 - 16*s**2. Solve h(f) = 0.
0, 12
Let i(f) = 2*f**4 - 14*f**3 + 20*f. Let p(x) = 10*x**4 - 69*x**3 + x**2 + 102*x. Let k(y) = 11*i(y) - 2*p(y). Factor k(n).
2*n*(n - 8)*(n - 1)*(n + 1)
Let b(r) be the first derivative of -3*r**5/35 - 9*r**4/28 - 3*r**3/7 - 3*r**2/14 - 64. Suppose b(y) = 0. What is y?
-1, 0
Factor -2/9*q**2 - 10/3 - 16/9*q.
-2*(q + 3)*(q + 5)/9
Let o(l) be the first derivative of -2*l**5/25 - 43*l**4/10 - 352*l**3/5 - 256*l**2/5 + 8192*l + 610. Determine c so that o(c) = 0.
-16, 5
Let i(o) = -14 + o**2 - 5 + 18 - o**3. Let m(b) = 6*b**3 - 12*b**2 + 6*b + 3. Let l = -2 - 1. Let v(a) = l*i(a) - m(a). Factor v(w).
-3*w*(w - 2)*(w - 1)
Let r(l) be the third derivative of l**6/300 - l**5/150 - l**4/30 - 534*l**2. Determine h, given that r(h) = 0.
-1, 0, 2
Let h = 7625 - 99123/13. Find s such that 6/13*s + 8/13 - h*s**2 = 0.
-1, 4
Let x(k) = -7*k**2 + 4*k. Let y(i) be the second derivative of -i**4/2 + 2*i**3/3 + 3*i. Let r = 31 - 26. Let a(n) = r*y(n) - 4*x(n). Find j such that a(j) = 0.
0, 2
Let j be 2 - (53/(-12) + (-36)/108). Let n(y) be the first derivative of 3 + j*y + 1/4*y**3 + 9/4*y**2. What is r in n(r) = 0?
-3
Let c = -43379 + 347035/8. Determine j, given that -3/4*j**2 + 3/8*j + c = 0.
-1/2, 1
Let a = -670/3 - -447/2. Let z(b) be the first derivative of -8 - 1/3*b**3 + 1/5*b**5 + 0*b**2 + 0*b + a*b**6 - 1/4*b**4. Solve z(k) = 0.
-1, 0, 1
Let w(q) = q**3 - q - 1. Let n(y) = -4*y**5 - 17*y**4 + 5*y**3 + 17*y**2 - y - 5. Let g(z) = -n(z) + 5*w(z). Solve g(o) = 0.
-4, -1, -1/4, 0, 1
Suppose -18*n = 645 - 15. Let t be 7 - (-7)/(n/25). Factor 0 + 0*j + 0*j**3 + 2/3*j**4 + 0*j**t + 2/3*j**5.
2*j**4*(j + 1)/3
Let s(c) = -9*c**2 - 47*c - 46. Let y(d) = 20*d**2 + 95*d + 93. Let r(i) = -9*s(i) - 4*y(i). Factor r(t).
(t + 1)*(t + 42)
Let l(a) be the third derivative of -1/6*a**3 + 0*a + 0 - 23*a**2 - 1/240*a**5 + 5/96*a**4. Let l(u) = 0. Calculate u.
1, 4
Solve -4 - 5 + 5*o**2 + 8 - 15*o + 11 = 0 for o.
1, 2
Suppose -8*y = 18*y - 7*y. Find l, given that -2/3*l - 4*l**3 + y - 8/3*l**2 - 2/3*l**5 - 8/3*l**4 = 0.
-1, 0
Let g = 17 - 15. Factor -44*l - l**2 + 69*l + 30 + l**g - 5*l**2.
-5*(l - 6)*(l + 1)
Let d(r) be the third derivative of r**9/5040 + r**8/1120 + 13*r**4/24 - 5*r**2. Let j(o) be the second derivative of d(o). Determine b so that j(b) = 0.
-2, 0
Let w(r) = r**2 - 9*r + 17. Let u(d) = -d**3 - d**2 + 4*d + 1. Let l be u(-3). Let m be w(l). Solve 0*n + 0 + 1/4*n**m + 1/4*n**2 = 0.
-1, 0
Let l(z) be the first derivative of -z**6/15 - z**5/5 + z**4/2 + 26*z + 27. Let i(d) be the first derivative of l(d). Determine k, given that i(k) = 0.
-3, 0, 1
Let g = -129/154 + 31/22. Solve 0*z + 32/7*z**3 - g*z**5 + 0 + 48/7*z**2 - 4/7*z**4 = 0 for z.
-2, 0, 3
Let g(x) be the first derivative of -x**5/15 - 11*x**4/12 - 38*x**3/9 - 26*x**2/3 - 8*x + 83. Factor g(a).
-(a + 1)*(a + 2)**2*(a + 6)/3
Let v = 64 - 59. Factor 5*c**4 + 11*c - 11*c + 10*c - 10*c**3 - v.
5*(c - 1)**3*(c + 1)
Suppose 14*b - 13*b - 5 = 0. Let q(h) be the third derivative of 0*h**b + 1/32*h**4 + 4*h**2 + 0 - 1/480*h**6 + 1/12*h**3 + 0*h. Let q(w) = 0. What is w?
-1, 2
Let y(k) = 14*k**4 - 28*k**3 + 14*k**2 - 20*k. Let z(s) = -2*s**4 + 4*s**3 - 2*s**2 + 3*s. Let l(a) = -3*y(a) - 20*z(a). What is u in l(u) = 0?
0, 1
Suppose -5*c + 46 - 6 = 0. Let b = -6 + c. Find q such that b*q**2 - 6*q + 6*q = 0.
0
Let i(r) be the second derivative of r**5/50 + 94*r**4/15 - 379*r**3/15 + 38*r**2 + 774*r. Suppose i(c) = 0. What is c?
-190, 1
Let n(a) = 3*a**2 - 20*a + 14. Let p(x) = 2*x**2 - 13*x + 9. Let g(k) = -5*n(k) + 8*p(k). Let t be g(4). Factor -l**2 - 3*l + 0*l - 3*l**3 + l**2 - 6*l**t.
-3*l*(l + 1)**2
Let p(v) be the second derivative of -8*v + 2*v**3 + 0*v**2 - 1/48*v**4 + 1/480*v**5 + 0 + 1/96*v**6. Let g(n) be the second derivative of p(n). Factor g(i).
(3*i - 1)*(5*i + 2)/4
Let n(f) be the second derivative of f**5/4 - 5*f**4/2 + 55*f**3/6 - 15*f**2 - 181*f. Factor n(l).
5*(l - 3)*(l - 2)*(l - 1)
Let s(y) be the third derivative of 0 + 1/120*y**5 + 20*y**2 + 0*y + 1/48*y**4 + 0*y**3. Factor s(d).
d*(d + 1)/2
Let o(i) = i**2 - 4*i - 5. Let s be o(-1). Let f be s - 15/(-7 - -2). Suppose 1/5*r**f - 4/5*r**2 + r - 2/5 = 0. What is r?
1, 2
Suppose 0 = 3*v - v - 2. Suppose -b = 0, p + 1 - 2 = -5*b. Factor -8*m**2 - v + 70*m**3 - 8*m + 0 + p.
2*m*(5*m - 2)*(7*m + 2)
Let z = 81 - 141. Let x = z + 60. Solve 0*j - 2/7*j**2 + 8/7*j**5 + x - 8/7*j**3 + 2/7*j**4 = 0.
-1, -1/4, 0, 1
Let a(u) be the third derivative of 1/15*u**3 + 23*u**2 + 13/120*u**4 + 2/25*u**5 + 0*u + 0 + 17/600*u**6 + 2/525*u**7. Factor a(i).
(i + 1)**2*(i + 2)*(4*i + 1)/5
Let s = -289 - -291. Suppose 0 = 2*x + 5 - 21. Find l, given that 2 + 36*l**4 - 4 - s - 24*l - 32*l**2 + x*l**3 + 16*l**5 = 0.
-1, -1/4, 1
Let a = -30 + 63. Let z be -3*(-2)/(-8) - 99/(-4). Suppose -z - 151*h - a*h**3 - 29*h - 378*h**2 - 114*h**3 = 0. Calculate h.
-2, -2/7
Let g(u) = 8*u**2 - 10*u + 2. Let s(a) = a**2 - 1. Let n(p) = -4*g(p) + 28*s(p). Determine z, given that n(z) = 0.
1, 9
Let k(a) be the third derivative of a**5/480 - 109*a**4/96 + 11881*a**3/48 + a**2 + 116. Determine t so that k(t) = 0.
109
Factor 7*j - 80*j**3 + 95*j**2 - 4 - 27*j**3 + 8*j**3 + 0 + j.
-(j - 1)*(9*j + 2)*(11*j - 2)
Find a, given that 0 + 80/7*a + 4/7*a**2 = 0.
-20, 0
Let x(y) be the first derivative of y**5 + 50*y**4 + 2960*y**3/3 + 9600*y**2 + 46080*y + 919. Determine k so that x(k) = 0.
-12, -8
Let g be (27/(-24))/(2925/(-78)). Let r(h) be the second derivative of -g*h**5 + 0 + 12*h + 1/5*h**4 - 1/2*h**3 + 3/5*h**2. Factor r(f).
-3*(f - 2)*(f - 1)**2/5
Let l = -542023/9 - -60289. Let g = 3394/45 - l. Factor -8/5 - 98/5*r**2 - g*r.
-2*(7*r + 2)**2/5
Suppose 33 = 14*l - 23. Let c(j) be the second derivative of -1/2*j**3 - 9/4*j**2 - 1/24*j**l + 0 - 4*j. Factor c(h).
-(h + 3)**2/2
Let n be (-8)/(-3) - 2 - 348/(-18). Find v such that -n*v**3 + 26*v + 8*v**4 + 48*v**2 + 1 + 3 + 54*v**3 = 0.
-2, -1, -1/4
Let q(j) be the third derivative of -j**5/540 + 29*j**4/36 - 841*j**3/6 + j**2 - 27. Factor q(s).
-(s - 87)**2/9
Let s(y) = -y - 10. Let d be s(-10). Let x(n) be the first derivative of 3/7*n**6 - 3 + 1/7*n**3 + d*n - 3/35*n**5 + 0*n**2 - 9/14*n**4. Solve x(q) = 0.
-1, 0, 1/6, 1
Let f = 42 + -30. Suppose 10 = -q + f. Suppose -4/7 - 6/7*s - 2/7*s**q = 0. What is s