- 1)**2/5
Let l(i) be the first derivative of i**4/8 - 7*i**3/6 + 5*i**2/2 + 225. Determine h, given that l(h) = 0.
0, 2, 5
Let k(t) be the second derivative of 0 - 1/1440*t**6 - 1/480*t**5 + 0*t**4 - 7/6*t**3 - 2*t + 0*t**2. Let r(j) be the second derivative of k(j). Factor r(x).
-x*(x + 1)/4
Let j be (2/(-6))/(4/(-6)). Let b be ((-105)/7 - -18) + (3 - 4). Solve -3/4 + 1/4*p**b - j*p = 0.
-1, 3
Suppose -10 = 2*s, -68*s = -j - 64*s + 24. Let f(x) be the third derivative of -1/270*x**5 + 3*x**2 - 1/18*x**j - 1/3*x**3 + 0*x + 0. What is i in f(i) = 0?
-3
What is c in -147/2*c - 21*c**2 + 0 - 3/2*c**3 = 0?
-7, 0
Suppose -2 + 12 = -4*u - 2*y, -10 = 3*u + 4*y. Let i be 15/18 + u/(-4). Factor -2 - 2/9*o**2 - i*o.
-2*(o + 3)**2/9
Let h(r) = -5*r**3 + r**2 + r + 1. Let w(n) = -48*n**3 + 26*n**2 + 36*n + 22. Let k(f) = -20*h(f) + 2*w(f). Find t such that k(t) = 0.
-6, -1
Let q(r) be the second derivative of -r**4 - 13*r - 50*r**2 + 0 - 10*r**3 - 1/25*r**5. Factor q(h).
-4*(h + 5)**3/5
Let s = -4101 + 4101. Let m = 17/144 + 5/48. Solve 0*f**2 + 0*f**3 + 2/9*f**5 + s*f - m*f**4 + 0 = 0 for f.
0, 1
Let a(v) be the first derivative of -5*v**6/21 + 76*v**5/35 - 47*v**4/7 + 152*v**3/21 + 3*v**2/7 - 36*v/7 - 459. Suppose a(w) = 0. Calculate w.
-2/5, 1, 3
Let f(r) = 4*r**3 + 3*r**2 - 3. Let g(l) = 11*l**3 + 10*l**2 - 8. Let m(k) = 8*f(k) - 3*g(k). Determine p so that m(p) = 0.
-6, 0
Let o(k) be the third derivative of -k**7/70 + k**6/10 - k**5/4 + k**4/4 + 25*k**2. Factor o(v).
-3*v*(v - 2)*(v - 1)**2
Let k(z) be the second derivative of z**7/840 - z**6/160 + z**4/24 + 7*z**2 + 17*z. Let a(b) be the first derivative of k(b). Factor a(q).
q*(q - 2)**2*(q + 1)/4
Let c(x) be the first derivative of 5*x**6 + 67*x**5 + 1095*x**4/4 + 815*x**3/3 - 225*x**2/2 - 250*x + 739. Determine l, given that c(l) = 0.
-5, -1, -2/3, 1/2
Let r = 203/10 - 391/20. Let n = 103/148 + 2/37. Determine m so that 0 + r*m**5 - n*m**2 - 3/4*m**3 + 3/4*m**4 + 0*m = 0.
-1, 0, 1
Let g(f) be the third derivative of -f**5/390 + 25*f**4/156 - 8*f**3/13 + 2*f**2 - 77. Suppose g(v) = 0. Calculate v.
1, 24
Let o(b) = -b**3 + 4*b**2 - 73*b + 292. Let t be o(4). Suppose 2*p - 1 = 3. Find f such that -8/5 + t*f + 2/5*f**p = 0.
-2, 2
Let i(l) = l**2 + 9*l + 10. Let n be i(-8). Suppose 0 = -n*o - 0*o + 10, -4*b - o = -41. What is v in -6*v**2 + 7 + b + 2*v**2 = 0?
-2, 2
Suppose -2*r + 3*h - 29 = 0, -4*r - h + 4*h - 43 = 0. Let y = 12 + r. Factor 76*d + 1 - 1 + d**4 + 8*d**2 - 72*d + y*d**3.
d*(d + 1)*(d + 2)**2
Let z(o) = -o**3 - 8*o**2 - 6*o + 2. Let a be z(-7). Let c be (7 + a)/(10/6). Find p such that 6/5*p**2 - c*p**3 + 0 - 2/5*p + 2/5*p**4 = 0.
0, 1
Let p(z) be the first derivative of -8*z - 3/40*z**5 - 1/16*z**4 + 1/4*z**3 + 0*z**2 - 7 + 1/40*z**6. Let i(f) be the first derivative of p(f). Solve i(o) = 0.
-1, 0, 1, 2
Let v(i) be the first derivative of 0*i + 19/7*i**3 - 18 + 3/7*i**2. Factor v(c).
3*c*(19*c + 2)/7
Factor 72/5*o - 27/5*o**2 - 12 + 3/5*o**3.
3*(o - 5)*(o - 2)**2/5
Let k be (-9)/(-21) - 182/637. Suppose -8/7 - 12/7*u - k*u**3 - 6/7*u**2 = 0. What is u?
-2
Let r(o) be the third derivative of -3*o**2 + 7/15*o**6 + 8/5*o**5 + 4/3*o**4 + 0 + 1/21*o**7 - 16/3*o**3 + 0*o. Factor r(x).
2*(x + 2)**3*(5*x - 2)
Let q(v) be the second derivative of v**5/110 - 7*v**4/66 + 10*v**3/33 - 82*v. Determine b, given that q(b) = 0.
0, 2, 5
Let d = -21 + 28. Factor -12 - 3*t**4 - 9*t + 9*t**2 + 17*t**3 - t**3 + 6*t**2 - d*t**3.
-3*(t - 4)*(t - 1)*(t + 1)**2
Let a(q) = 2*q**2 + 13*q + 6. Let w be a(-11). Suppose 5*p = 0, x - 6*x + p = -w. Determine b so that b**3 - 6*b**2 - x*b**4 + 24*b**4 + 2*b**3 = 0.
-2, 0, 1
Let f = 20584/51485 - -2/10297. Factor -2/5*i**3 + 4/5*i + f*i**2 + 0.
-2*i*(i - 2)*(i + 1)/5
Let a(g) be the second derivative of -3*g**5/20 + 3*g**4/2 + 13*g**3/2 - 63*g**2 + 2*g - 24. Factor a(t).
-3*(t - 7)*(t - 2)*(t + 3)
Let k be -1 - -20*63/1155. Solve -8/11*g - 12/11 - k*g**2 = 0.
-6, -2
Suppose -9*u + 10 = -4*u. Solve 6*k**u + 10 + 6*k**2 - 34*k - 4*k**2 - 2 = 0 for k.
1/4, 4
Let t(v) = -v**2 + 5*v + 3. Let r(l) = -4*l**2 + 1. Let p be r(1). Let m(g) = 2*g**2 - 6*g - 4. Let i(s) = p*m(s) - 4*t(s). Find b such that i(b) = 0.
-1, 0
Let u(v) = v**2 - 11*v - 2. Let s(g) = -5*g**2 + 46*g + 9. Let w(t) = 2*s(t) + 9*u(t). Factor w(i).
-i*(i + 7)
Let r(j) = -j**3 - 14*j**2 - 39*j + 4. Let d be r(-4). Let q(z) = -z**3 + 12*z**2 + 13*z + 3. Let i be q(13). Let 0*a**2 + 0*a + 2/17*a**i + d = 0. What is a?
0
Let r = -57 + 60. Find d, given that 37*d - 3*d**2 - 37*d + 4*d**2 - d**r = 0.
0, 1
Let m = 133/6 - 5317/240. Let z(r) be the third derivative of -1/32*r**4 - 2*r**2 - 1/24*r**3 - m*r**5 + 0 + 0*r - 1/480*r**6. Find t, given that z(t) = 0.
-1
Let g be 798/(-189) - (-2)/9. Let y be 0*(g - 42/(-12)). Suppose -6/7*v**3 + y + 0*v - 2/7*v**2 = 0. Calculate v.
-1/3, 0
Let x = -7/12 - -115/156. Let w = 9/26 + x. Determine q, given that 9/4*q**2 - w*q + 0 = 0.
0, 2/9
Let l(j) be the third derivative of j**6/720 - 4*j**3/3 + 6*j**2. Let v(a) be the first derivative of l(a). Factor v(b).
b**2/2
Let c(d) = -10*d**4 - 50*d**3 - 110*d**2 - 90*d - 30. Let s(g) = g**3 + 4*g**3 + g**4 + 12*g**2 - 11*g**2 - g - 4*g**3. Let b(a) = c(a) + 5*s(a). Factor b(w).
-5*(w + 1)**3*(w + 6)
Factor 4*v**3 - 74*v**2 - v**3 + 110*v**2 + 144*v + 192.
3*(v + 4)**3
Let t(r) = 129*r - 26. Let c be t(-1). Let w = c + 157. Solve -3/8*v - 1/4*v**w + 1/4 + 3/8*v**3 = 0 for v.
-1, 2/3, 1
Let r(j) be the first derivative of 1/2*j**2 - 31 - 1/15*j**3 - 4/5*j. Factor r(v).
-(v - 4)*(v - 1)/5
Let j(m) = -16*m**3 - 118*m**2 + 94*m + 38. Let r(x) = 81*x**3 + 591*x**2 - 470*x - 191. Let i(a) = 11*j(a) + 2*r(a). Factor i(n).
-2*(n - 1)*(n + 9)*(7*n + 2)
Solve -46*c - 36*c**4 + 4 + 37*c**2 + 23*c**2 + 2*c**3 + 16*c**4 = 0.
-2, 1/10, 1
Let m(k) = 28*k**4 + 62*k**3 + 4*k**2 - 7*k - 7. Let x(c) = 9*c**4 + 21*c**3 + 2*c**2 - 2*c - 2. Let i(l) = -2*m(l) + 7*x(l). Find u such that i(u) = 0.
-3, -2/7, 0
Let g(h) = -13*h**2 + 1088*h - 36997. Let r(a) = -6*a**2 + 544*a - 18498. Let v(p) = 2*g(p) - 5*r(p). Factor v(n).
4*(n - 68)**2
Let m = 30403 - 30401. Determine a, given that 10/9*a + 2/9*a**m + 8/9 = 0.
-4, -1
Let p(l) = 7*l**3 + 5*l**2 - 8*l + 4. Let y(j) = 8*j**3 + 7*j**2 - 7*j + 2. Let q(d) = -5*p(d) + 4*y(d). Factor q(u).
-3*(u - 2)*(u - 1)*(u + 2)
Let r = -109 - -111. Factor 47*p + 56 - 33*p - 78*p**r + 62*p + 66*p**2.
-4*(p - 7)*(3*p + 2)
Let a(o) be the second derivative of -3*o**5/20 + o**4/4 + 8*o**3 + 30*o**2 + 29*o. Determine q so that a(q) = 0.
-2, 5
Let c(g) be the first derivative of g**6/150 + 2*g**5/75 - g**4/30 - 4*g**3/15 - 16*g**2 - 23. Let j(h) be the second derivative of c(h). Factor j(v).
4*(v - 1)*(v + 1)*(v + 2)/5
Let r(c) be the first derivative of -5*c**6/2 - 36*c**5/5 + 12*c**4 + 18*c**3 - 33*c**2/2 - 18*c - 262. Find v such that r(v) = 0.
-3, -1, -2/5, 1
Let f = -122989/26 - -9461/2. Find l such that -2/13*l**2 + 0*l + f = 0.
-1, 1
Let z be (-6 - -16)/5 + 1. Suppose -5*q + 30 = -z*h, -8*q + 3*h = -5*q - 24. Factor -54/11*d - 54/11*d**2 - 2/11*d**4 + 0 - 18/11*d**q.
-2*d*(d + 3)**3/11
Let r(b) = -b**2 + 4*b - 4. Let o be r(3). Let p be (o*1)/((-12)/24). Factor -3*a**4 + 9*a - 14*a**3 - 5*a**2 - a**2 + 6 + 3*a**p + 5*a**3.
-3*(a - 1)*(a + 1)**2*(a + 2)
Let t(g) be the second derivative of 5*g**7/42 - 9*g**5/4 + 5*g**4/3 + 10*g**3 + g - 9. Solve t(n) = 0.
-3, -1, 0, 2
Let p = 2182/3645 + 1/729. Factor 3/5*n**3 + p*n**2 - 3/5*n**4 + 0 - 3/5*n.
-3*n*(n - 1)**2*(n + 1)/5
Let u(z) = 2*z - 1. Let m be u(8). Let -25*b + 5*b**4 + 45*b**2 - 8*b**4 - 2*b**4 + 5 + m*b**4 - 35*b**3 = 0. Calculate b.
1/2, 1
Let g(p) be the first derivative of -15 + 0*p - 4/55*p**5 + 0*p**3 - 1/33*p**6 + 0*p**2 - 1/22*p**4. Factor g(x).
-2*x**3*(x + 1)**2/11
Let z be 39/21 + (-3)/(-21). Let 7*p + 6*p**z - 10 - 17*p**2 + 10*p**2 = 0. Calculate p.
2, 5
Suppose 0*k = k - u + 5, 4*k + 21 = 3*u. Let b be k - ((-340)/15 - -6). Factor 16/3*p - b - 2/3*p**2.
-2*(p - 4)**2/3
Let k(s) = -4*s**3 + 8*s**2 - 21*s - 30. Let w(g) = g**3 + g**2 - g - 2. Let q(c) = -2*k(c) - 6*w(c). Factor q(p).
2*(p - 6)**2*(p + 1)
Let f(w) = -w**2 + w + 4. Let o(t) = -6*t**2 + 10*t + 28. Let h(a) = -14*f(a) + 2*o(a). Factor h(v).
2*v*(v + 3)
Let h(q) be the third derivative of 0 - 1