 3759*f + 26365. Let i be v(-7). Find n, given that -82/5*n**2 - 2/15*n**i - 137842/15 - 3362/5*n = 0.
-41
Find p such that -1/3*p**2 - 87616/3 + 592/3*p = 0.
296
Let s(k) = -k**3 + 6*k**2 - 11*k + 8. Let b be s(1). Find g such that 1/4*g**3 + 3/4*g**b + 1/2*g + 0 = 0.
-2, -1, 0
Let -174 + 958*t + 617*t**3 - 2795/2*t**2 - 7/2*t**4 = 0. What is t?
2/7, 1, 174
Let y(b) be the third derivative of b**5/45 - 47*b**4/18 + 164*b**3/3 + 2*b**2 - 32*b. Factor y(f).
4*(f - 41)*(f - 6)/3
Let g(l) be the third derivative of -l**5/15 - 39*l**4/2 + 199*l**2. Suppose g(v) = 0. Calculate v.
-117, 0
Suppose 5*d = -2*z + 337098, 5*d - 2*z - 337074 = 2*z. Suppose -67414*w**2 - 18*w - 10*w + d*w**2 - 32 = 0. What is w?
-1, 8
Suppose 60*j = f + 64*j - 164, 3*j = -4*f + 721. Suppose 39*i - f = -7*i. Factor 2/3*m**i + 8*m**2 - 16/3*m - 4*m**3 + 0.
2*m*(m - 2)**3/3
Let b(c) be the second derivative of -c**6/480 - 3*c**5/80 - 5*c**4/32 + 5*c**3/6 - 13*c**2/2 + 108*c. Let z(r) be the second derivative of b(r). Factor z(i).
-3*(i + 1)*(i + 5)/4
Let l be (-10)/16*((-28)/(-24) + (-7896)/5040). Let 9/4*p**3 - 1/4*p**5 - 11/4*p**2 - l*p**4 + 0 + p = 0. What is p?
-4, 0, 1
Let y(d) be the first derivative of d**3 + 255*d**2/2 - 1068*d + 3693. Factor y(r).
3*(r - 4)*(r + 89)
Factor -464*t**2 - 2486 - 2*t**3 - 770*t - 1062*t - 756 + 1418.
-2*(t + 2)**2*(t + 228)
Let k(w) = 424*w - 868. Let m(f) = -2*f**2 - 2*f + 2. Let c(v) = -k(v) + 2*m(v). Factor c(x).
-4*(x - 2)*(x + 109)
Let k(a) be the second derivative of 6859*a**6/50 - 46569*a**5/100 + 3078*a**4/5 - 416*a**3 + 768*a**2/5 - 1207*a. Find o, given that k(o) = 0.
8/19, 1
Let o be (4/8)/(3/(-504)). Let i = o - -89. Factor 3*c**4 + 6*c**2 - i*c**4 + 4*c**5 - 6*c**2.
2*c**4*(2*c - 1)
Let z(w) = 1664*w + 16640. Let p be z(-10). Factor p + 0*i + 8/15*i**2 + 0*i**3 - 2/15*i**4.
-2*i**2*(i - 2)*(i + 2)/15
Factor -50/9*o**4 + 2870/9*o**3 + 0 - 39712/9*o**2 - 42632/9*o.
-2*o*(o + 1)*(5*o - 146)**2/9
Let f(w) be the third derivative of 1/30*w**6 - w**2 + 0 - 1/6*w**4 + 13*w - 2/3*w**3 + 1/15*w**5. Factor f(y).
4*(y - 1)*(y + 1)**2
Factor -1/3*l**2 + 632/3*l + 0.
-l*(l - 632)/3
Let i(l) be the first derivative of 3*l**5/10 + 45*l**4/2 + 173*l**3/2 + 171*l**2/2 - 9994. Solve i(h) = 0 for h.
-57, -2, -1, 0
Let g = 3611/132 + -177/44. Factor -1225/3 - g*v - 1/3*v**2.
-(v + 35)**2/3
Let r be 84*(6 + 48/(-9)). Let h be 5 - (-11 - (-768)/r). Solve 4/7*c**2 - 12/7*c - h = 0.
-1, 4
Suppose -5*q + 3*h = -8 - 11, 2*q = -h + 1. Factor -52*m + 900 - q*m**2 - 900.
-2*m*(m + 26)
Let f(m) be the second derivative of 7*m + 0*m**4 + 0*m**3 + 0*m**2 + 1/10*m**5 + 18. Factor f(h).
2*h**3
Let h(i) be the second derivative of 3*i**5/40 + 73*i**4/4 + 289*i**3/4 + 108*i**2 + 4*i + 62. Factor h(k).
3*(k + 1)**2*(k + 144)/2
Let k(x) be the first derivative of -x**4/12 - 22*x**3/9 + 47*x**2/6 - 8*x + 587. Factor k(p).
-(p - 1)**2*(p + 24)/3
Let g = 1103 + -6617/6. Let r(m) be the first derivative of 3*m + 1/4*m**2 - g*m**3 + 33. What is w in r(w) = 0?
-2, 3
Let u be (21 + -4 - -1)*(-18)/(-12). Suppose 37*r**2 + 384*r - 61*r**2 + u*r**2 + 12288 = 0. What is r?
-64
Let m(r) = 11022*r + 44091. Let o be m(-4). Factor -3/4*d + 9/8 - 5/4*d**o + 7/8*d**4 - 4*d**2.
(d - 3)*(d + 1)**2*(7*d - 3)/8
Let x be (74 - 71)/(-9 - -11). Factor -3/2*p + 3/2*p**2 + 3/2*p**3 - x.
3*(p - 1)*(p + 1)**2/2
Let z(h) be the third derivative of h**7/4620 - h**6/396 - h**5/30 - 4*h**4/33 + 169*h**3/6 - 88*h**2. Let b(j) be the first derivative of z(j). Factor b(c).
2*(c - 8)*(c + 1)*(c + 2)/11
Let c be (((-10)/(-2) - 5)/1)/(-2). Let s be ((-44)/(-8) - 6)*c. Factor -5/11*h**4 - 3/11*h**3 + s*h + 0 + 2/11*h**2.
-h**2*(h + 1)*(5*h - 2)/11
Let s(u) = -u**2 - 2*u - 1. Let i(d) be the third derivative of d**5/12 + 31*d**4/24 - 14*d**3/3 + 2*d**2 + 1. Let n(g) = i(g) + 2*s(g). Factor n(y).
3*(y - 1)*(y + 10)
Let o(t) be the third derivative of t**6/24 + 11*t**5/60 - 17*t**4/6 + 26*t**3/3 + 2*t**2 + 292*t. Find z such that o(z) = 0.
-26/5, 1, 2
Let j(o) be the third derivative of -o**6/40 + o**5/5 + 25*o**4/8 - 14*o**3 + 3545*o**2. Factor j(p).
-3*(p - 7)*(p - 1)*(p + 4)
Let n = -4624/13 + 9261/26. Let j be (-3)/18 - (-2)/3. Suppose n*v**2 - j + 0*v = 0. What is v?
-1, 1
Factor -32*o**3 - 4220*o + 91*o**3 + 10800 - 32*o**3 + 392*o**2 - 23*o**3.
4*(o - 5)**2*(o + 108)
Let t = -51 - -109. Factor -34*c + 4*c**2 + 36 - t*c + 132.
4*(c - 21)*(c - 2)
Let x(m) be the second derivative of 0*m**2 - 1/18*m**6 - 18*m + 5/36*m**4 - 5/18*m**3 + 1/12*m**5 + 2. Factor x(z).
-5*z*(z - 1)**2*(z + 1)/3
Let f(b) be the first derivative of -b**5/2 + 295*b**4/8 + 995*b**3/2 + 5065*b**2/4 + 1190*b - 1121. Determine n so that f(n) = 0.
-7, -1, 68
Let v(p) be the second derivative of 44/3*p**3 + 12*p - 484*p**2 - 1/6*p**4 + 0. Factor v(b).
-2*(b - 22)**2
Factor 78/5*u**2 - 3/5*u**3 - 207/5*u + 0.
-3*u*(u - 23)*(u - 3)/5
Factor 92/3*l**2 + 0 + 28/3*l**3 + 8*l.
4*l*(l + 3)*(7*l + 2)/3
Factor -1/3 + 4/3*m**3 - 2/3*m - 4/3*m**4 + m**2.
-(m - 1)**2*(2*m + 1)**2/3
Let y be 20/(-60) - (-3)/((-27)/(-570)). Let u be (3/6)/(7*6/y). Factor -1/4*t**4 - t + u*t**3 + 0 + 0*t**2.
-t*(t - 2)**2*(t + 1)/4
Find l such that 2348/5*l**2 - 564/5 + 424/5*l**4 + 106/5*l - 2*l**5 + 2112/5*l**3 = 0.
-3, -1, 2/5, 47
Let r be 20/8*(-48)/(-216). Let c(l) be the second derivative of -r*l**3 + 0 + 5/36*l**4 + 0*l**2 + 31*l. Factor c(j).
5*j*(j - 2)/3
Let d be -619 - (7 + -6) - (-10 - -6). Let c = -613 - d. Solve 1/4*w**4 + 0*w + 0 + 3/4*w**c + 1/2*w**2 = 0.
-2, -1, 0
Let s(i) be the second derivative of -i**7/21 + 5*i**6/3 - 23*i**5/5 - 1210*i. Determine r, given that s(r) = 0.
0, 2, 23
Let 834*a**2 + 1162*a - 1585*a - 162 + 12*a**4 - 221*a**3 - 40*a**3 = 0. Calculate a.
-1/4, 1, 3, 18
Let i(k) be the first derivative of -2*k**5/45 + k**4/3 - 2*k**3/9 - 10*k**2/9 + 816. Find m such that i(m) = 0.
-1, 0, 2, 5
What is u in 1/2*u**2 - 56*u + 327/2 = 0?
3, 109
Factor 1/7*f**3 + 2924207/7 + 429/7*f**2 + 61347/7*f.
(f + 143)**3/7
Let n = 290 - 288. What is h in 2 + h - 2 + 344*h**n - 343*h**2 = 0?
-1, 0
Let m(v) be the third derivative of -8/15*v**6 + 0 + 240*v**2 + 0*v**3 + 0*v + 1/5*v**5 + 2/7*v**7 - 1/21*v**8 + 1/3*v**4. Solve m(x) = 0 for x.
-1/4, 0, 1, 2
Let h = 236 + -234. Factor 24*c**2 - 145*c - 3*c**4 + 12*c**h - 33 + 175*c - 30*c**3.
-3*(c - 1)**2*(c + 1)*(c + 11)
Let o(d) be the first derivative of -d**4/4 + d**3/3 + 17*d**2 + 56*d + 50. Suppose o(i) = 0. Calculate i.
-4, -2, 7
Let t be 12/(-14)*(2 - (3 - 124/12))/(-9). Solve 2/3*a + 2/9*a**2 - t = 0 for a.
-4, 1
Let f(c) = -c**4 - 68*c**3 - 953*c**2 + 1147*c + 2048. Let r(o) = -o**3 + o**2 - o. Let q(d) = -f(d) + 5*r(d). Factor q(s).
(s - 2)*(s + 1)*(s + 32)**2
What is l in 108 + 530/11*l - 2/11*l**3 - 36/11*l**2 = 0?
-27, -2, 11
Let x(k) be the second derivative of k**6/6 + 151*k**5/10 + 8087*k**4/20 + 22046*k**3/15 + 10658*k**2/5 + 2048*k. Factor x(a).
(a + 1)**2*(5*a + 146)**2/5
Factor 160*t - 321/2 + 1/2*t**2.
(t - 1)*(t + 321)/2
Let q(b) be the second derivative of 6/35*b**5 + 8/21*b**4 + 8*b + 1 + 0*b**2 + 4/105*b**6 + 8/21*b**3 + 1/294*b**7. Solve q(s) = 0.
-2, 0
Let -3/4*g**3 + 621/2 + 3/4*g - 621/2*g**2 = 0. What is g?
-414, -1, 1
Let b(h) be the third derivative of 7*h**6/300 - 127*h**5/90 + 325*h**4/12 - 25*h**3 + 59*h**2 - 19*h - 2. Factor b(w).
2*(w - 15)**2*(21*w - 5)/15
Let 4435*l - 5*l**2 - 8757*l + 1265 + 4382*l = 0. Calculate l.
-11, 23
Factor 9680 - 11000/3*p - 5/3*p**3 + 455/3*p**2.
-5*(p - 44)**2*(p - 3)/3
Let s be 1/((-6)/104 + 3472/11284). Let 18*p + 27/2*p**s + 12 - 21*p**2 - 45/2*p**3 = 0. What is p?
-2/3, 1, 2
Let r(n) = -n**2 + n + 3. Let m be r(4). Let o be (6/(-5))/(m/80). Factor 2/9*d**3 + o*d - 128/9 - 8/3*d**2.
2*(d - 4)**3/9
Let a(r) be the first derivative of -5*r**6/162 - 13*r**5/135 - r**4/54 + 8*r**3/3 - 5*r**2 - 32. Let u(l) be the third derivative of a(l). Factor u(t).
-4*(t + 1)*(25*t + 1)/9
Let t(n) be the third derivative of -n**7/42 - 25*n**6/24 - 41*n**5/4 - 875*n**4/24 - 190*n**3/3 + 537*n**2. Determine k so that t(k) = 0.
-19, -4, -1
Let n(b) be the first derivative of -11/6*b**3 - b + 13/4*b**2 - 19. Find s, given that n(s) = 0.
2/11, 1
Let i(l) = 3*l**4 + 135*l**3 + 1818*l**2 + 6456*l + 4812. Let r(p) = -3*p**4 - 135*p**3 - 1819*p**2 - 6452*p