/5
Let v be 4 + 4/(-1 - 0) - -6. Let s be 19/v + (-1)/6. Suppose -48/5*z**2 - 6/5*z**5 + 24/5*z + 0 + 18/5*z**s + 12/5*z**4 = 0. Calculate z.
-2, 0, 1, 2
Let x(r) be the first derivative of 1/2*r**6 + 117/2*r**4 + 486*r - 189 + 216*r**3 + 42/5*r**5 + 891/2*r**2. Find q, given that x(q) = 0.
-3, -2
Factor -319/2 + 9*o + 1/2*o**2.
(o - 11)*(o + 29)/2
Let z(s) be the third derivative of -s**6/1200 - 349*s**5/600 - 347*s**4/120 + 13795*s**2. Factor z(q).
-q*(q + 2)*(q + 347)/10
Let r(a) be the third derivative of -a**6/24 + 145*a**5/6 - 25915*a**4/6 - 106580*a**3/3 + 13*a**2 + 25*a. Let r(z) = 0. What is z?
-2, 146
Let k(w) be the second derivative of -1/50*w**6 - 27/100*w**5 + 62*w - 3/2*w**4 - 36/5*w**2 - 22/5*w**3 + 0. Find n, given that k(n) = 0.
-3, -2
Let c be (2 - 30/12)*0. Let q be c + 6/(-4) + 1127/490. What is l in 0 - 6/5*l + q*l**2 - 2/15*l**3 = 0?
0, 3
Let m(l) be the first derivative of -2*l**3/3 - 630*l**2 - 198450*l - 7583. Find h such that m(h) = 0.
-315
Factor 49*z + 241*z - 100*z**2 + 98*z**2 - 14*z + 78*z.
-2*z*(z - 177)
Suppose -x + 2*f - 2075 = -2080, 3*x - 4*f - 19 = 0. Find j such that -x*j + 12 + 3/2*j**2 = 0.
2, 4
Suppose 236 = 2*v + 232. What is s in -4639 - 39*s + 7*s + 4627 + 4*s**4 - 8*s**v - 16*s**2 = 0?
-1, 3
Suppose -40*j - 6 = 5 - 11. Let x(y) be the first derivative of -2/15*y**3 + 1/25*y**5 - 9 + 0*y + j*y**2 - 1/20*y**4. Factor x(f).
f**2*(f - 2)*(f + 1)/5
Let a(n) = -405*n + 3. Let s be a(1). Let d be s/(-33) + (-12)/66. Let -40 + d*t + 20*t**2 + 65 - 33 = 0. What is t?
-1, 2/5
Let m(o) = 2*o**2 - 27*o - 205. Let g be m(19). Let u(j) be the second derivative of -1/27*j**g - 2/9*j**3 + 8/9*j**2 + 0 + 15*j. What is k in u(k) = 0?
-4, 1
Let j = -2/58887 + 117788/412209. Factor -j*x**2 - 4/7*x + 0.
-2*x*(x + 2)/7
Let r(p) be the first derivative of 2*p**5/5 - 143*p**4/2 - 2*p**3/3 + 143*p**2 + 2947. Factor r(m).
2*m*(m - 143)*(m - 1)*(m + 1)
Let p = 3188125/850172 - -5/212543. Let -3/4*o**3 - 7/4 + 19/4*o**2 + p*o = 0. Calculate o.
-1, 1/3, 7
Let j(l) be the second derivative of -2*l**7/63 - 4*l**6/15 + 9*l**5/5 + 10*l - 183. Factor j(d).
-4*d**3*(d - 3)*(d + 9)/3
Let k(l) be the third derivative of l**7/105 + 3*l**6/2 + 1933*l**5/30 - 345*l**4 + 2116*l**3/3 + 2619*l**2. Let k(r) = 0. What is r?
-46, 1
Let p = 118/5627 - -10900/16881. Factor -4/3*d**2 - 1/6*d**4 + 0 + 5/6*d**3 + p*d.
-d*(d - 2)**2*(d - 1)/6
Let x(h) be the first derivative of 2*h**5/25 - 3*h**4/5 + 32*h**2/5 - 1000. Let x(s) = 0. Calculate s.
-2, 0, 4
Let p(k) be the second derivative of k**5/20 - 13*k**4/9 - 37*k**3/18 + 3*k**2 - 8*k - 115. Factor p(m).
(m - 18)*(m + 1)*(3*m - 1)/3
Factor 16*r + 6*r**2 + 2/9*r**3 + 0.
2*r*(r + 3)*(r + 24)/9
Let q(n) be the first derivative of 7*n**4/8 + 4*n**3/3 - 13*n**2/4 - n + 1013. Determine f so that q(f) = 0.
-2, -1/7, 1
Let b(c) be the second derivative of -1/100*c**5 - 40/3*c**3 - 1 + 0*c**2 + 69*c - 2/3*c**4. Suppose b(v) = 0. Calculate v.
-20, 0
Let x(a) be the second derivative of -a**6/480 - a**5/120 - 11*a**2 - 45*a - 1. Let o(m) be the first derivative of x(m). Factor o(w).
-w**2*(w + 2)/4
Let i(o) = -o**2 - 2*o - 1. Let u(x) = -6*x**2 - 3*x + 1. Suppose 3*d - 3*f = 3, -23 = 3*d - 5*f - 24. Let c(b) = d*i(b) - u(b). Suppose c(v) = 0. Calculate v.
-3/4, 1
Let p = -748 - -862. Find a such that -51*a**2 - 15*a**2 + 0*a**2 - 3*a**3 + 23*a + 6*a**2 - 74*a + p = 0.
-19, -2, 1
Let q(k) = 19*k - 95. Suppose 2*o = c + 1, 49*c - 54*c = o - 28. Let f be q(c). What is i in -2/11*i**2 + 0 + f*i = 0?
0
Suppose 0 = h, -8*c - 2545 = -13*c - 3*h. Factor -3*d + 3 - 255*d**3 + c*d**3 - 3*d**2 - 251*d**3.
3*(d - 1)**2*(d + 1)
Let m(f) = -4*f - 3*f - 345 + 226. Let v be m(-17). Factor -2/3*y**5 - 4/3*y**2 + v*y + 0 - 8/3*y**4 - 10/3*y**3.
-2*y**2*(y + 1)**2*(y + 2)/3
Let l be 4913/1785 + 55/(-20). Let d(j) be the third derivative of 0 + 0*j - j**2 + 4/21*j**4 + 4/7*j**3 + l*j**6 + 1/30*j**5. Factor d(c).
2*(c + 2)**2*(c + 3)/7
Let d(u) = 407*u + 9770. Let s be d(-24). Factor 4/9 + 2/9*a - 2/9*a**s.
-2*(a - 2)*(a + 1)/9
Let o(l) = l**2 + 13*l + 24. Let i(k) = k**2 + 8*k - 11. Let t be i(-8). Let y be o(t). Determine n so that -16*n**3 + 55*n**3 + 4*n**y - 18*n**3 - 19*n**3 = 0.
-2, 0
Let y = 325 - 322. Suppose -2*v + 11 = 2*v + 5*r, y*r + 23 = 5*v. Factor 0*j + 4/9*j**2 - 2/9*j**v + 0 - 2/9*j**3.
-2*j**2*(j - 1)*(j + 2)/9
Let q = 7344/145 + -1202/29. Let z(f) be the first derivative of 7/3*f**6 - 38 + 2*f**2 + 26/3*f**3 + 0*f + 27/2*f**4 + q*f**5. Factor z(s).
2*s*(s + 1)**3*(7*s + 2)
Let q(d) be the third derivative of d**5/60 + d**4/6 - 16*d**3/3 - 112*d**2 + d - 2. Factor q(y).
(y - 4)*(y + 8)
Let c(z) be the first derivative of -z**3/3 - 392*z**2 - 153664*z - 909. Factor c(w).
-(w + 392)**2
Let s = -20241 - -20243. Factor -13*i + 1/2*i**s + 169/2.
(i - 13)**2/2
Suppose -k + 2*m + 5 = m, 3*k + m - 7 = 0. Suppose 291 - k = 2*d. What is n in 13*n**5 + 108*n**2 + d*n - 44*n**3 - 236*n**4 - 44*n**4 + 228*n**2 + 87*n**5 = 0?
-3/5, 0, 2
Let l be -12 + (-231)/(-540) - 1/4. Let p = l + 110/9. Let 2*c**4 + 6/5*c**5 - p*c**3 + 0 - 2*c**2 - 4/5*c = 0. What is c?
-1, -2/3, 0, 1
Let j be 34/(-12)*(24 - (-89550)/(-3675))*14/3. Factor 4/7 + 30/7*x**2 - j*x.
2*(x - 1)*(15*x - 2)/7
Let p(v) be the first derivative of v**4/4 + 2*v**3/3 + 24*v**2 + 156*v + 292. Let s be p(-3). What is l in 16/7*l + 17/7*l**2 + 5/7*l**s + 4/7 = 0?
-2, -1, -2/5
Let o(z) be the first derivative of 1/40*z**5 + 4 + 0*z**2 + 0*z - 1/24*z**3 - 1/48*z**6 + 1/32*z**4. Find b, given that o(b) = 0.
-1, 0, 1
Let x be (-12257)/(-77) - 6/33. Let v = x + -783/5. Let 0 - 6/5*h**2 - 6/5*h**3 + v*h = 0. What is h?
-2, 0, 1
Suppose 0 = -22*d - 11 - 297. Let l(j) = 8*j**4 + 12*j**3 + 99*j**2 + 74*j - 7. Let v(h) = -h**4 + h**3 + h + 1. Let c(y) = d*v(y) - 2*l(y). Factor c(q).
-2*q*(q + 1)*(q + 9)**2
Let o(l) be the first derivative of -6/5*l**5 + 116 - 15/4*l**4 + 0*l**2 + 1/6*l**6 + 0*l - 8/3*l**3. Factor o(s).
s**2*(s - 8)*(s + 1)**2
Let i(g) = -7*g**2 - g. Let k(p) = 3*p**3 - 12685*p**2 + 17918291*p - 8427568593. Let h(m) = -2*i(m) - k(m). Factor h(b).
-3*(b - 1411)**3
Suppose -153/2 - 1/2*i**3 - 23/2*i**2 - 111/2*i = 0. What is i?
-17, -3
Let u = -3080319/7 + 440900. Let s = u + -854. Suppose 24/7 + 30/7*n**2 + 51/7*n + s*n**3 = 0. What is n?
-8, -1
Let j(y) be the first derivative of 10*y**2 - 103 - 116*y**5 - 380/3*y**3 + 0*y + 1345/4*y**4. Solve j(v) = 0 for v.
0, 2/29, 1/4, 2
Suppose -5 = -3*y - 4*s - 0, -34 = -2*y + 5*s. Let c be 1/(y - (-162)/(-24)). Factor 0 + 1/3*k + 1/3*k**5 - 2/3*k**3 + 0*k**2 + 0*k**c.
k*(k - 1)**2*(k + 1)**2/3
Let q(w) be the first derivative of -2*w**5/45 - 10*w**4/9 - 226*w**3/27 - 214*w**2/9 - 80*w/3 - 5497. Find n such that q(n) = 0.
-12, -5, -2, -1
Suppose 1/4*o**2 + 795/4 - 67*o = 0. What is o?
3, 265
Let z be 132/(-154)*(-56)/72. Let 2*n**4 - 4/3*n**2 - 2/3*n**5 - 4/3*n**3 + 2*n - z = 0. What is n?
-1, 1
Let n be (-5)/(-35) - 999/(-18) - (-10)/(-70). Factor 27 + 30*m**2 - 3/2*m**3 - n*m.
-3*(m - 18)*(m - 1)**2/2
Factor 8*a**2 + 16*a**2 - 27*a + 156 - 38*a**2 + 11*a**2.
-3*(a - 4)*(a + 13)
Let m(l) = 12*l**3 - 164*l**2 - 308*l - 139. Let g(f) = 5*f**3 - 82*f**2 - 155*f - 71. Let d(q) = 14*g(q) - 6*m(q). Factor d(j).
-2*(j + 1)**2*(j + 80)
Let h = 895 + -893. Let j(u) be the second derivative of 5*u + 0 + 9/40*u**5 - 2*u**h + 7/3*u**3 - 5/4*u**4. Factor j(w).
(w - 2)*(3*w - 2)**2/2
Let v = -34 + 48. Let d = -4 + v. Suppose d*t**2 - 200 + 195 - 5*t**2 = 0. What is t?
-1, 1
Determine t, given that 207/2*t + 3969/8*t**2 - 3/2 = 0.
-2/9, 2/147
Let t(n) = 30*n - 1437. Let b be t(48). Let x(l) be the first derivative of -29 + 0*l + 1/8*l**b + 3/32*l**4 - 3/8*l**2. Suppose x(a) = 0. What is a?
-2, 0, 1
Let v(a) = -a**2 + a + 1. Let p(y) = -580 - 11*y + 2*y + 561 + 4*y**2. Let b(g) = 2*p(g) + 6*v(g). Factor b(t).
2*(t - 8)*(t + 2)
Factor 87/5*f - 1/5*f**2 + 54.
-(f - 90)*(f + 3)/5
Suppose 28*r = 14*r + 11*r. Let d be (6/4)/(2/4). Find u, given that 8*u**2 + r + 8 - 10 + 6 + 8*u**d - 14*u = 0.
-2, 1/2
Let s(b) = -14*b**4 + 40*b**3 - 12*b**2 - 43*b + 11. Let u(d) = -39*d**4 + 119*d**3 - 35*d**2 - 127*d + 34. Let o(i) = 8*s(i) - 3*u(i). What is r in o(r) = 0?
-1, 2/5, 1, 7
Let y(t) = 16*t**2 - 68*t + 5. Let b be y(11). Let z = 1196 - b. Fact