 h so that -7 - 114*h**2 + 89*h + 37 + 27*h**3 - s*h = 0.
-1, 2/9, 5
Let d(j) be the first derivative of -j**4/60 - 3*j**3/5 - 17*j**2/10 - 35*j - 103. Let p(h) be the first derivative of d(h). Determine r, given that p(r) = 0.
-17, -1
Factor -2/5*n**2 - 648/5*n - 1288/5.
-2*(n + 2)*(n + 322)/5
Find v such that 21563*v**4 - 3*v**2 + 3*v - 3*v**3 + 21559*v**4 - 43119*v**4 = 0.
-1, 0, 1
Let a(h) be the second derivative of -h**4/16 - 101*h**3/8 - 291*h**2/2 - 105*h - 3. Suppose a(m) = 0. What is m?
-97, -4
Let x(h) = -3*h + 62. Let o be x(20). Solve -134*d + d**2 - 24*d**3 - 17*d**4 + 51*d**o + 118*d + 5*d**5 = 0 for d.
-2, 0, 2/5, 1, 4
Let t(x) be the first derivative of -2/21*x**3 - 1/7*x**2 + 266 + 40/7*x. Factor t(p).
-2*(p - 4)*(p + 5)/7
Let t(x) be the first derivative of 10*x**6 - 44*x**5 + 135*x**4/4 + 170*x**3/3 - 30*x**2 - 40*x + 593. Suppose t(f) = 0. What is f?
-1/2, 2/3, 2
Let z(m) be the second derivative of -5*m**4/12 - 3425*m**3/3 - 2346125*m**2/2 - 141*m + 4. Factor z(y).
-5*(y + 685)**2
Let b be (-2 - 170/204) + (-15)/(-36)*8. Factor 10*q - 50 - b*q**2.
-(q - 10)**2/2
Let r = -624 - -641. Suppose 0 = 3*z - 5*x - r, -23 = z + x - 26. Factor 0*m**3 + 0*m + 6/5*m**2 - 3/5*m**z - 3/5.
-3*(m - 1)**2*(m + 1)**2/5
Factor -93*c + c**3 + 24*c + 50 + 24*c**2 + 4 - 10*c.
(c - 2)*(c - 1)*(c + 27)
Let l = 156459 - 156454. Let 18/5*f**l - 174/5*f**4 + 288/5*f - 8 - 666/5*f**2 + 542/5*f**3 = 0. What is f?
1/3, 2, 5
Suppose 3*i + 3 = 0, -72*g + 85 = -69*g + 5*i. Let x(k) be the first derivative of 1/6*k**4 - 1/3*k**2 + g + 0*k**3 + 0*k. Solve x(r) = 0 for r.
-1, 0, 1
Let d be (-14368)/898 + 98/6. Factor d*p**2 - 5*p + 0.
p*(p - 15)/3
Let n(w) = -47*w**3 - 818*w**2 - 1607*w - 801. Let s(t) = 27*t**3 + 410*t**2 + 803*t + 400. Let x(b) = 4*n(b) + 7*s(b). Factor x(c).
(c - 404)*(c + 1)**2
Let b(a) = 44*a**4 - 152*a**3 + 120*a**2 + 52*a. Let s(u) = -44*u**4 + 153*u**3 - 120*u**2 - 65*u. Let r(w) = 5*b(w) + 4*s(w). Find h, given that r(h) = 0.
0, 15/11, 2
Let h be -32 + -3 - (-9625)/220. Solve -h*g - 75/4 - 5/4*g**3 + 35/4*g**2 = 0 for g.
-1, 3, 5
Factor -23/3 + 25/6*d - 1/6*d**2.
-(d - 23)*(d - 2)/6
Let a(r) = -r**2 - 929*r - 9187. Let o be a(-10). Suppose 0 - 14/5*s**2 + 0*s + 2/5*s**o = 0. What is s?
0, 7
Let g(s) be the second derivative of 3/7*s**2 + 16 + 2/21*s**3 - 2*s - 1/42*s**4. Let g(o) = 0. What is o?
-1, 3
Suppose 118/11*v**2 - 60/11 + 98/11*v**3 + 6/11*v**4 - 34/11*v = 0. What is v?
-15, -1, 2/3
Let c be (20/(-14))/((-615)/1722). Let n(w) be the second derivative of 0*w**2 + 0 - 1/70*w**6 - 11*w - 3/28*w**c + 9/140*w**5 + 1/14*w**3. Factor n(o).
-3*o*(o - 1)**3/7
Let v(a) be the first derivative of -a**5/60 - 2*a**4/3 + a**2/2 - 151*a - 167. Let s(l) be the second derivative of v(l). Determine i, given that s(i) = 0.
-16, 0
Let j be (2/(-10))/((-1)/2). Let n be (12/4)/((-1397)/(-44) + -28). Factor n + j*u - 2/5*u**2.
-2*(u - 2)*(u + 1)/5
Let w(k) = -15*k**2 + 47100*k - 56929965. Let o(v) = 8*v**2 - 23488*v + 28464983. Let l(m) = -5*o(m) - 3*w(m). Solve l(h) = 0.
2386
Let g be (-182)/14 - -3 - (10 + 328/(-16)). Suppose -59*f**2 - 171/2 - 138*f - 6*f**3 + g*f**4 = 0. What is f?
-3, -1, 19
Suppose 0 = -4*d - 2*n - 0*n + 136, 0 = 4*d - 3*n - 156. Suppose -d = -6*l - 0. Factor 0*j**4 + 21*j**2 + 5*j**4 + l*j**3 - 14*j**4 + 6*j.
-3*j*(j - 2)*(j + 1)*(3*j + 1)
Suppose 15 - 28 = -21*b + 50. Let u(r) be the first derivative of -5/16*r**4 + 7 + 0*r**2 + 0*r**b + 0*r. Determine f so that u(f) = 0.
0
Let p(c) be the third derivative of -c**6/360 + 91*c**5/60 - 6517*c**4/24 + 123823*c**3/18 - 3720*c**2. Factor p(n).
-(n - 133)**2*(n - 7)/3
Let l(k) be the third derivative of k**3 + 1/6*k**4 + 0*k + 0 + 139*k**2 + 1/90*k**5. Factor l(t).
2*(t + 3)**2/3
Suppose -45 = -4*t - 25. Let m = -1/133 - -543/1463. Let 0*a**2 + 2/11*a**t + 0 + m*a**3 + 6/11*a**4 + 0*a = 0. What is a?
-2, -1, 0
Let 16/15*s**4 - 26/15 + 44/3*s**3 - 16/3*s + 10*s**2 = 0. What is s?
-13, -1, -1/4, 1/2
Let l(p) be the second derivative of 1449*p**5/10 + 113*p**4/2 + 176*p**3/21 + 4*p**2/7 + 4989*p. Factor l(f).
2*(21*f + 2)**2*(23*f + 1)/7
Let h = 3718996/5 + -743787. Suppose -h*r**3 - 1/5*r**5 - 20*r - 36*r**2 + 18/5*r**4 + 0 = 0. Calculate r.
-1, 0, 10
Let b(k) be the third derivative of 0*k + 0 - 3*k**2 + 0*k**4 + 1/260*k**5 + 7/2*k**3 + 1/2340*k**6. Let d(v) be the first derivative of b(v). Factor d(j).
2*j*(j + 3)/13
Suppose 3*j - 59*r + 61*r - 8 = 0, j = 4*r + 12. Factor -4/7*v**j + 0*v**2 + 0 - 16/7*v**3 + 0*v.
-4*v**3*(v + 4)/7
Let l(u) be the first derivative of u**4/4 + 6*u**3 + 81*u**2/2 + 57*u - 153. Let p(n) be the first derivative of l(n). What is m in p(m) = 0?
-9, -3
Suppose 0 = 15*s - 62706 + 62616. What is w in 6*w - 9/2*w**2 + 3/2*w**4 - 3*w**3 + s = 0?
-1, 2
Let f(m) be the second derivative of -2/3*m**3 + 0 + 10*m - 1/2*m**4 - 1/5*m**5 + 15/2*m**2 - 1/30*m**6. Let k(p) be the first derivative of f(p). Factor k(r).
-4*(r + 1)**3
Let u(t) be the third derivative of t**7/525 - 19*t**6/150 - 73*t**5/50 + 551*t**4/3 + 16820*t**3/3 - 115*t**2. What is v in u(v) = 0?
-10, 29
Let l(k) be the first derivative of 4/5*k**5 - 20/3*k**3 + 6*k**2 + 0*k - 50 + k**4. Factor l(c).
4*c*(c - 1)**2*(c + 3)
Suppose 15*c - 307 = -22. Suppose -35 - 45 + 572*a**2 + 28*a**4 + 30 - 236*a - c - 51 - 244*a**3 = 0. Calculate a.
-2/7, 1, 3, 5
Let i(h) be the first derivative of -h**5/12 + 245*h**4/24 - 47*h**2/2 + 192. Let m(c) be the second derivative of i(c). Determine w, given that m(w) = 0.
0, 49
Let b(n) = n**2 + 948*n + 2. Let g be b(0). Factor -g*i**3 - 4 + 26/3*i - 8/3*i**2.
-2*(i - 1)*(i + 3)*(3*i - 2)/3
Let j(a) = 17*a**2 + 232*a + 243. Let f(t) = -7*t**2 - 116*t - 121. Let v(p) = -7*f(p) - 3*j(p). Factor v(d).
-2*(d - 59)*(d + 1)
Let a(s) = 7*s**2 + s. Let f be a(1). Suppose -f*z = -68 - 44. Solve -z*p**4 + p**3 + 15*p**3 + 18*p**4 = 0.
-4, 0
Let w = -7369960/7 - -1052858. Factor 3*d - w + 1/7*d**2.
(d - 2)*(d + 23)/7
Let i be (151504/(-3248) - -47) + 10/(-145). Factor 24/7 + 16/7*f + i*f**2.
2*(f + 2)*(f + 6)/7
Let q(t) be the third derivative of -t**5/80 + 45*t**4/8 + 91*t**3/2 + 4*t**2 - 1431*t. Solve q(g) = 0.
-2, 182
Let o(r) be the third derivative of -r**5/30 + 13*r**4/12 + 16*r**3 - 1218*r**2. Determine h so that o(h) = 0.
-3, 16
Let t(n) be the second derivative of 3*n**5/80 + 3*n**4/2 - 25*n**3/8 + 2542*n - 1. Find a such that t(a) = 0.
-25, 0, 1
Let b = -501 + 524. Suppose -b*p + 40 = -3*p. What is y in -12/7*y**p + 16/7*y**3 - 16/7*y - 4/7*y**4 + 16/7 = 0?
-1, 1, 2
Let x be 0 - 2*(-13)/234. Let y(p) be the third derivative of 0*p - 1/24*p**4 - 1/180*p**5 + 11*p**2 + 0 - x*p**3. Factor y(m).
-(m + 1)*(m + 2)/3
Let d(b) be the first derivative of 4*b**3/27 - 212*b**2/3 + 11236*b + 728. Suppose d(a) = 0. Calculate a.
159
Suppose -3206*f + 3184*f = -66. Let j(b) be the first derivative of -1/20*b**4 - 8/5*b - 6/5*b**2 + 13 - 2/5*b**f. Suppose j(a) = 0. Calculate a.
-2
Let m(t) be the second derivative of -t**7/84 - t**6/4 - 53*t**5/40 + 5*t**4/8 + 9*t**3/2 - 12867*t. Find d, given that m(d) = 0.
-9, -6, -1, 0, 1
Let x(i) be the first derivative of 2*i**3/27 - 133*i**2/9 - 460*i/3 + 4104. Factor x(s).
2*(s - 138)*(s + 5)/9
Let i(y) = -98*y**2 - 835*y + 3205. Let d(r) = 45*r**2 + 417*r - 1602. Let q(g) = 13*d(g) + 6*i(g). Factor q(v).
-3*(v - 133)*(v - 4)
Let m be (49/490)/((-13)/(-260)). Factor 6/7*s + 15/7*s**m + 0.
3*s*(5*s + 2)/7
Let s be (-1)/9*(-20)/2. Let b be ((-74)/(-333))/((-58)/(-8) + -7). Find c, given that -16/9*c**2 - 2/9 + s*c + b*c**3 = 0.
1/2, 1
Let n be ((-28)/(-21) + -2)/(8/(-14)). Let b be 9/(-5) + 2/(-10) - -6. Factor -3/2*o**3 - n*o**2 + 0 + o - 1/3*o**b.
-o*(o + 2)*(o + 3)*(2*o - 1)/6
Let m(x) = -x**3 + x**2 - 3*x - 3. Let c(p) = 4*p**4 - 350*p**3 - 382*p**2 + 758*p + 30. Let f(z) = -c(z) - 10*m(z). Determine s, given that f(s) = 0.
-2, 0, 1, 91
Let a(k) be the second derivative of -17*k**5 - 826*k**4/3 + 488*k**3/3 + 80*k**2 - 50*k - 3. Suppose a(u) = 0. Calculate u.
-10, -2/17, 2/5
Find v such that -v**3 + 482*v**2 + 507 - 91*v - 236*v**2 - 269*v**2 = 0.
-13, 3
Let u(d) = -d**3 + 12*d**2 + 2. Let t be u(12). Let o(n) = -4*n**2 - 1 + n**2 - 10*n**t. Let a(w) = 7*w**2 + 1. Let m(c) = 7*a(c) + 4*o(c). Factor m(j).
-3*(j - 1)*(j + 1)
Let b = 20617/