Let x(t) = 19*t**2 + 11*t + 64. Let o be x(-8). Let d = o + -1188. Find c, given that -117*c**2 - 312/5*c + 621/5*c**d - 36/5 + 111*c**3 - 243/5*c**5 = 0.
-1, -2/9, 1, 3
Let i = 2745826/7 - 392258. Factor -i*a**2 - 2/7*a**3 + 0 - 32/7*a.
-2*a*(a + 2)*(a + 8)/7
Let r be 6286/(-4) - 8/32. Let b = r + 1572. Suppose y + 0 - 3/4*y**3 + 5/4*y**4 - b*y**5 - 5/4*y**2 = 0. What is y?
-1, 0, 1, 4
Let p = -65 + 66. Factor 394*x**2 - 2*x**4 - p - 2*x**5 + 7 - 10*x + 12*x**3 - 398*x**2.
-2*(x - 1)**3*(x + 1)*(x + 3)
Let i(k) = k**2 - 4. Let g(u) = u. Let n(x) = x. Let w(s) = -7*g(s) + 6*n(s). Suppose 2 = -0*f - 2*f. Let v(h) = f*i(h) - 3*w(h). Let v(o) = 0. Calculate o.
-1, 4
Suppose -21 + 28 = -10*m + 3*n, 0 = -4*m - n + 17. Factor 0*i**m + 0 - 1/4*i**4 + 1/4*i**3 + 0*i.
-i**3*(i - 1)/4
Let c(k) = -k**3 - 3*k**2 + 4*k + 5. Let b be c(-5). Determine n so that -14*n + 38*n + 6*n + b*n**2 + 5*n**3 = 0.
-6, -1, 0
Suppose -2*c - 21 = -3*j, -5*j + 2*c + 38 = 3. Suppose j*d + 7 - 42 = 0. Factor -4 + d*u**4 - u**2 + 172*u**3 + 0*u**2 - u**5 + 8*u - 179*u**3.
-(u - 2)**2*(u - 1)**2*(u + 1)
Let j(x) = 4*x**2 - 3*x - 1. Suppose -3*n + 116 = 107. Let t(s) = -4*s**2 + 4*s. Let o(z) = n*t(z) + 4*j(z). Factor o(a).
4*(a - 1)*(a + 1)
Factor -2*v**2 - 227 + 66 - 189 + 8*v**2 + 45*v - v**2.
5*(v - 5)*(v + 14)
Let x(k) be the third derivative of k**5/60 - 103*k**4/12 + 404*k**3/3 - 4678*k**2. Solve x(p) = 0.
4, 202
Let m = -68 + 16. Let n = 54 + m. Solve 0*j**4 - 4*j**3 + 67 + 2*j**4 - 67 - 6*j**n = 0.
-1, 0, 3
Let d be (-33)/(-55) - (5/((-50)/6))/(-1). Let s(x) be the first derivative of 0*x**3 - 26 + d*x**2 + 1/30*x**4 + 0*x. Suppose s(u) = 0. Calculate u.
0
Let w = -62324 + 62326. Factor j + 0 - 1/7*j**w.
-j*(j - 7)/7
Let x(o) be the third derivative of 0*o**4 + 0 - 4/15*o**5 - 65*o**2 + 1/84*o**8 + 0*o + 0*o**3 - 2/21*o**7 + 4/15*o**6. Let x(u) = 0. What is u?
0, 1, 2
Factor 529*o**2 + 253*o + 1383*o - 76*o - 526*o**2 + 1557.
3*(o + 1)*(o + 519)
Let x(f) be the second derivative of -2*f**7/21 + 56*f**6/15 - 53*f**5/5 + 26*f**4/3 - 1061*f. Factor x(n).
-4*n**2*(n - 26)*(n - 1)**2
Let b(z) be the second derivative of 1/8*z**5 - 49*z - 5*z**2 - 5/4*z**4 + 1 + 15/4*z**3. Suppose b(w) = 0. Calculate w.
1, 4
Let w = 245444/3 + -81814. Let f be (-10)/(-18) + (-1)/(-3). Factor -f - 16/9*v - w*v**2.
-2*(v + 2)*(3*v + 2)/9
Let q be (-460)/(-110) + (-8)/44. What is u in 5*u**3 - 1067*u**5 + 12*u**q + 1063*u**5 - 13*u**3 = 0?
0, 1, 2
Let v = 78 - 81. Let b be 6/((-6)/171*v*1). What is f in 8*f**2 - 21*f + b*f - 32*f - 4*f**5 - 8*f**4 = 0?
-1, 0, 1
Let m(n) be the first derivative of 101 - 2/3*n**3 - 31/7*n**2 + 40/7*n. Factor m(z).
-2*(z + 5)*(7*z - 4)/7
Let a = -97 + 99. Factor -1 - 11 - a*z**2 - 6 + 14*z - 2.
-2*(z - 5)*(z - 2)
Let p be ((-3)/(-11) + 11592/3960)*6. Factor -216/5 - p*m + 6/5*m**2.
6*(m - 18)*(m + 2)/5
Suppose 5*y + x - 34 = 0, 0 = -2*y - 0*x + 4*x - 4. Suppose -8 = -y*w + 4. Factor -5 + 5 - 6 + s**w + 5*s.
(s - 1)*(s + 6)
Let t be (8 - (-5463)/(-18) - -6)*(-96)/216. Factor 160*w**3 - 40*w + 8/3 + t*w**2 + 128/3*w**4.
2*(w + 2)**2*(8*w - 1)**2/3
Suppose -4*p - 14 = 2*i, 5*p - 8*p = 15. Let l(b) be the first derivative of 6/5*b**2 - 17 + 2/15*b**i + 2*b. Factor l(r).
2*(r + 1)*(r + 5)/5
Find u such that -3/7*u**4 + 747/7*u**3 - 48375/7*u - 46119/7*u**2 + 93750/7 = 0.
-2, 1, 125
Let v(a) be the second derivative of 4/3*a**3 + 48*a - 1/10*a**5 + 1/2*a**4 + 0*a**2 + 0. Determine t so that v(t) = 0.
-1, 0, 4
Suppose -47 + 5 = -6*w. Let z be (-35 + 0)/(-5) - w. Suppose z + 2/9*g + 2/9*g**2 = 0. Calculate g.
-1, 0
Solve 864*m + 2*m**3 + 701 + 92 + 835 - 55*m**2 + 133*m**2 + 316 = 0.
-18, -3
Let s be -3 - (-11 - (-9 - -5)). Factor 40*w**3 - 28*w**3 - 188*w**2 - 4*w**5 + 40*w**3 + 7*w**s + 192*w - 64 + 5*w**4.
-4*(w - 4)*(w - 1)**3*(w + 4)
Let q = 0 + -36. Let u = 258/7 + q. Find g such that -9/7*g**3 - 3/7*g**4 + 9/7*g + u - 3/7*g**2 = 0.
-2, -1, 1
Let p(i) be the third derivative of -3/20*i**5 + 0 + 1/420*i**7 - 7/12*i**3 - 82*i**2 + 5/12*i**4 - i + 1/60*i**6. Factor p(b).
(b - 1)**3*(b + 7)/2
Let n(w) be the first derivative of -5*w**4/12 - 21*w**3 - 2926. Factor n(k).
-k**2*(5*k + 189)/3
Let y = 4429292/15 + -295286. Solve -2/3*x**2 + 32/5 - 16/15*x + y*x**3 = 0.
-3, 4
Let d(r) be the third derivative of -r**2 + 4*r - 270*r**3 + 15/2*r**4 - 1/12*r**5 + 0. Factor d(q).
-5*(q - 18)**2
Suppose 202 - 32*d**3 + 4*d**4 + 232*d + 150 - 7721*d**2 + 7565*d**2 = 0. What is d?
-4, -1, 2, 11
Let y(o) be the first derivative of 49 + 1/2*o**2 + 8/9*o**3 + 0*o. Let y(i) = 0. What is i?
-3/8, 0
Let a(n) = -67*n - 2540. Let h be a(-38). Let v(m) be the third derivative of 15*m**2 - 1/280*m**h + 0*m**3 + 0 - 1/70*m**5 - 1/56*m**4 + 0*m. Factor v(w).
-3*w*(w + 1)**2/7
Let f(v) be the third derivative of v**8/84 + 8*v**7/105 - 4*v**6/15 - 14*v**5/15 + 7*v**4/6 + 20*v**3/3 - 9*v**2 + 10*v. Determine i, given that f(i) = 0.
-5, -1, 1, 2
Let m(v) be the second derivative of 9*v**7/28 + 27*v**6/20 + 27*v**5/20 - v**4/6 - 2*v**3/3 + 1916*v. Find p such that m(p) = 0.
-2, -2/3, 0, 1/3
Suppose 317*r**2 - 300 - 652*r**2 - 2680*r + 692*r - 546*r**2 - 1824*r**4 + 5668*r**3 - 739*r**2 + 64*r**5 = 0. What is r?
-1/4, 1, 3, 25
Let j be 2/5 - (1578/170 + -9). Suppose 167 = 8*y + 151. Factor 12/17*q + j*q**y + 16/17.
2*(q + 2)*(q + 4)/17
Let o(k) = k**3 - 1. Let s be (-1 + 27/15)/(2/(-15)). Let a(d) = -2*d**4 + 10*d**3 + 6*d**2 - 16*d + 2. Let p(f) = s*o(f) + a(f). Suppose p(n) = 0. What is n?
-2, 1, 2
Let q(o) be the second derivative of 217/24*o**4 - 34/3*o**3 + 49/40*o**5 + 0 + 66*o + 5*o**2. Determine k so that q(k) = 0.
-5, 2/7
Suppose 0 = -9*t - 6952 + 6970. What is x in 2*x**3 - 8/3*x**4 + 0 + 6*x**t + 4/3*x = 0?
-1, -1/4, 0, 2
Let h(w) be the first derivative of -w**8/336 - w**7/126 + w**6/180 - 5*w**2/2 - 27. Let s(p) be the second derivative of h(p). Factor s(g).
-g**3*(g + 2)*(3*g - 1)/3
Let a(c) be the first derivative of 5*c**4/4 + 70*c**3/3 + 205*c**2/2 - 280*c + 1425. Factor a(r).
5*(r - 1)*(r + 7)*(r + 8)
Let a(t) be the third derivative of -t**6/300 - 11*t**5/15 - 1755*t**2. Find w, given that a(w) = 0.
-110, 0
Let l(f) be the first derivative of f**3/8 + 51*f**2/16 + 45*f/4 + 457. Factor l(j).
3*(j + 2)*(j + 15)/8
Let s(t) be the second derivative of t**4/16 - 38*t**3 + 8664*t**2 + 1320*t. What is l in s(l) = 0?
152
Let c(l) be the first derivative of -l**6/1800 + l**5/50 - 11*l**4/120 + 202*l**3/3 + 32. Let x(y) be the third derivative of c(y). Factor x(r).
-(r - 11)*(r - 1)/5
Let f = -237043 + 237045. Factor 1/10*h + 0 + 1/10*h**f.
h*(h + 1)/10
Suppose 1076*x - 1208 = 1484 - 400 - 140. Let 169/2*t + 1/2*t**3 + 0 - 13*t**x = 0. What is t?
0, 13
Suppose -3/2*y - 1/6*y**2 + 95/3 = 0. Calculate y.
-19, 10
Suppose 2*t - 4 - 4 = 0. Suppose 5*b + 3*d = 3, -b = -t*d - 3 + 7. Determine q, given that b*q**2 + 0*q**2 + 2*q - 8*q + 3*q**2 = 0.
0, 2
Let h = 19 + -15. Suppose s - 20 = -h*s. Factor 10*l**2 - 3*l**s - 20*l**3 - 5*l**5 + 12*l + 7*l + 10 - 17*l**4 + 6*l.
-5*(l - 1)*(l + 1)**3*(l + 2)
Let x be ((-36)/4 + 0)/1 + 11. Let v = -11 - -45/4. Determine p so that -p + v*p**x - 3 = 0.
-2, 6
Let u(k) be the second derivative of -1/8*k**6 - 9/16*k**4 - 5*k - 3 + 0*k**2 + 9/20*k**5 + 1/4*k**3. Factor u(y).
-3*y*(y - 1)**2*(5*y - 2)/4
Let h(g) be the second derivative of -1/2*g**4 + 0 - 3/2*g**2 + 23*g + 3/2*g**3 - 1/14*g**7 - 3/10*g**5 + 3/10*g**6. Solve h(v) = 0.
-1, 1
Let d = -172893 - -172893. Factor d - 2/7*m**2 - 12/7*m + 2/7*m**3.
2*m*(m - 3)*(m + 2)/7
Let x(j) be the first derivative of -5*j**6/6 + 17*j**5 + 35*j**4/4 - 625*j**3/3 + 255*j**2 + 770. Suppose x(t) = 0. What is t?
-3, 0, 1, 2, 17
Let k(x) be the first derivative of 2*x**6/3 - 24*x**5/5 - x**4 + 136*x**3/3 - 24*x**2 - 160*x + 5847. Suppose k(w) = 0. What is w?
-2, -1, 2, 5
Let d be -2 - -72 - 61938/888. Factor 1/4*u**4 - u**2 - d*u**3 + 0 + u.
u*(u - 2)*(u - 1)*(u + 2)/4
Let b(r) = -r - 3. Let l be b(-6). Suppose -32*n - 18 = -146. Let -4*f**n + 8*f**3 - 6*f**l - 4*f**3 + 2*f**4 = 0. Calculate f.
-1, 0
Let c = 925202/15 - 61680. Find j, given that 44/15 - 6/5*j - c*j**2 = 0.
-11, 2
Let y be (-808)/(-80) + (-10)/1. Let i = y + 1. Determine z, given that 1/10*z**3 - 1/2 - 7/10*z**2 + i*z = 0.
1, 5
Suppose 4*s - 3*p + 540 = 0, 