4
Let d = 234 + -229. Suppose -d*t + 20 = -0*t - 4*r, -3*t + 12 = -2*r. Suppose -5/2*b - 25/4*b**t + 0 - 5/4*b**5 - 45/4*b**3 - 35/4*b**2 = 0. Calculate b.
-2, -1, 0
Let m(g) be the first derivative of 3*g**5/20 - 23*g**4/4 + 11*g**3 - 124*g - 162. Let w(u) be the first derivative of m(u). Let w(t) = 0. What is t?
0, 1, 22
Determine l, given that 64/5*l**3 - 608/5*l**2 + 804/5*l - 288/5 = 0.
3/4, 8
Let y(d) = -d - 27. Let o be y(-11). Let v be 6/(-4) - 3/18*-3. Let b(w) = -4*w**2 + 20*w + 16. Let z(c) = -c - 1. Let a(f) = o*z(f) + v*b(f). Factor a(x).
4*x*(x - 1)
Let h(k) be the first derivative of -67 + 69/4*k**4 + 21/5*k**5 + 6*k + 39/2*k**2 + 27*k**3. What is p in h(p) = 0?
-1, -2/7
Let q(p) be the third derivative of -11/2*p**3 + 0*p + 0 + 1/20*p**5 - 5/4*p**4 - 26*p**2. Factor q(d).
3*(d - 11)*(d + 1)
Let h = -14357 - -27235/2. Let t = h - -740. Let 0 + 0*x + x**2 + 0*x**4 - 3/2*x**3 + t*x**5 = 0. Calculate x.
-2, 0, 1
Suppose -12 = -4*n - 4*h, 0*n = -2*n + 2*h + 6. Let b be ((-8)/84)/((-4)/18). Factor -b*g**4 + 9/7*g**n + 0 - 12/7*g + 0*g**2.
-3*g*(g - 2)**2*(g + 1)/7
Let p(v) be the second derivative of -v**4/12 - 59*v**3/2 - 175*v**2 - 205*v + 22. Factor p(j).
-(j + 2)*(j + 175)
Let p be -7 + 1296/6 + -5. Find i such that 9*i**2 - 6*i**2 + p*i + 301 + 3167 = 0.
-34
Factor -22801/4 - 151/2*a - 1/4*a**2.
-(a + 151)**2/4
Let j(u) be the first derivative of u**3/3 - 21*u**2/2 + 20*u + 802. Find y, given that j(y) = 0.
1, 20
Let a(n) be the third derivative of n**6/24 + 25*n**5/12 - 35*n**4/2 - 45*n**2 - 4. Factor a(w).
5*w*(w - 3)*(w + 28)
Factor 3610*a + 52 - 3565*a + 38 + 5*a**2.
5*(a + 3)*(a + 6)
Let b(c) be the second derivative of -13*c**7/1540 - 19*c**6/330 + c**5/55 - 15*c**4/4 + 52*c. Let l(r) be the third derivative of b(r). Factor l(w).
-6*(w + 2)*(39*w - 2)/11
Let w(a) be the third derivative of -a**6/720 + 31*a**5/180 - 275*a**4/48 - 121*a**3 + a**2 - 546*a. Factor w(o).
-(o - 33)**2*(o + 4)/6
Let l(m) be the first derivative of 375*m**4/4 + 10*m**3 + 2*m**2/5 + 77*m + 58. Let j(y) be the first derivative of l(y). Find w, given that j(w) = 0.
-2/75
Let x(l) = -2*l**3 - l - 1. Let w be x(-1). Let f(n) = -10*n**3 + 112*n**2 + 3*n - 272. Let o be f(11). Solve -2/3*z**4 + 2*z**o + 0 - 8/3*z + 0*z**w = 0 for z.
-1, 0, 2
Let k(s) = 13*s**4 + 83*s**3 + 80*s**2 - 106*s - 78. Let l(m) = -220*m**4 - 1410*m**3 - 1360*m**2 + 1805*m + 1325. Let t(d) = 35*k(d) + 2*l(d). Solve t(v) = 0.
-4, -2, -2/3, 1
Let i(l) be the second derivative of -l**7/252 + l**6/18 + 13*l**5/30 + 7*l**4/9 + 15*l - 11. Factor i(k).
-k**2*(k - 14)*(k + 2)**2/6
Solve 30*h + 0 - 5/3*h**5 - 25/3*h**4 - 5/3*h**3 + 35*h**2 = 0.
-3, -1, 0, 2
Let f be 128/5568 + (-767740)/(-28014). Factor -304/7*n - 24*n**2 - 36/7*n**3 - 2/7*n**4 - f.
-2*(n + 2)**3*(n + 12)/7
Determine f, given that 24*f + 43*f + 96 + f**3 - 2*f**2 - 99*f = 0.
-6, 4
Let m(b) = -3*b - 41. Let d be m(-15). Determine t so that -d*t**3 + 243*t - 45*t + 116*t**2 - 26 + 150 + 46*t = 0.
-1, 31
Let r(q) = 23*q**3 - 2180*q**2 + 4290*q + 7338. Let o(a) = 11*a**3 - 1090*a**2 + 2145*a + 3636. Let k(d) = -13*o(d) + 6*r(d). Factor k(x).
-5*(x - 216)*(x - 3)*(x + 1)
Let -64*d - d**4 - 62*d**2 - 9*d**4 + 133 - 172 + 111 + 66*d**3 - 2*d**5 = 0. Calculate d.
-9, -1, 1, 2
Suppose 62*j + 27*j = 356. Let o be ((-156)/(-780))/(6/j + 0). Factor o*w**2 - 44/15*w + 242/15.
2*(w - 11)**2/15
Suppose -2360/3*i + 587*i**2 + 3*i**3 + 788/3 = 0. What is i?
-197, 2/3
Find k such that -12/7 + 4/7*k**4 + 26/7*k + 10/7*k**5 - 36/7*k**3 + 8/7*k**2 = 0.
-2, -1, 3/5, 1
Let z(k) = -9*k**4 + 144*k**3 - 153*k**2 - 3*k. Let s(m) = 7*m**4 - 147*m**3 + 152*m**2 + 2*m. Let x(n) = 3*s(n) + 2*z(n). Suppose x(j) = 0. Calculate j.
0, 1, 50
Let s be 222/(-24) - (-14)/56 - (-447)/45. Determine i, given that 16/15*i + 2/15*i**2 + s = 0.
-7, -1
Let d(p) be the third derivative of -p**8/1848 - p**7/1155 + 37*p**6/330 - 57*p**5/55 + 189*p**4/44 - 9*p**3 + 6*p**2 + 37. Let d(c) = 0. What is c?
-11, 1, 3
Let c(w) be the first derivative of -1444*w**5/25 - 912*w**4/5 - 768*w**3/5 + 3872. Factor c(n).
-4*n**2*(19*n + 24)**2/5
Factor 2*b + 551/5 - 1/5*b**2.
-(b - 29)*(b + 19)/5
Let w be (-231)/154*5/(-6). Let f(z) be the first derivative of 0*z**3 - 15 + w*z**4 + 0*z + 0*z**2. Suppose f(p) = 0. Calculate p.
0
Suppose 1620*x - 2*x**5 + 2617*x**3 - 1111*x**3 - 241*x**3 + 7*x**5 + 1329*x**2 - 4389*x**2 + 170*x**4 = 0. What is x?
-18, 0, 1
Solve 32/11*f + f**4 + 12 - 103/11*f**2 + 9/11*f**3 - 1/11*f**5 = 0 for f.
-3, -1, 2, 11
Let a be 4/5*(9436/392 + -23). Suppose 4/7*p**2 + 5/7*p - 4/7*p**4 + 1/7*p**5 - a*p**3 + 0 = 0. Calculate p.
-1, 0, 1, 5
Let y = 1552037/3 - 517331. Suppose 242/3 + y*p + 2/3*p**2 = 0. What is p?
-11
Let l be (12 + -13)/((6/(-4))/3). What is m in -11*m**3 + 2*m**4 - 28*m**3 + 51*m**2 - 37*m**2 - 34*m**l = 0?
-1/2, 0, 20
Let a be (14 - -35) + 6 + -1. Let u = 56 - a. Solve 22*k**u - k**4 + 13*k**5 - 12*k**3 + 4 - 1 + 0*k**2 - 14*k - 11*k**5 = 0 for k.
-3, 1/2, 1
Let m be (12/(-90))/(-9 - -8 - 2262/(-2280)). Factor 0*c + 722/9*c**4 + m*c**3 + 0 + 8/9*c**2.
2*c**2*(19*c + 2)**2/9
Factor 2/7*r**3 + 93312/7*r + 864/7*r**2 + 0.
2*r*(r + 216)**2/7
Let y(c) be the first derivative of c**5/6 - c**4/3 + 4*c**3/15 - 39*c**2/2 - 2*c - 70. Let w(u) be the second derivative of y(u). Determine h so that w(h) = 0.
2/5
Let b(k) be the third derivative of k**5/60 - 496*k**4/3 + 1968128*k**3/3 - 10*k**2 + 14*k + 2. Factor b(d).
(d - 1984)**2
Let q(a) be the third derivative of a**5/160 - 145*a**4/64 + 143*a**3/8 - 418*a**2. Solve q(w) = 0 for w.
2, 143
Let m be (-1127)/(-2415)*(-2)/(-35)*5. Let -14/15 - 16/15*j - m*j**2 = 0. Calculate j.
-7, -1
Suppose 4*c - 30 = -2*p, -3*p + 23 = 2382*c - 2387*c. Factor 0*y + 1/5*y**c - 2/5*y**3 + 0 + 1/5*y**4.
y**2*(y - 1)**2/5
Let r = -2819599/140 - -20140. Let l(i) be the third derivative of 5/14*i**3 + 0*i - 1/14*i**4 + 0 - r*i**5 + 36*i**2. Suppose l(v) = 0. Calculate v.
-5, 1
Let g = 276 + -274. Factor -87*f - f**2 + 3*f**g + f**2 - 123*f + 3675.
3*(f - 35)**2
Let w(j) = -116*j**2 - 134*j + 6. Let p(f) = -2*f + 6. Let t(n) = 3*p(n) - w(n). Determine u so that t(u) = 0.
-1, -3/29
Suppose -16 = -s + 4*z, s - 16 = -4*s + 4*z. Suppose 9 = 3*g + 3*n, 2*g + s*n = n + 15. Factor 3*k**2 + 0*k - 3*k - g*k**2 + 6.
-3*(k - 1)*(k + 2)
Let z be (222/15 - 0) + (-12)/(-60). Solve 0 + 3*u + 11 - 2 + 6*u**2 - 3*u**3 - z*u**2 = 0 for u.
-3, -1, 1
Let v(d) = -d**4 + 13*d**3 + 25*d**2 - 17*d - 4. Let a(t) = -t**2 - 8*t - 1. Let l(g) = -4*a(g) + v(g). Factor l(n).
-n*(n - 15)*(n + 1)**2
Suppose -1548*l + 2468 = -291 - 337. Let a = 4 - 4. Factor a - 2/5*n**l - 3/5*n + 1/5*n**3.
n*(n - 3)*(n + 1)/5
Let k = 541 + -538. Let v(o) be the second derivative of 0*o**k - 16*o + 0 - 1/90*o**4 + 1/15*o**2. Factor v(c).
-2*(c - 1)*(c + 1)/15
Factor -500000000*c - 900000*c**3 + 10000000000/3 + 30000000*c**2 + 13500*c**4 - 81*c**5.
-(3*c - 100)**5/3
Let g(f) be the second derivative of -f**7/63 + 34*f**6/45 - 349*f**5/30 + 170*f**4/3 - 100*f**3 - 895*f. Solve g(n) = 0.
0, 2, 15
Factor -948 - 3*a**3 - 64*a - 191*a - 311*a**2 - 705*a + 62*a**2.
-3*(a + 2)**2*(a + 79)
Let n be (4/2)/(-7 + (-460)/(-60)). Let t be 1 + (n - (-192)/(-54)). Let t*f**3 - 1/9*f**4 - 2/9*f**2 + 1/3 - 4/9*f = 0. What is f?
-1, 1, 3
Let f = -882350 + 4411751/5. Solve -f*i**5 + 2/5*i**3 - 2/5 + 7/5*i + 2/5*i**4 - 8/5*i**2 = 0 for i.
-2, 1
Let z = 2384 - 2381. Suppose -3*q + 4 = -2. Suppose q*h**3 - 8*h + 4*h + 2*h**z = 0. What is h?
-1, 0, 1
Let q be (47/3)/((95/(-630))/19). Let l = -1972 - q. Suppose t + 1/3*t**l + 2/3 = 0. Calculate t.
-2, -1
Suppose 35*s - 359 - 656 = 0. Factor 9*z**2 + 3*z**3 - 32*z - s*z + 58*z + 0*z**3 - 9.
3*(z - 1)*(z + 1)*(z + 3)
Let j(q) = -3*q**3 + 23*q**2 - 56*q + 44. Let v(a) = -54 - 50 + 26*a**3 - 20*a**3 + 113*a - 47*a**2 + 18. Let r(p) = -7*j(p) - 4*v(p). Factor r(g).
-3*(g - 6)*(g - 2)*(g - 1)
Suppose 16*c - 116 = -13*c. Solve 3*y**4 + 4*y**3 + 0*y**4 + 0*y**2 + 3*y**2 - c*y - 4*y**4 - 2*y**2 = 0 for y.
-1, 0, 1, 4
Let s(x) be the third derivative of -x**6/1020 - 3*x**5/170 + 11*x**4/102 - 826*x**2. Suppose s(a) = 0. Calculate a.
-11, 0, 2
Let s be (4/(-56)*-4)/(18/126). Let t = -8 + 41. Factor -s - 9 + t*u - 20 + 13 - 9*u**2.
-3*(u - 3)*(3*u - 2)
Find p,