92*d**3/3 - 14*d**2 - 27. Find c, given that u(c) = 0.
-276, -1
Factor 48*r**3 - 5*r**4 - 2573*r**2 + 822*r**2 - 9000*r - 1356*r**2 - 1993*r**2 - 358*r**3.
-5*r*(r + 2)*(r + 30)**2
Let y(r) = 22*r**5 + 33*r**4 - 19*r**3 + 3*r**2 - 78. Let l(u) = 5*u**5 + 8*u**4 - 5*u**3 + u**2 - 18. Let m(c) = 26*l(c) - 6*y(c). Factor m(q).
-2*q**2*(q - 2)**2*(q - 1)
Let k(r) be the third derivative of r**4/12 - r**3/6 - 10*r**2. Let b be k(2). Let -b*c - 6*c**2 - 3*c**3 + 5*c**2 - 5*c**2 = 0. What is c?
-1, 0
Let z(m) be the second derivative of 16*m**6/45 - 14*m**5/5 - 743*m**4/72 + 259*m**3/3 + 1369*m**2/3 + 10*m + 71. Factor z(f).
(f + 2)**2*(8*f - 37)**2/6
Let s(u) = 9*u**3 - 27*u**2 - 80*u. Let l(x) = -4*x - 227*x**3 - 9*x**2 - 24*x + 457*x**3 - 227*x**3. Let i(d) = -11*l(d) + 4*s(d). Let i(b) = 0. Calculate b.
-1, 0, 4
Let y(u) be the second derivative of -u**7/14 - 13*u**6/10 + 9*u**5/20 + 41*u**4/4 + 13*u**3 + 27*u + 14. Determine r, given that y(r) = 0.
-13, -1, 0, 2
Suppose -20556*d**4 - 9*d + 20520*d**4 + 14*d + 76*d - 6*d**2 - 84*d**3 + 42 + 3*d**5 = 0. What is d?
-1, 1, 14
Suppose 2*j - 2*t + 198 = 0, 32*j + 4*t = 28*j - 388. Let i be (-56)/j*7/2. Factor 1/2*h**3 + 0*h + 0 - 5/2*h**i.
h**2*(h - 5)/2
Factor 74/3*n**2 + 40/3 + 32*n + 6*n**3.
2*(n + 1)*(n + 2)*(9*n + 10)/3
Let t(k) be the first derivative of -2*k**5/55 + 1579*k**4/11 - 4992794*k**3/33 + 4983324*k**2/11 - 4980168*k/11 + 4987. Factor t(v).
-2*(v - 1578)**2*(v - 1)**2/11
Let u(b) be the first derivative of 2*b**5/95 - 2*b**4/19 - 44*b**3/57 + 4*b**2/19 + 42*b/19 + 1300. Suppose u(s) = 0. What is s?
-3, -1, 1, 7
Let t(x) = 120*x**3 + 412*x**2 + 152*x + 16. Let u(j) = -41*j**3 - 137*j**2 - 51*j - 6. Let d(i) = 3*t(i) + 8*u(i). Let d(q) = 0. What is q?
-4, -3/8, 0
Let d = 78/355 + -241/1420. Let n(j) be the first derivative of 4/15*j**3 + 19 + 6/5*j + d*j**4 - 11/10*j**2. Suppose n(i) = 0. What is i?
-6, 1
Factor -180 + 603 + 5*h**2 + 694 + 13 - 383*h - 192*h.
5*(h - 113)*(h - 2)
Let z(c) be the second derivative of -27/140*c**5 - 5 + 85/14*c**3 + 1/70*c**6 + 9/28*c**4 - 225/7*c**2 - 9*c. Solve z(s) = 0.
-3, 2, 5
Let w = -1041582/7 + 148798. Factor w*r**4 + 0*r**3 + 0 + 8/7*r - 12/7*r**2.
4*r*(r - 1)**2*(r + 2)/7
Let k(g) be the first derivative of -14 - 1/10*g**5 + 0*g**2 - 2*g**3 - 7/6*g**4 - 13*g. Let m(r) be the first derivative of k(r). Factor m(u).
-2*u*(u + 1)*(u + 6)
Let g(t) be the first derivative of -t**4/8 + 5*t**3/2 - 12*t**2 - 32*t + 985. Determine n, given that g(n) = 0.
-1, 8
Let p(o) be the first derivative of o**6/180 - 13*o**5/30 + 25*o**4/12 - 128*o**3/3 - 62. Let w(d) be the third derivative of p(d). Factor w(l).
2*(l - 25)*(l - 1)
Let z be (-3)/(-1) + -3 + 2. Let j = -799 + 805. Factor -j*v**3 - v**3 + 4*v**3 + 9*v**z + 13*v - v.
-3*v*(v - 4)*(v + 1)
Let j be 44/28 - (-40)/(-70). Factor 284*c**2 + 23 + 8*c - 15 - j - 7 + 276*c**3.
4*c*(c + 1)*(69*c + 2)
Let k be (1/3)/(1/9). Factor 4 - k*i**2 + 3*i**3 - i**2 - 10*i + 12*i**2 - 5*i**3.
-2*(i - 2)*(i - 1)**2
Let f(t) be the third derivative of -t**5/540 - 311*t**4/72 + 467*t**3/27 - 15*t**2 - 75*t. Factor f(x).
-(x - 1)*(x + 934)/9
Find y, given that 21/4*y + 1/4*y**5 - 11/2*y**3 - y**2 + 0 + y**4 = 0.
-7, -1, 0, 1, 3
Let m(q) be the first derivative of 3*q**5/5 + 519*q**4/4 + 7568*q**3 + 11094*q**2 - 3090. Factor m(g).
3*g*(g + 1)*(g + 86)**2
Suppose 4*s + 2*j + 191 - 399 = 0, 4*s - 184 = j. Factor 4/3*g**2 + s + 16*g.
4*(g + 6)**2/3
Let o(f) = -31*f + 901. Let k be o(29). Let i(p) be the second derivative of 0*p**k - 1/12*p**3 + 8*p + 1/16*p**4 + 0. Factor i(t).
t*(3*t - 2)/4
Factor -3/2*s**3 - 2853/2*s**2 - 904401/2*s - 95565039/2.
-3*(s + 317)**3/2
Suppose 2*x = -5*w + 16, 14 + 4 = 3*w + 4*x. Suppose 10 + 3 - 20*a + 4*a**w + 12 - 9 = 0. What is a?
1, 4
Let p(a) = a**2 - 2*a - 11. Let k be p(5). Suppose k*l = 5*z + 1118, -5*l + 2*z = 173 - 1562. Factor y**2 - 277*y + l*y + y**3.
y**2*(y + 1)
Factor -47*p + 6*p**2 + p**2 - 14*p - 2*p**2 - 44*p - 360.
5*(p - 24)*(p + 3)
Let i(s) = -s**2 - 4*s + 16. Let u be i(-6). Factor -3*w**4 - 4*w**5 + 128*w + 83*w**2 - 5*w**u + 77*w**2 + 48*w**3.
-4*w*(w - 4)*(w + 2)**3
Let q(i) be the third derivative of -49*i**6/40 + 73*i**5/10 + 3*i**4/8 - 2*i**2 - 2736. Factor q(w).
-3*w*(w - 3)*(49*w + 1)
Suppose 13 - 13 = 312*g. Let h(y) be the second derivative of -1/5*y**5 + 1/3*y**6 + g*y**2 + 0*y**3 + 0*y**4 - 1/7*y**7 + 17*y + 0. Factor h(j).
-2*j**3*(j - 1)*(3*j - 2)
Let o = -353 - -358. Determine a, given that -8*a**5 + 6*a**o - 6*a**4 + 10*a**3 + 10*a**2 - 8*a - 4*a**2 = 0.
-4, -1, 0, 1
Suppose 0 = 5*o + 20, 5*d + 4*o + 0 - 4 = 0. Determine f so that -24*f**3 - 751*f + 72*f**2 + 374*f + 2*f**d + 377*f = 0.
0, 6
Let d(v) be the second derivative of -v**5/30 + 121*v**4/18 - 1301*v. Solve d(u) = 0.
0, 121
Let s(l) be the third derivative of -l**6/180 - l**5/10 - 3*l**4/4 - 13*l**3/6 - 8*l**2 + l. Let r(x) be the first derivative of s(x). Solve r(o) = 0 for o.
-3
Find f such that -82*f**3 + 22*f**3 + 8*f + 35*f**3 + 152 + 23*f**3 - 38*f**2 = 0.
-19, -2, 2
Let u = 153 - 77. Let m = u - 19. Factor -m - 4*f**4 + 57 + 4*f**2.
-4*f**2*(f - 1)*(f + 1)
Let u(l) be the second derivative of -l**4/90 + 194*l**3/45 + 1277*l. Factor u(z).
-2*z*(z - 194)/15
Solve -9*g**2 - 91*g**2 + 25*g**4 - 16*g - 13640*g**5 + 13610*g**5 - 4*g + 125*g**3 = 0.
-2, -1/6, 0, 1, 2
Let m be -3 - (-1 - (-3 - -8)). Suppose -26*t - 3*t**3 - 8*t**2 + 2*t**m - 6*t**2 - 14*t**2 - 16 + 17*t**2 = 0. Calculate t.
-8, -2, -1
Factor 19/2 + 3/2*d**3 + 77/2*d + 61/2*d**2.
(d + 1)*(d + 19)*(3*d + 1)/2
Let a(t) = -5*t**2 + t**3 - 4 + 1 - 3*t - 11. Let d be a(6). Determine x so that -d*x**4 + 5*x**4 + 2*x**3 - 2*x**2 + 3*x**2 = 0.
-1, 0
Let y(g) = -g**3 + 11*g**2 - 68*g + 97. Let z(b) = -4*b + 3*b - 3*b**2 + 2*b**2 - 1. Let p(n) = 2*y(n) - 6*z(n). Suppose p(h) = 0. Calculate h.
4, 5
Suppose -r + 4*b - 7 = 12, -3*r + b - 68 = 0. Let m(q) = q**2 + 24*q + 26. Let f be m(r). Solve -1/3*a**2 + 0 + 1/3*a**4 + 0*a + 0*a**f = 0.
-1, 0, 1
Factor 7038409/6 + 1/6*r**2 + 2653/3*r.
(r + 2653)**2/6
Let w(s) be the second derivative of s**7/21 - 13*s**6/15 - 3*s**5/2 + 171*s**4/2 - 162*s**3 - 526*s. Find i, given that w(i) = 0.
-6, 0, 1, 9
Let t(m) be the first derivative of -5/6*m**2 + 1/9*m**3 + 1/15*m**5 + 7/12*m**4 + 62 - 2/3*m - 1/9*m**6. Find q, given that t(q) = 0.
-1, -1/2, 1, 2
Let u(l) be the third derivative of -l**7/105 + 3*l**6/20 - 19*l**4/3 + 32*l**3 + 2195*l**2 + 2. Factor u(q).
-2*(q - 8)*(q - 2)**2*(q + 3)
Suppose 18*o = 22*o - 8. Determine b, given that -22*b**3 + 20*b**3 + 2*b**o - 12*b + 8*b**2 + 0*b**2 = 0.
0, 2, 3
Let x(o) be the second derivative of -o + 26/3*o**3 + 22 + 14/15*o**6 + 2/21*o**7 + 22/3*o**4 + 6*o**2 + 18/5*o**5. Factor x(u).
4*(u + 1)**4*(u + 3)
Suppose 0*h = -4*h. Suppose -j + 3 = 3*x + 2, h = -5*x + 5*j + 35. What is q in -2*q**x + 11*q**2 + 6*q - q**4 - q**4 - q**4 = 0?
-1, 0, 2
Factor 2/3*k**2 + 100/3*k + 150.
2*(k + 5)*(k + 45)/3
Let n(a) = a**3 + 3*a**2. Let o(k) = 12*k**3 - 228*k**2 - 588*k - 148. Let i(t) = -20*n(t) + 4*o(t). Factor i(b).
4*(b - 37)*(b + 2)*(7*b + 2)
Let h = 553729/3 - 184568. Solve 1/3*i**2 + 46/3 - h*i = 0 for i.
2, 23
Let z(f) be the first derivative of -3*f**5/25 - 19*f**4/20 + f**3/2 + 175*f - 162. Let g(c) be the first derivative of z(c). Factor g(q).
-3*q*(q + 5)*(4*q - 1)/5
Let l be 2/((-6)/3)*-324. Let n = l - 647/2. Suppose -w - n - 1/2*w**2 = 0. What is w?
-1
Factor 2/9*m**5 - 8080/9*m**2 + 920/9*m**3 + 17920/9*m - 12544/9 + 100/9*m**4.
2*(m - 2)**3*(m + 28)**2/9
Let k(p) be the first derivative of 3*p**4/4 + 198*p**3 + 1761*p**2/2 + 1170*p - 9928. Factor k(b).
3*(b + 1)*(b + 2)*(b + 195)
Solve -400/3 + 1/3*b**2 - 14*b = 0.
-8, 50
Let 12 + s + 1/4*s**3 - 2*s**2 = 0. Calculate s.
-2, 4, 6
Let k = 273011/5 + -267239/5. Let m = 1156 - k. Determine o, given that -m + 4/5*o**2 - 4/5*o = 0.
-1, 2
Determine z, given that 1168/7 - 134/7*z**3 + 852/7*z**2 - 2/7*z**4 - 248*z = 0.
-73, 2
Factor -28*d**2 + 59885 + 480*d - 61613 - 6536*d.
-4*(d + 216)*(7*d + 2)
Let f(j) be the second derivative of -864/5*j**5 - 416/3*j**3 + 0 + 32*j**2 - 162*j**6 + 486/7*j**7 + 856/3*j**4 - 8*j. Let f(x) = 0. Calculate x.
-1, 2/9, 2
Suppose -3*k + 949 + 41 = 0. Let 514*u**3 - 200 - k*u**2 + 462*u**4 