r 16/3 + r*k**2 - 8*k.
(3*k - 4)**2/3
Let x(c) be the first derivative of -c**4/7 + 32*c**3/7 + 102*c**2/7 + 104*c/7 + 1359. Determine a, given that x(a) = 0.
-1, 26
Let o(i) = i**2 + 2850*i - 5721. Let u(q) = 2*q**2 + 9. Let t(a) = o(a) + u(a). Factor t(b).
3*(b - 2)*(b + 952)
Let a(y) be the third derivative of y**6/30 + 26*y**5/5 + 387*y**4/2 - 29584*y**3/3 - 1818*y**2 - 2. Let a(t) = 0. What is t?
-43, 8
Let x(j) be the first derivative of -98*j**5/5 - 364*j**4/5 + 472*j**3/5 + 2944*j**2/5 + 2048*j/5 + 1115. Suppose x(m) = 0. Calculate m.
-16/7, -2/5, 2
Let u be (2 + -4)*(-79)/(-14)*43. Let n = 487 + u. Solve -15/7*i - 3/7*i**3 - 6/7 - n*i**2 = 0.
-2, -1
What is k in k**2 - 11*k**2 + 4*k**3 + 23*k**3 - 17*k - 23*k**2 + 12 - 31*k = 0?
-1, 2/9, 2
Let l(s) be the first derivative of 2*s**5/3 + 43*s**4/6 + 44*s**3/9 - 16*s**2/3 + 1535. Solve l(p) = 0.
-8, -1, 0, 2/5
Let r(z) = 11*z + 37. Let a = 81 - 65. Let l be r(a). Factor s + l*s**2 + 3*s - 223*s**2.
-2*s*(5*s - 2)
Suppose 73*j - 386*j - j - 105 + 794003*j**2 + j**4 - 102*j**3 - 794315*j**2 = 0. What is j?
-1, 105
Let q(k) be the third derivative of 0 - 1/90*k**6 + 11*k**2 + 0*k**5 + 1/6*k**4 - 11/3*k**3 + 0*k. Let w(s) be the first derivative of q(s). Factor w(g).
-4*(g - 1)*(g + 1)
Let g(z) be the first derivative of z**3/7 - 978*z**2/7 + 318828*z/7 + 3249. Find r such that g(r) = 0.
326
Let t(k) be the first derivative of k**6/6 - 5*k**5/4 - 5*k**4/12 + 25*k**3/6 - 53*k - 3. Let d(u) be the first derivative of t(u). What is b in d(b) = 0?
-1, 0, 1, 5
Let g(n) be the second derivative of -n + 8 + 1/60*n**5 + 0*n**3 + 0*n**2 - 7/36*n**4. Factor g(m).
m**2*(m - 7)/3
Suppose -g + 2*l + 110 = g, -3*g - 4*l + 193 = 0. Let u = g + 729. Determine m so that -u*m + 4*m**3 - m**2 + 3*m**4 + 786*m + 0*m**3 = 0.
-1, 0, 2/3
Let r(g) = -g**3 + 4*g**2 - g + 9. Let i be r(4). Let 7*u**5 + 9*u**5 + 10*u**5 + 85*u**2 + 115*u**4 - 11*u**i + 265*u**3 - 180 - 300*u = 0. Calculate u.
-3, -2, -2/3, 1
Let l(b) be the second derivative of -b**5/540 - b**4/72 + b**3/3 + 37*b**2 - 146*b. Let x(z) be the first derivative of l(z). Determine v, given that x(v) = 0.
-6, 3
Determine o, given that 1459/3*o - 4/3*o**3 + 365/3 + 1456/3*o**2 = 0.
-1/2, 365
Let c(u) = u**2 - 5*u - 33. Let d be c(9). Find s, given that 96*s - d*s**2 - 545 + 53 - 276 + 0*s**2 = 0.
16
Let h(r) = -5*r**3 - 3*r**2 - 3*r + 7. Let p(v) = 34*v + 303. Let q be p(-9). Let i(b) = 4*b**3 + 4*b**2 + 2*b - 7. Let k(l) = q*h(l) - 4*i(l). Factor k(u).
-(u - 1)*(u + 1)*(u + 7)
Let t(y) be the first derivative of -147/4*y**4 - 1596*y**3 - 1350*y**2 + 29 - 384*y. Let t(r) = 0. Calculate r.
-32, -2/7
Let p(s) be the third derivative of s**7/105 - 2*s**6/15 - 8*s**5/5 + 64*s**4/3 + 1024*s**3/3 - 1187*s**2. Solve p(f) = 0.
-4, 8
Let w be -14*(((-1862)/35 - 5) + -4). Let y = -868 + w. Determine a so that 2/5*a**3 - 12/5 + 0*a**2 - y*a = 0.
-2, -1, 3
Let s = 36482/1147875 - -2/9183. Let j = 383/250 - s. Factor j*r + 0 - 1/4*r**2 - 5/4*r**3.
-r*(r - 1)*(5*r + 6)/4
Let u be ((-372)/(-24) - 15)*(-56)/(-566). Let t = 7652/5943 - u. Factor -t*k**2 + 22/21*k + 4/21.
-2*(k - 1)*(13*k + 2)/21
Let m(j) be the third derivative of -j**6/720 - 187*j**5/360 - 277*j**4/72 - 92*j**3/9 - 2*j**2 - 441*j - 3. Factor m(f).
-(f + 1)*(f + 2)*(f + 184)/6
Suppose 3 = -3*h, -7*h + 9*h - 8 = -5*y. Suppose 7*j = 2*j + 5, y*z + j = 9. Factor -2*l + 657*l**4 - 9*l**3 - 7*l**2 + z - l**5 - 662*l**4 - 4.
-l*(l + 1)**3*(l + 2)
Let c(p) be the second derivative of p**6/240 + 19*p**5/160 + 9*p**4/8 + 8*p**3/3 - 16*p**2 + 540*p + 2. Factor c(f).
(f - 1)*(f + 4)*(f + 8)**2/8
Let d be (2 + (-2 - 2))*13. Let q = d - -29. Factor -b**2 + 2*b**q - b**4 + 2*b**4 - 8*b + 6*b.
b*(b - 1)*(b + 1)*(b + 2)
Suppose 299 - 150*c**4 - 102*c**2 - 485*c + 61*c**2 - 143*c**2 + 31 - 5*c**5 + 4*c**2 + 490*c**3 = 0. What is c?
-33, -1, 1, 2
Factor 3/8*p**3 + 63/4*p + 0 + 69/8*p**2.
3*p*(p + 2)*(p + 21)/8
Let k(p) be the first derivative of -p**3/18 + 29*p**2/12 + 31*p/3 + 1475. Factor k(s).
-(s - 31)*(s + 2)/6
Let f be (1/15)/((-1)/(-143)) - (9 - (-138)/(-18)). Determine z so that 1/5 + f*z**2 - 22/5*z - 4*z**3 = 0.
1/20, 1
Let j be (((-3)/300)/1)/((-2)/4). Let s(f) be the second derivative of -3/25*f**5 + 1/10*f**4 + 2/5*f**3 + 0 + j*f**6 - 9/10*f**2 - 24*f. Solve s(q) = 0.
-1, 1, 3
Let n(u) be the first derivative of 35*u**4/24 - 64*u**3/9 - 4*u**2 - 6243. Factor n(o).
o*(o - 4)*(35*o + 12)/6
Let m(u) = 35*u**2 - 9 - 26*u**2 - 12*u - 17*u**2 - 7*u. Let h(i) = -2*i**2 - 4*i - 2. Let l(j) = -9*h(j) + 2*m(j). Factor l(r).
2*r*(r - 1)
Let a(h) = -h**2 - 7*h + 21. Let b be a(-5). Factor -11*u**3 - b + 11 - 11*u**2 - 68*u**2 - 168*u + 44*u.
-(u + 2)*(u + 5)*(11*u + 2)
Solve 34/13*w**3 + 240/13*w + 0 - 2/13*w**4 - 164/13*w**2 = 0 for w.
0, 3, 4, 10
Let n(k) be the first derivative of -2*k**5/45 + 104*k**4/9 - 20348*k**3/27 - 22256*k**2/3 - 22898*k + 1188. Factor n(f).
-2*(f - 107)**2*(f + 3)**2/9
Find t such that 159/4*t**2 - 804*t + 315 + 15/4*t**3 = 0.
-21, 2/5, 10
Suppose 1286*y + 469*y - 489 - 2509 = 512. Factor -4/7*m**y - 6/7*m**3 + 54/7*m + 36/7.
-2*(m - 3)*(m + 3)*(3*m + 2)/7
Let d be -3 - 9/(4*1/(-48)). Suppose -78*m = -d*m. Factor m - y + 10/9*y**2 - 1/9*y**3.
-y*(y - 9)*(y - 1)/9
Let f be 145/(-2175) + (-10)/(-15). Factor f + 11/5*l**2 + 14/5*l.
(l + 1)*(11*l + 3)/5
Let p = -348 + -493. Let y = 843 + p. Determine l, given that -4/3*l**4 + l**y - 2/3 + 5/3*l - 8/3*l**3 = 0.
-2, -1, 1/2
Let g(x) be the first derivative of -1/6*x**4 + 1/3*x + 2/9*x**3 + 1/2*x**2 - 62 - 1/18*x**6 - 1/5*x**5. Solve g(h) = 0 for h.
-1, 1
Let r = -351732 - -1407135/4. What is i in r*i**2 + 3/8*i**4 + 39 - 93/8*i**3 - 159/2*i = 0?
1, 2, 26
Suppose -3 = -2*k + 1. Factor -108*f**3 - 8*f**k + 2*f**2 + 3*f + 111*f**3.
3*f*(f - 1)**2
Let w(x) be the third derivative of 9*x**7/7 - 87*x**6/40 + x**5/2 + 181*x**2 - 3. Factor w(o).
3*o**2*(6*o - 5)*(15*o - 2)
Suppose c = 7*c - 18. Suppose -r + 10 = 5*y, r - c*r + 4*y = 8. Solve -30*l + 0 + r - 3*l**2 + 8*l**3 - 8 - 21*l**2 = 0.
-1/2, 4
Let d = -1259034 - -1259034. Factor -3*k**2 + 0*k - 8/5*k**3 - 1/5*k**4 + d.
-k**2*(k + 3)*(k + 5)/5
Let k(i) = -i**3 - 15*i - 69. Let l be k(-3). Determine w, given that 8*w**2 + 0 - 18*w + 1/2*w**l = 0.
-18, 0, 2
Suppose -45*x + 7263 = -2412. Let r = -213 + x. Let 7/6*o**r - o - 1/6 = 0. What is o?
-1/7, 1
Suppose 5*z - 161 - 69 = 0. Suppose 4*c - z = 54. Determine w so that 5*w**2 - c*w**2 + 36 - 297*w + 309*w + 4*w**3 = 0.
-1, 3
Suppose -11/3*u**4 + 14/3*u**2 - 5*u**3 + 0*u + 0 = 0. What is u?
-2, 0, 7/11
Let j(h) be the first derivative of 21/4*h**4 - 16*h**3 - 3/2*h**2 + 30*h + 56. Factor j(x).
3*(x - 2)*(x - 1)*(7*x + 5)
Suppose -8 - 12 = 7*g - 41. Let d(u) be the second derivative of 0*u**4 + 1/20*u**5 + 0 + 0*u**2 - 1/6*u**g + 18*u. Factor d(h).
h*(h - 1)*(h + 1)
Let w(y) be the first derivative of 2*y**5/55 - 5*y**4/22 + 4*y**3/33 + 8*y**2/11 - 1985. Determine x so that w(x) = 0.
-1, 0, 2, 4
Determine m, given that 23*m**3 - 41/3*m**4 + 7/6*m + 5/2*m**5 + 1 - 14*m**2 = 0.
-1/5, 2/3, 1, 3
Let y(l) be the third derivative of -l**8/112 - l**7/30 + 3*l**6/10 + 13*l**5/15 - 2*l**4 + 10*l**2 + l - 2. Solve y(b) = 0 for b.
-4, -2, 0, 2/3, 3
Let m(v) be the second derivative of -v**9/3024 - v**8/1344 + v**7/56 + v**6/16 + 8*v**4 + 108*v. Let j(t) be the third derivative of m(t). Factor j(l).
-5*l*(l - 3)*(l + 1)*(l + 3)
Let f(i) = 10*i**2 + i - 11. Let d(k) = 9*k**2 + k - 10. Let a(u) = 5*d(u) - 4*f(u). Let n(p) = -p**2 + p. Let b(g) = -a(g) - 4*n(g). Find w such that b(w) = 0.
-6, 1
Let m be (-2)/(((-20)/(-50))/((-21)/5)). Suppose m = 13*y - 31. Factor 70*t - t**2 + y - 2*t**2 - 76*t + 5.
-3*(t - 1)*(t + 3)
Let g(d) be the second derivative of 172*d - 1 - 7/9*d**3 + 1/18*d**4 - 8/3*d**2. Find f such that g(f) = 0.
-1, 8
Suppose -4*x + 2*y - 9005 + 8999 = 0, 0 = -3*x - 5*y + 67. Solve -72/7*n**2 + 108/7*n**x + 54*n - 220/7*n**3 + 108/7 - 2*n**5 = 0.
-1, -2/7, 3
Let c(s) = 35*s - 6*s**2 - 60*s + 10 + 1. Let d(r) = 17*r**2 + 74*r - 33. Let u(k) = -11*c(k) - 4*d(k). Let u(m) = 0. What is m?
-11, 1/2
Let c = 1305176 - 3915526/3. Suppose 0 - 4/3*q - c*q**2 = 0. What is q?
-2, 0
Let y(g) be the third derivative of -50 + 0*g + 1/78*g**5 - 10/39*g**3 - 2*g**2 + 23/15