g - 2)
Let c(k) = k**3 - 17*k**2 - 40*k - 43. Let n be c(19). Let l be (32/(-3))/(270/n). What is j in -10*j**3 - 16/5*j**4 - 2/5*j**5 - 76/5*j**2 - 56/5*j - l = 0?
-2, -1
Let r(b) be the first derivative of 3*b**4/8 - 12*b**3 + 60*b**2 + 901. What is u in r(u) = 0?
0, 4, 20
Let l(v) be the second derivative of 0*v**2 + 39*v + 0 + 1/6*v**3 - 11/48*v**4 + 7/80*v**5. Factor l(n).
n*(n - 1)*(7*n - 4)/4
Let a be 15*(-176)/(-330) + (-324)/42. Factor 40/7*w + 200/7 + a*w**2.
2*(w + 10)**2/7
Let 16751307/2 + 3/2*s**2 - 7089*s = 0. Calculate s.
2363
Let y be 2/(-8) - (-349)/4. Let b = y + -71. Let -2*j**2 - 5*j**4 + 11*j - 15*j**3 - 13*j**2 + 0*j**2 - b*j = 0. Calculate j.
-1, 0
Suppose -h + 7*p + 23 = 0, -21*h + 20*h + 5*p = -17. What is j in 1/5*j**h + 2*j + 9/5 = 0?
-9, -1
Let v(l) be the third derivative of 2*l**2 + 1/350*l**7 + 0*l**4 + 0*l**6 - 3*l - 1/25*l**5 + 0*l**3 + 0. Let v(t) = 0. What is t?
-2, 0, 2
Suppose -92*d**5 + 83*d**5 - 16*d**2 - 310*d**4 + 326*d**2 + 54*d**5 - 45*d**3 = 0. Calculate d.
-1, 0, 1, 62/9
Let s(y) be the third derivative of 0*y - 85*y**2 - 1/10*y**3 + 0 + 1/100*y**6 + 1/350*y**7 + 0*y**5 - 1/20*y**4. Factor s(t).
3*(t - 1)*(t + 1)**3/5
Let g = 13273 + -13271. Let o be 9/(126/32) + -2. Factor 12/7*b + o - g*b**2.
-2*(b - 1)*(7*b + 1)/7
Let p(n) be the third derivative of 1/24*n**6 + 0 - 35/6*n**3 + 0*n - 3/4*n**5 + 154*n**2 + 25/8*n**4. Determine l so that p(l) = 0.
1, 7
Let l(t) be the second derivative of -2*t**6/15 + t**5/2 + 5*t**4/6 - 5*t**3/3 - 3*t**2 - 1319*t. Solve l(x) = 0 for x.
-1, -1/2, 1, 3
Suppose -o + 472 + 8 = -5*y, 470 = o - 3*y. Let h be (7 + o/(-15))*(-3 - 0). Factor 61*i**2 + h*i**2 - 3*i - 134*i**2.
-3*i*(i + 1)
Let m(i) = -17*i**2 - 328*i - 873. Let g(y) = 2*y**2 + 3*y - 2. Let f(r) = 6*g(r) + m(r). Solve f(p) = 0 for p.
-59, -3
Let i(h) be the first derivative of -h**3/15 + 442*h**2/5 + 177*h - 3618. Find v, given that i(v) = 0.
-1, 885
Suppose -1014 = -514*d + 520*d. Let g = d + 169. Factor g*k**2 - 21/4*k - 9/2 + 3/4*k**3.
3*(k - 3)*(k + 1)*(k + 2)/4
Let l be 0 - ((-14)/133 + 756/(-399)). Factor 0*j**l + 1/4*j**4 + 1/4*j**5 + 0*j - 1/2*j**3 + 0.
j**3*(j - 1)*(j + 2)/4
Find b such that 54/5 + 69/5*b**3 - 33*b**2 - 9/5*b**4 + 99/5*b = 0.
-1/3, 2, 3
Let n(m) = 3*m**2 - 140*m - 4532. Let w be n(-22). Let j = 5 - 3. Determine g, given that -3/4*g**j + g + w = 0.
0, 4/3
Factor 96/7 + 75/7*o**2 + 6/7*o**3 + 228/7*o.
3*(o + 4)*(o + 8)*(2*o + 1)/7
Let h(c) be the third derivative of 7/150*c**5 - 1/150*c**6 - 1/525*c**7 + 0*c**3 + 12*c**2 + 8 - 1/15*c**4 + 0*c. Factor h(z).
-2*z*(z - 1)**2*(z + 4)/5
Factor -1367631*m - 3/5*m**5 - 90*m**4 - 5106*m**3 - 131424*m**2 - 11244966/5.
-3*(m + 2)*(m + 37)**4/5
Let l(c) = -2*c**2 + 72*c + 92. Let i(y) = -y**2 + 76*y + 92. Let f(w) = -6*i(w) + 5*l(w). Factor f(g).
-4*(g + 1)*(g + 23)
Let i = -377434 + 377436. Factor -972*o - 54*o**i + 0 - 3/4*o**3.
-3*o*(o + 36)**2/4
Let r(v) be the first derivative of -2*v**3/3 - 4*v**2 + 3*v - 131. Let t be r(-4). Let -1/3*w**t + w + 0*w**2 - 2/3 = 0. What is w?
-2, 1
Let w be (-12)/130*28652/(-1102). Let -21/5*n**3 + 57/5*n - w*n**4 + 66/5*n**2 - 18/5 = 0. Calculate n.
-3, -1, 1/4, 2
Suppose -4*i + 2*d + 10 = 0, 6*i - 4*i - 4*d = -10. Suppose 8*n**2 + 150 + 5*n**2 + 42 - 5*n**2 - i*n**2 + 48*n = 0. Calculate n.
-8
Suppose 36*f - 1203 - 1569 = 0. Let x be (7 + (-517)/f)/((-9)/(-35)). Solve x*k**2 - 2/9*k**3 - 16/9*k + 8/9 = 0.
1, 2
Let m(r) be the first derivative of -2*r**3/3 + 107*r**2 - 420*r - 9454. What is x in m(x) = 0?
2, 105
Let t be (9 - -3)*(-5)/10. Let n be (3/(0 - t))/(2/12). What is f in 7*f**3 + 49*f**5 - 2 + 4*f**2 - 2*f - 51*f**5 - n*f**3 - 2*f**4 = 0?
-1, 1
Let w(s) be the third derivative of -s**6/840 - 31*s**5/140 - 705*s**4/56 + 2209*s**3/42 + 22*s**2 + 16*s. Find y, given that w(y) = 0.
-47, 1
Let k(d) be the first derivative of d**4/12 - 134*d**3/9 + 512*d**2/3 - 672*d - 630. Factor k(t).
(t - 126)*(t - 4)**2/3
Let q = 101 - 97. Factor -3*v**3 + 21*v**2 - 30*v**3 + 37*v**4 + 6*v**3 - 6*v - 22*v**q - 3*v**5.
-3*v*(v - 2)*(v - 1)**3
Solve -57/4*g**2 - 117/2*g - 3/4*g**3 + 0 = 0.
-13, -6, 0
Let z(l) = -3*l + 5. Let x be z(-13). Suppose 0 = -3*f - 3*m + 66, 2*f + 3*m - x = -m. Determine b, given that 18*b + b**2 + 6 - f*b - 3*b**2 = 0.
-3, 1
Let w(k) = k**2 - 1. Let x be w(-3). Factor 11734*h**3 - h**2 - 11731*h**3 - 11*h**2 + x*h + h.
3*h*(h - 3)*(h - 1)
Let s = -161943 - -161946. Suppose 7/2*z**s - 3*z - 1/2*z**5 + 0 + 1/2*z**2 - 1/2*z**4 = 0. Calculate z.
-3, -1, 0, 1, 2
Let q(d) be the third derivative of d**5/240 + 107*d**4/96 + 485*d**3/12 + 5240*d**2. Factor q(f).
(f + 10)*(f + 97)/4
Let i = 82 - 87. Let l(o) = -5*o**4 - 30*o**3 + 40*o**2 + 140*o - 275. Let c(a) = 2*a**4 - a**3 + a**2 - a + 1. Let t(d) = i*c(d) - l(d). Factor t(y).
-5*(y - 3)**3*(y + 2)
Suppose -30 = -23*u + 13*u. Factor 900*n - u*n**3 - 96 + 853*n - 1669*n - 12*n**2.
-3*(n - 2)**2*(n + 8)
Let t be 248/(15 - 7) + -6. Factor -15 + 21 - 4*x**2 + t + 5.
-4*(x - 3)*(x + 3)
Let g(y) be the first derivative of -y**4 + 4*y**3/3 + 18*y**2 - 36*y + 166. Find k, given that g(k) = 0.
-3, 1, 3
Factor -8/5*d + 2/5*d**3 + 58/5*d**2 - 232/5.
2*(d - 2)*(d + 2)*(d + 29)/5
Let o(s) be the second derivative of s**7/126 - s**6/45 - s**5/5 + 19*s**4/18 - 37*s**3/18 + 2*s**2 - 2*s - 297. Determine m so that o(m) = 0.
-4, 1, 3
Suppose -5*x + 3*s = s - 11, 4*s + 4 = 4*x. Find i, given that -4*i**4 - 216*i**2 + 8*i**3 + 432*i - 324 + 21*i**3 + 14*i**3 + 5*i**x = 0.
3
Let b(v) be the third derivative of -1/5*v**5 - 2/525*v**7 + 0*v + 5/6*v**4 - 3/50*v**6 + 38*v**2 + 0*v**3 + 0. Factor b(w).
-4*w*(w - 1)*(w + 5)**2/5
Let b(z) be the second derivative of z**7/77 + 21*z**6/55 + 387*z**5/110 + 127*z**4/22 - 630*z**3/11 - 1944*z**2/11 - 3*z - 233. Find u, given that b(u) = 0.
-9, -4, -1, 2
Let n(g) be the second derivative of -g - 33/8*g**2 + 5 + 5/4*g**3 + 1/16*g**4. Solve n(r) = 0 for r.
-11, 1
Let j(n) be the first derivative of 2025/2*n**2 + 3/4*n**4 - 10125*n - 45*n**3 + 54. Factor j(f).
3*(f - 15)**3
Let q(m) be the first derivative of 11/2*m**2 + 12*m - 85 - 1/4*m**4 - 2/3*m**3. Suppose q(b) = 0. Calculate b.
-4, -1, 3
Let v(j) be the first derivative of 5/3*j**3 + 155*j**2 + 4805*j + 209. Factor v(b).
5*(b + 31)**2
Factor -21120*g**2 - 2590 - 3976 - 605*g**3 + 23580*g + 86.
-5*(g + 36)*(11*g - 6)**2
Let y(q) be the second derivative of -q**6/180 - q**5/60 - q**3/2 + 7*q**2 - 4*q + 1. Let n(k) be the second derivative of y(k). Factor n(h).
-2*h*(h + 1)
Let a(v) = -v**5 + v**3 + 2. Let x(p) = -25*p**5 + 276*p**4 + 613*p**3 - 420*p**2 - 588*p + 140. Let w(b) = -2*a(b) - x(b). Solve w(d) = 0 for d.
-2, -1, 2/9, 1, 12
Suppose 30 = 3*d + 3*j, 12*d - 59*j - 32 = -60*j. Factor 2/7*q + 6/7*q**3 - 2/7 + 10/7*q**d.
2*(q + 1)**2*(3*q - 1)/7
Let m(j) be the third derivative of -j**6/300 - 43*j**5/50 + 87*j**4/20 - 131*j**3/15 - j**2 + 55. Solve m(o) = 0 for o.
-131, 1
Let m = -1851 + 1822. Let f(v) = -v**2 - 27*v + 61. Let j be f(m). Solve -1/2*s**4 + 1/2*s**2 + 0 - 1/2*s**5 - s + 3/2*s**j = 0 for s.
-2, -1, 0, 1
Suppose 4*p - 2*p - k + 32 = 0, -6 = -p - 5*k. Let s be 49/p*8/(-14). Find y such that 29*y**s + 2*y - 32*y**2 + y = 0.
0, 1
Let f = 213 - 211. Factor 4*m**f + 35*m - 38*m - 28 - 21*m.
4*(m - 7)*(m + 1)
Determine u, given that -660*u**2 - 701*u**3 + 805*u**3 - 4*u**4 - 416*u - 483 + 3187 = 0.
-2, 2, 13
Let k(j) = -j + 26. Let r be k(29). Let f be (192/1280)/(r/(-4)). Factor 0*x + 0 + f*x**2 + 1/5*x**3.
x**2*(x + 1)/5
Let h be (-48)/54*5/(-4). Let u = 43/18 + h. Solve 12*v**2 - 7/2*v + 1/4*v**4 + u*v**3 - 49/4 = 0 for v.
-7, -1, 1
Let g(a) be the third derivative of 0 + a - 3*a**2 + 1/10*a**5 - 29/6*a**4 + 19/3*a**3. What is m in g(m) = 0?
1/3, 19
Factor 358*w - 121023 - 5*w**2 + 2*w**2 + w**2 + 886*w - 72419.
-2*(w - 311)**2
Suppose 5*o - 20 = 4*u, -3*u + 4 = u + o. Suppose 10*m = 3*l + 8*m + 2, u = 4*l - 2*m. Suppose -2/9*c**l - 32/9 - 16/9*c = 0. Calculate c.
-4
Let s(l) be the first derivative of -l**3/3 + 446*l**2 - 4810. Factor s(k).
-k*(k - 892)
Let r(z) = 6*z**2 - 523*z + 69691. Let x(q) = -11*q**2 + 1047*q - 139383. Let b(v) = -9*r(v) - 5*x(v). Factor b(s).
(s - 264)**2
Let t(w) be the third derivative of 1/160*w**5 - 1/16*w**4 + 0*w + 65*w**2 + 0 + 3