be (-10)/3 - 192/(-144). Let w(b) = o*r(b) - 3*u(b). Find j such that w(j) = 0.
-29
Let i be 0 + (-9595)/(-2052) + (-4)/(-54). Solve 1/2 - i*g**2 - 1/4*g - 31/4*g**3 - 19/4*g**4 - g**5 = 0 for g.
-2, -1, 1/4
What is w in 230/3 - 5/6*w**2 + 110/3*w = 0?
-2, 46
Factor -16832*l**2 - 2000 - 10716*l**2 - 9275*l - 3325*l + 7703*l**2.
-5*(63*l + 20)**2
Suppose -8138*v + 7934*v - 24*v**2 + 95*v**2 - v**5 + 2*v**5 - 71*v**4 + 200*v**3 + 3*v**3 = 0. Calculate v.
-1, 0, 1, 3, 68
Let d(x) be the first derivative of -x**7/210 + x**5/100 - 30*x - 8. Let h(b) be the first derivative of d(b). Find i, given that h(i) = 0.
-1, 0, 1
Let a = 402 + -400. Factor -20*j**3 + 1609*j - 9 + 38*j**a - 1621*j + 0*j**4 + 3*j**4.
(j - 3)**2*(j - 1)*(3*j + 1)
Let l(p) be the third derivative of 17/80*p**5 - 6*p**2 - 17/160*p**6 + 10*p + 0*p**3 + 0 - 3/16*p**4 + 1/40*p**7 - 1/448*p**8. Let l(w) = 0. What is w?
0, 1, 2, 3
Suppose 8*z = 6*z + 6 + 4. Let u(x) be the third derivative of -1/6*x**4 + 26*x**2 - 1/150*x**z + 0 - 5/3*x**3 + 0*x. Solve u(d) = 0.
-5
Let u(m) be the third derivative of 138*m**2 - 1/28*m**6 + 1/735*m**7 + 0*m - 16/7*m**4 + 160/21*m**3 + 41/105*m**5 + 0. Determine v, given that u(v) = 0.
2, 4, 5
Let s(r) be the third derivative of r**9/3024 + 11*r**8/5040 - r**7/630 - 7*r**3/6 - 58*r**2. Let b(a) be the first derivative of s(a). Factor b(v).
v**3*(v + 4)*(3*v - 1)/3
Let d(h) = -7*h**3 - 5*h**2 + 6*h + 24. Let b be d(-10). Factor 270*r - 389 + 3*r**2 + 0*r**2 + b.
3*(r + 45)**2
Suppose -2 = 3*t - 14. Suppose t*z + 4 - 16 = 0. Solve -23*f**2 - 5*f**3 + 4*f**3 - 10*f**2 + 4*f**z + 108 + 72*f = 0 for f.
-1, 6
Find i, given that 508/3 - 532/3*i**4 + 1124*i**2 - 935/3*i**3 - 2401/3*i - 4*i**5 = 0.
-127/3, -4, 1/2, 1
Let 0 + 4/7*a**3 + 104976/7*a + 1296/7*a**2 = 0. Calculate a.
-162, 0
Suppose -17 = -20*p + 3*p. Suppose -3*d + 2*d = -1. Find z, given that -4*z**3 - d - 8*z**2 + p + 16*z + 32 = 0.
-2, 2
Let o(r) = 13*r - 177. Let g be o(15). Factor 5*y**4 + 72 + 68*y**3 + 98*y + g*y + 112*y + 3*y**4 + 200*y**2.
4*(y + 2)*(y + 3)**2*(2*y + 1)
Let v(z) be the first derivative of 3*z**4/4 - 12*z**3 + 33*z**2/2 - 116. Find a such that v(a) = 0.
0, 1, 11
Let k = -15 - 5. Let o = -17 - k. Let 18*j**4 + 14*j - 8*j - 6*j**3 - 12*j**2 - o*j**2 + 3*j**3 = 0. Calculate j.
-1, 0, 1/2, 2/3
Let g(j) = 4*j + 3. Let m be g(12). What is y in 120 - 66*y + m*y - 39*y - 3*y**2 = 0?
-20, 2
Let v be (-2 - -2) + (-2)/8*4. Let g be -3*v/(36/30). Suppose g*a**3 - 5/4 + 0*a**2 + 5/4*a**4 - 5/2*a = 0. What is a?
-1, 1
Suppose 5*j + 12 = -8. Let z(q) = -q**2 - 4*q + 3. Let x be z(j). Find p, given that -1151 + 1151 + 2*p - 2*p**x = 0.
-1, 0, 1
Let l(v) be the third derivative of 0 + 1/24*v**4 - 2*v**2 + 0*v**3 + 1/120*v**5 - 27*v. Find b such that l(b) = 0.
-2, 0
Let z = -1294689/181 + 7153. Let t = 169/543 + z. What is m in 1/3*m + 1/3*m**2 - 1/3 - t*m**3 = 0?
-1, 1
Let r(a) be the first derivative of -a**5/20 + 91*a**4/16 + 514. Factor r(y).
-y**3*(y - 91)/4
Let s(b) = 11*b**4 - 40*b**3 + 629*b**2 - 1792*b - 12293. Let f(x) = 2*x**4 + x**3 + x**2 - 1. Let p(g) = -15*f(g) + 3*s(g). Factor p(v).
3*(v - 16)**3*(v + 3)
Let p(h) be the first derivative of 2*h**5/115 - 91*h**4/46 + 178*h**3/23 - 265*h**2/23 + 176*h/23 + 4810. Suppose p(d) = 0. Calculate d.
1, 88
Suppose -302136 + 31338 + 5333*j + 1202719 + 1011315 + 243*j + 4*j**2 = 0. What is j?
-697
Let p(n) = 1200*n + 706803. Let c be p(-589). Let 1/4*z**c - 7*z**2 + 221/4*z - 169/2 = 0. Calculate z.
2, 13
Let y(t) be the second derivative of t**7/21 + 16*t**6/15 + 12*t**5/5 - 144*t**4 - 1872*t**3 - 10368*t**2 + 1732*t. Determine p, given that y(p) = 0.
-6, 8
Let f be 0 + -6*4/(-8). Suppose -3*t + 21 = 3*i, -5*t - i - 12 + 27 = 0. Solve 1/5*c**f + 4/5*c**2 - t - 7/5*c = 0.
-5, -1, 2
Let l(q) be the second derivative of 1 - 20/27*q**3 - 1/135*q**6 - 8/9*q**2 - 1/3*q**4 - 5*q - 7/90*q**5. Factor l(g).
-2*(g + 1)*(g + 2)**3/9
Let d(r) be the first derivative of -r**4/4 - 6*r**3 - 36*r**2 + 606. Factor d(c).
-c*(c + 6)*(c + 12)
Suppose u + 192 = 15*q, -72 = -94*q + 89*q + u. Determine w so that 0 - 7/3*w**4 - q*w**2 - 10*w**3 - 1/6*w**5 + 0*w = 0.
-6, -2, 0
Factor -555*r**2 + 0*r + 0 + 1115/2*r**3 - 5/2*r**4.
-5*r**2*(r - 222)*(r - 1)/2
Factor -2/17*a**4 + 0*a + 0 - 208/17*a**3 - 206/17*a**2.
-2*a**2*(a + 1)*(a + 103)/17
Suppose 104*w + 42*w = -83*w. Let g(b) be the second derivative of 0*b**2 + 0 + 9/10*b**6 + 4*b**4 + 1/14*b**7 + w*b**3 + 18/5*b**5 - 21*b. Factor g(o).
3*o**2*(o + 1)*(o + 4)**2
Let m = -55774 - -223097/4. Suppose 5/2*s - s**3 + 7/4*s**2 + 0 - m*s**4 = 0. Calculate s.
-5, -1, 0, 2
Let t be 2/4*32/8. Factor -58*n - 7*n**t + 8*n**2 + 0*n**2 - 16 - 8*n**2 + 0*n**2.
-(n + 8)*(7*n + 2)
Let u be (7 + (-1377)/(-42))/9. Let d = u - -1/42. Find y such that -2*y**4 - d*y + 16/9 + 4/9*y**2 + 14/3*y**3 = 0.
-1, 2/3, 2
Let z be ((396/54)/(-22))/(7/(-12)). Suppose 3*s + 5*f - 4*f = 5, -5*s - 4*f = -20. Factor s*i**3 - 6/7*i**2 + z*i + 0 + 2/7*i**4.
2*i*(i - 1)**2*(i + 2)/7
Suppose 68 = 6*l - 22. Factor -125 + 5*z**3 + 64 + l*z**2 + 61 - 20*z.
5*z*(z - 1)*(z + 4)
Suppose h = 2*s - 35 - 25, -150 = -5*s + 5*h. Factor 56*o + 23 - s - 71*o**2 + 67*o**2 - 45.
-4*(o - 13)*(o - 1)
Let a(m) be the second derivative of 1/9*m**3 - 2/3*m**2 - 12*m + 0 + 1/18*m**4. Find q such that a(q) = 0.
-2, 1
Let z(d) = d**3 + 6*d**2 - 2*d. Let j be z(-5). Let t be (6/(-10))/((-7)/j). Determine x so that 6*x**5 - 15*x - 10 - 11*x**5 + 7*x**2 + 20*x**t + 3*x**2 = 0.
-1, 1, 2
Let d(n) be the third derivative of -n**5/15 - n**4/6 + 8*n**3 + 1717*n**2. Factor d(s).
-4*(s - 3)*(s + 4)
Let s be 22/2 - (1 - 5). Suppose -11*i = -s - 18. Factor -22*z**2 + 4*z - 12*z**2 + 4*z**i + 26*z**2.
4*z*(z - 1)**2
Suppose 156*c + 162 = 165*c. Suppose 42 = 8*h + c. Factor -5/2*p**h + 0*p**4 + 0 + 0*p**2 + 0*p + 5/2*p**5.
5*p**3*(p - 1)*(p + 1)/2
Solve 0 - 2/5*a**2 + 2058/5*a = 0.
0, 1029
Let y(o) be the third derivative of 0*o + 2/3*o**4 + 1/15*o**5 + 60*o**2 + 0 - 8*o**3. Factor y(g).
4*(g - 2)*(g + 6)
Let r = -75 - -78. Factor r*p**3 + 9*p**2 + p + 9*p**2 + p**4 - 15*p**2.
p*(p + 1)**3
Let k(q) = -2*q + 17. Let t be k(7). Factor -45*u - 256 - 4*u**t + 9*u**3 + 30*u**2 + 0*u**3 + 186.
5*(u - 2)*(u + 1)*(u + 7)
Let z(i) be the third derivative of i**6/24 + 14*i**5/3 + 490*i**4/3 - 29*i**2 - 13*i. Factor z(m).
5*m*(m + 28)**2
Let n(d) be the first derivative of d**4 - 304*d**3/3 + 146*d**2 + 600*d - 5487. Factor n(j).
4*(j - 75)*(j - 2)*(j + 1)
Let j = -337140 - -337144. Suppose 0 + 0*l - 5/2*l**3 - 1/2*l**j + 0*l**2 = 0. What is l?
-5, 0
Let q(d) be the first derivative of d**5/180 - 7*d**4/72 - 4*d**3/9 - d**2 + 10*d - 114. Let u(h) be the second derivative of q(h). Factor u(r).
(r - 8)*(r + 1)/3
Suppose -376*v + 4101 = 991*v. Find w such that -360*w**v + 0 - 1900/13*w**2 - 4752/13*w**4 - 250/13*w - 1728/13*w**5 = 0.
-5/6, -1/4, 0
Let n(u) = 41*u**2 - 5741*u + 1376660. Let s(w) = 12*w**2 - 1914*w + 458886. Let h(f) = -2*n(f) + 7*s(f). Suppose h(g) = 0. Calculate g.
479
Let o(q) = 7*q - 133. Let i be o(19). Let d be (-1 - i)*(-5 + -5)/5. Let -9/4*w + 3/2 + 0*w**d + 3/4*w**3 = 0. What is w?
-2, 1
Let z = 33 - 31. Factor -12*i**3 - 7*i**2 - 2*i**4 + 12 + 3*i**z - 5*i**2 + 12*i - i**4.
-3*(i - 1)*(i + 1)*(i + 2)**2
Let p(m) be the second derivative of -m**7/28 - 21*m**6/4 - 927*m**5/40 - 307*m**4/8 - 51*m**3/2 + 119*m + 4. Factor p(a).
-3*a*(a + 1)**3*(a + 102)/2
Let y(k) be the third derivative of k**7/70 - 83*k**6/20 + 9573*k**5/20 - 55693*k**4/2 + 900482*k**3 + 9299*k**2. Find x such that y(x) = 0.
22, 61
Let b(k) be the third derivative of -19/180*k**5 + 158*k**2 + 1/672*k**8 + 0*k**4 - 1 - 31/630*k**7 + 97/720*k**6 + 0*k**3 + 0*k. Solve b(m) = 0 for m.
0, 2/3, 1, 19
Let p(l) be the first derivative of l**3/9 - l**2/6 - 1724. Factor p(s).
s*(s - 1)/3
Suppose 23 = b - 3*h, -8*b + 10 = -79*h + 84*h. Factor -9/2*z**3 + b*z**2 + z**4 - 3/2*z + 0.
z*(z - 3)*(z - 1)*(2*z - 1)/2
Let f be 15/80 - (-620)/960. Suppose 1/6*p**2 - 1/6*p**3 + f*p + 1/2 = 0. What is p?
-1, 3
Let q(p) be the first derivative of p**6/10 - 3*p**5/4 + 7*p**4/4 - 3*p**3/2 - 24*p - 8. Let x(v) be the first derivative of q(v). Factor x(y).
3*y*(y - 3)*(y - 1)**2
Let l(n) = -11*n**3 + 30*n**2 - 997. Let b(t) = -47*t**3 