en that k(y) = 0.
-2, -1, 0
Let i = 1481 + -856. Let q = i - 621. Factor -4/3 + 4*t**4 - q*t - 8/3*t**2 + 4/3*t**5 + 8/3*t**3.
4*(t - 1)*(t + 1)**4/3
Suppose -155*q = -225 - 240. Let p(v) be the first derivative of v**q - 5/2*v**2 - 2*v - 6. Factor p(o).
(o - 2)*(3*o + 1)
Let c(m) be the second derivative of -m**4/60 + 73*m**3/15 + 1071*m**2/10 + 7765*m. What is z in c(z) = 0?
-7, 153
Let l be (-4)/22 + 12171/(-33)*1. Let h = l + 381. Factor 2/3*q**3 - h + 8/3*q**2 - 2*q.
2*(q - 2)*(q + 3)**2/3
Let a(n) be the first derivative of -n**6/300 + n**4/20 + 2*n**3/15 + 16*n**2 + 11. Let p(j) be the second derivative of a(j). Solve p(i) = 0 for i.
-1, 2
Factor 0*z**2 + 105 - 211 - 441*z - 2*z**2 + 379*z - 334.
-2*(z + 11)*(z + 20)
Let a(f) = -f**3 - f - 1. Let r(y) = -7*y**3 + 2*y**2 - 17*y - 17. Let s = -102 + 105. Let k = s + 15. Let p(x) = k*a(x) - 2*r(x). Factor p(i).
-4*(i - 2)*(i + 1)*(i + 2)
Let t(q) = q**4 + q**3 + q**2 + 2*q + 1. Let x(i) = 503*i**4 + 5495*i**3 + 4211*i**2 - 755*i + 26. Let m(l) = -4*t(l) - x(l). Suppose m(f) = 0. Calculate f.
-10, -1, 1/13
Let g(h) be the first derivative of 5/6*h**2 + 3/2*h - 40 + 1/18*h**3. Solve g(o) = 0.
-9, -1
Let r(a) = 17*a + 1326. Let x be r(-78). Factor -12/5*v**3 + x - 3/5*v**2 + 12/5*v + 3/5*v**4.
3*v*(v - 4)*(v - 1)*(v + 1)/5
Let y be -4 + -8*(4 + -5). Let c be y*(-2)/24*-3. Find k such that -1/2*k + k**2 - c + 1/2*k**3 = 0.
-2, -1, 1
Let l(m) be the first derivative of -m**4/114 - 12*m**3/19 - 35*m**2/19 + 120*m + 191. Let y(k) be the first derivative of l(k). Factor y(h).
-2*(h + 1)*(h + 35)/19
Let v(w) = -4*w**3 + w**2 - w - 2. Let b be v(-1). Suppose -288*o**2 + 315*o**3 + 77*o**b - 29*o + 89*o - 2*o**4 = 0. Calculate o.
-5, 0, 2/5
Let g(v) be the third derivative of -v**8/252 - 5*v**7/189 - 11*v**6/540 + v**5/5 + 7*v**4/27 - 40*v**3/27 + 1235*v**2. What is p in g(p) = 0?
-2, 5/6, 1
Let k(x) = -5*x - 21*x + 9*x**2 + 4*x**3 + 11*x**2 - 8*x - 2*x**2. Let t(u) = -u**3 - u**2 + 2*u + 2. Let m(b) = k(b) + 6*t(b). Solve m(d) = 0 for d.
1, 2, 3
Let -14/3*c**2 - 2/9*c**4 - 26/9*c + 26/9*c**3 + 44/9 = 0. Calculate c.
-1, 1, 2, 11
Let n be ((-2)/(-4))/(5 + (-117)/24). Suppose 2*d - 3 = -2*q - 7, -2*q - n*d - 8 = 0. Factor b**3 + 4*b**2 + 0 + q + 295*b - 291*b.
b*(b + 2)**2
Let z(x) be the second derivative of 11*x**4/4 - 331*x**3/2 + 45*x**2 - 3*x - 1610. Factor z(n).
3*(n - 30)*(11*n - 1)
Let t(l) be the third derivative of -l**8/168 + 41*l**7/105 - 13*l**6/20 - 41*l**5/30 + 10*l**4/3 - 613*l**2 + 3. Suppose t(p) = 0. What is p?
-1, 0, 1, 40
Let q(x) be the second derivative of -13/5*x**5 + 32/15*x**3 + 1/5*x**4 + 260*x + 4/3*x**6 - 8/5*x**2 + 0. Solve q(t) = 0.
-1/2, 2/5, 1
Let z be (1/6 - 1)*31/(62/(-12)). Let s(w) be the third derivative of -35/72*w**4 + 10/9*w**3 + 2*w**2 + 0*w + 1/72*w**6 + 0 + 1/18*w**z. Factor s(d).
5*(d - 1)**2*(d + 4)/3
Let a(u) be the third derivative of u**7/42 + u**6/24 - 59*u**5/12 + 185*u**4/8 - 45*u**3 - 36*u**2 - 35. Factor a(x).
5*(x - 6)*(x - 1)**2*(x + 9)
Let q(z) be the first derivative of z**4/10 + 248*z**3/5 + 46128*z**2/5 + 3813248*z/5 - 1438. Determine s so that q(s) = 0.
-124
Let a(j) be the third derivative of -7/12*j**4 + j - 1/180*j**6 - 2*j**3 - 4/45*j**5 + 0 - 7*j**2. Determine w so that a(w) = 0.
-3, -2
Let f be -3 + 4 - (0 + (0 - 65)). Let t = f - 62. Solve -12*g**2 + 0*g - 4*g**5 + 20*g**5 + 15*g**4 - 3*g**t + 4*g - 20*g**3 = 0.
-1, 0, 1/4, 1
Suppose -32 = -11*w - 10. Find h, given that 38*h**w - 34 - 40*h**2 - 62*h - 10*h - 36 = 0.
-35, -1
Let g = -332 + 335. Factor -15*o**g - 16*o**2 - 33*o + 49*o + 4*o**4 + 11*o**3.
4*o*(o - 2)*(o - 1)*(o + 2)
Let y = 33 + -31. Suppose 0 = -w + 3*p + 3, -5*w + 15 = -y*p + p. Factor 15*n + 0*n**2 + 4*n**w - 14*n**2 - 6*n**2 + n**3.
5*n*(n - 3)*(n - 1)
Let a(y) be the second derivative of y**6/135 - 4*y**5/45 + y**4/6 + 2*y**3/3 - 3617*y. Find o such that a(o) = 0.
-1, 0, 3, 6
Suppose 37*o = 57*o. Let m(y) be the second derivative of -5/39*y**3 + 26*y + o + 1/78*y**4 - 6/13*y**2. Factor m(t).
2*(t - 6)*(t + 1)/13
Suppose -18 - 6/7*i**2 + 60/7*i = 0. Calculate i.
3, 7
Let r(u) be the third derivative of u**7/168 - u**6/12 + 3*u**5/8 - 5*u**4/6 - 5*u**3/2 - 15*u**2 - u. Let n(i) be the first derivative of r(i). Factor n(o).
5*(o - 4)*(o - 1)**2
Let r(i) be the first derivative of 0*i**4 + 0*i + 0*i**3 + 52/5*i**5 + 2/3*i**6 + 0*i**2 + 59. Factor r(h).
4*h**4*(h + 13)
Determine s, given that 216000 + 223157*s + 2528*s**3 + 1585*s**3 + 189*s**4 - 75557*s + 37095*s**2 + 3*s**5 = 0.
-24, -5
Let k = 396265 - 396265. Find v such that -2/25*v**3 + k*v + 0 + 0*v**2 = 0.
0
Suppose -2180*l - 228 = -2256*l. Let z(c) be the first derivative of 1/2*c + 1/16*c**4 - 39 + 0*c**l - 3/8*c**2. Let z(y) = 0. Calculate y.
-2, 1
Let r(c) = -c**3 - 5*c**2 + 14*c + 2. Let d be r(2). Suppose -b = d*b + 3*b. Factor -104/5*k**2 + 338/5*k**3 + 8/5*k + b.
2*k*(13*k - 2)**2/5
Let f be 1056/(-216) - (4/(-6))/(53/477). Determine p, given that -8/9*p**3 - 8/9*p**4 + 4/9 + 4/9*p**2 - 2/9*p**5 + f*p = 0.
-2, -1, 1
Let p(d) = -5*d**4 + 30*d**3 - 20*d**2 + 13*d + 48. Let x(q) = -4*q**4 + 26*q**3 - 20*q**2 + 10*q + 48. Let s(j) = -6*p(j) + 7*x(j). Factor s(z).
2*(z - 2)**2*(z + 2)*(z + 3)
Let q be (-4 - -2)/(1 + -2). Suppose -13*b - q*b**2 + 134*b + 15*b - 1816 - 496 = 0. Calculate b.
34
Let g be ((-1)/2)/((-16)/(-41664)). Let p = g + 1304. Factor 44/9*t + 16/9*t**p - 4/3.
4*(t + 3)*(4*t - 1)/9
Suppose 17*z - 76 = 46 - 88. Factor 1/5*r**3 - 1/5*r - 2/5*r**z + 2/5.
(r - 2)*(r - 1)*(r + 1)/5
Let a(k) be the first derivative of -2*k**3/3 + 44*k**2 + 184*k - 1470. Suppose a(v) = 0. Calculate v.
-2, 46
Let o(c) be the third derivative of -1/40*c**5 + 0*c - 3/140*c**7 + 0*c**4 + 0*c**3 + 0 + 60*c**2 - 1/20*c**6. Factor o(v).
-3*v**2*(v + 1)*(3*v + 1)/2
Let j be (-6)/(-10) + (15674/10 - 2). Let -1260*x - x**4 - 216*x**2 - 52*x**2 - 60*x**3 + 243 - 158*x**2 - 2*x**4 - j = 0. Calculate x.
-7, -3
Let r(k) be the third derivative of -1/210*k**5 - 100/21*k**3 + 5/21*k**4 + 0*k + 18*k**2 + 0. Factor r(m).
-2*(m - 10)**2/7
Let c = 47653/3 - 15879. Let d(n) be the first derivative of 32 + 4/3*n**2 - c*n - 1/9*n**3. Determine s, given that d(s) = 0.
4
Let n(i) = -6*i**3 + 18*i**2 - 180*i + 545. Let k be n(3). Factor 0*t**2 - 1/5*t**k - 196/5*t**3 + 0 - 28/5*t**4 + 0*t.
-t**3*(t + 14)**2/5
Let v be (-62)/(-5) + (-763)/545. Suppose 2*o + o = -v*o. Suppose -8/9*g + o + 1/9*g**5 + 2/3*g**3 - 4/9*g**2 + 5/9*g**4 = 0. What is g?
-2, 0, 1
Suppose -2700*h - 1851*h + 9102 = 0. Determine m so that 148/3*m**3 + 2882/3*m**h + 864 + 2/3*m**4 + 1776*m = 0.
-36, -1
Let r = -617 + 620. Solve 1 - 7*q**2 - 3*q**r - 2*q**2 - 1 + 12*q = 0.
-4, 0, 1
Factor 3*x**2 + 44/5*x + 0 + 1/5*x**3.
x*(x + 4)*(x + 11)/5
Let r(b) be the first derivative of b**3/7 - 69*b**2/14 + 306*b/7 - 826. Solve r(k) = 0 for k.
6, 17
Let n(p) = 1. Let s = -16 + 14. Let k be -8 - (-3 - (-2 - (3 - s))). Let m(g) = g**2 - 3*g - 6. Let u(l) = k*n(l) + 3*m(l). Find r such that u(r) = 0.
-2, 5
Determine k so that -35 + 121/3*k - 1/3*k**3 - 5*k**2 = 0.
-21, 1, 5
Let 12798/19*p + 12482/19 + 318/19*p**2 + 2/19*p**3 = 0. What is p?
-79, -1
Factor -944*s - 951*s - 8*s**2 - 923*s + 2848*s.
-2*s*(4*s - 15)
Let x be 1863/(-276) + 1/(-4) - (-6 - 60/52). Let o = 1507 + -19551/13. Factor -x*n**2 + o*n - 200/13.
-2*(n - 10)**2/13
Suppose 16*z - 97 = -81. Let y be ((-88)/(-33) - z) + 2/6. Factor 2*l - 8/7*l**3 - 4/7 + 10/7*l**y.
-2*(l - 2)*(l + 1)*(4*l - 1)/7
Let r(o) = 3*o**3 + 38*o**2 - 67*o - 274. Let z(p) = -5*p**3 - 75*p**2 + 130*p + 550. Let g(s) = -5*r(s) - 2*z(s). Factor g(t).
-5*(t - 3)*(t + 2)*(t + 9)
Factor 269*r - 950*r - 17*r**2 + 12*r**3 - 791*r + 912 + 163*r**2 + 2*r**2.
4*(r - 6)*(r + 19)*(3*r - 2)
Solve 4/5*t**2 + 772/5*t + 768/5 = 0.
-192, -1
Let f = -276/28499 - 762256405/655477. Let p = 1163 + f. Suppose 0*c + 6/23*c**4 - 8/23*c**2 + p + 4/23*c**5 - 4/23*c**3 = 0. Calculate c.
-1, 1/2, 1
Factor 40*o - 1/2*o**3 + 192 - 4*o**2.
-(o - 8)*(o + 4)*(o + 12)/2
Let y(p) be the second derivative of 0*p**2 - 4/15*p**6 - 2/21*p**7 + 4/3*p**4 - 8/3*p**3 - 2 + 29*p + 3/5*p**5. Factor y(l).
-4*l*(l - 1)**2*(l + 2)**2
Let p(i) = 4*i**4 - 58*i**3 + 118*i**2 - 48*i. Let k(c) = -4*c**4 + 58*c**3 - 120*c**2 + 48*c. Let m(g) = 3*k(g