e 130/(-78)*g/(-1) + 2. Factor a*y**3 + 0 + 2/3*y + y**2.
y*(y + 1)*(y + 2)/3
Suppose 1/9*s**2 - 4/9*s - 7/3 = 0. What is s?
-3, 7
Let d(i) be the second derivative of i**7/56 + i**6/20 - i**4/8 - i**3/8 - 19*i. Find s, given that d(s) = 0.
-1, 0, 1
Determine d, given that -d**2 + 1/3*d + 1 - 1/3*d**3 = 0.
-3, -1, 1
Let l(g) be the first derivative of -g**3/33 + g**2/11 + 24*g/11 + 85. Factor l(o).
-(o - 6)*(o + 4)/11
Let i be 1 - (24/6 - 4). Let h be 3/4*i/3. Determine m so that -3/8*m + h + 5/4*m**3 - 9/8*m**2 = 0.
-1/2, 2/5, 1
Let c(k) be the second derivative of -k**5/50 - 17*k**4/15 + 109*k**3/15 - 74*k**2/5 + 174*k. Suppose c(s) = 0. Calculate s.
-37, 1, 2
Let n(v) = -v**3 + 2*v**2 + 4*v - 3. Let s be n(3). Suppose -6 = 3*a - 18. Factor s*x - a*x**3 - 4 - 4*x**2 + x**2 + 7*x**2 + 4*x.
-4*(x - 1)**2*(x + 1)
Let j(o) be the first derivative of -o**5 + 25*o**4/4 - 40*o**3/3 + 10*o**2 + 93. Factor j(i).
-5*i*(i - 2)**2*(i - 1)
Let r be (3/15)/((-8 + 4)/(-3084)). Let d = r - 153. Determine l so that 0 - 2/5*l - d*l**3 + 8/5*l**2 = 0.
0, 1/3, 1
Let u(q) be the second derivative of q**7/210 - 7*q**6/50 + 39*q**5/100 - 19*q**4/60 + 413*q. Factor u(i).
i**2*(i - 19)*(i - 1)**2/5
Factor 134*x - 242 - 30*x + 58 - 40 + 2*x**2 + 2*x**2.
4*(x - 2)*(x + 28)
Let y(q) be the first derivative of -7*q**4/4 - 13*q**3/3 + 2*q**2 - 4*q - 3. Let m(r) = 15*r**3 + 27*r**2 - 9*r + 9. Let p(f) = -4*m(f) - 9*y(f). Factor p(s).
3*s**2*(s + 3)
Let m(i) be the second derivative of 3*i**5/5 + 19*i**4/4 + 11*i**3/2 - 6*i**2 + 2*i - 4. Factor m(h).
3*(h + 1)*(h + 4)*(4*h - 1)
Let b(w) be the first derivative of -w**5/240 - w**4/12 - 2*w**3/3 + 7*w**2/2 - 3. Let t(j) be the second derivative of b(j). Suppose t(l) = 0. What is l?
-4
Let y(c) be the first derivative of c**3/15 + c**2/5 - 3*c/5 - 71. Factor y(v).
(v - 1)*(v + 3)/5
Let g(i) = i + 8. Let x be g(-3). Factor -8 - 2*l**3 + l**3 - x*l**4 + 7*l**2 + 3*l + 6 - 2*l**3.
-(l - 1)*(l + 1)**2*(5*l - 2)
Let l(u) be the second derivative of u**7/14 - u**6/5 - 3*u**5/5 + u**4/2 + 3*u**3/2 - 40*u - 2. Factor l(b).
3*b*(b - 3)*(b - 1)*(b + 1)**2
Suppose 3 = 3*h - 9. Suppose -13*d - 23 + 75 = 0. Let h - 10*l + 4 + 3*l - 5*l + d*l**2 = 0. What is l?
1, 2
Let j = 301/4 + -1387/12. Let u = -40 - j. Solve -2/3 + 1/3*b**2 + u*b = 0.
-2, 1
Let s = 24281 - 145685/6. Find m such that 0 - s*m - 2/3*m**2 - 2/3*m**3 = 0.
-1/2, 0
Let i be 12/(-90) - 93/(-360). Let w(j) be the first derivative of -i*j**4 - 1/2*j**3 + 3 + 0*j - 1/2*j**2. Let w(f) = 0. What is f?
-2, -1, 0
Solve -27*b - 28*b**3 - 39*b**3 + 12 + 64*b**3 + 18*b**2 = 0 for b.
1, 4
Let p(r) = -r**3 - 4*r**2 - r + 1. Let v be p(-4). Determine q, given that -4*q + 44*q + 46 - v*q**2 - 126 = 0.
4
Let h = -6 - -11. Suppose 5*k - k = -h*v + 26, -12 = -4*v - k. Solve -3*d**v + 10*d**4 + 5*d**2 - 12*d**4 = 0.
-1, 0, 1
Let p(q) be the second derivative of 0 + 1/2*q**5 - 3*q - 15/2*q**2 - 1/6*q**6 + 5/3*q**4 - 5/3*q**3. Solve p(y) = 0.
-1, 1, 3
Solve -32*l**2 + 34*l**2 - 59 + 79 - 22*l = 0 for l.
1, 10
Let a = -1/20 - -11/20. Let n(s) be the second derivative of 0 - 1/3*s**3 + a*s**4 + 1/10*s**5 - 5*s + 0*s**2 - 1/5*s**6. Let n(f) = 0. What is f?
-1, 0, 1/3, 1
Let y(o) be the second derivative of 21*o**6/25 + 142*o**5/25 + 64*o**4/5 + 48*o**3/5 + 16*o**2/5 + o + 54. Suppose y(k) = 0. Calculate k.
-2, -2/7, -2/9
Let n(b) be the second derivative of -b**5/4 - 27*b**4/8 - 5*b**3 - 18*b**2 + 36*b. Let a(d) be the first derivative of n(d). Factor a(l).
-3*(l + 5)*(5*l + 2)
Let m(z) be the first derivative of 3*z**5/5 + 6*z**4 - 9*z**3 + 223. Factor m(q).
3*q**2*(q - 1)*(q + 9)
Let b(v) = -7*v**2 + 692*v - 23801. Let f(l) = 15*l**2 - 1385*l + 47600. Let n(g) = 5*b(g) + 2*f(g). Let n(c) = 0. What is c?
69
Solve 0*u**3 + 4/3*u**5 - 8*u**4 + 128/3*u**2 + 0*u + 0 = 0 for u.
-2, 0, 4
Let d(a) be the second derivative of a**6/6 + 27*a**5/4 + 565*a**4/12 + 95*a**3/2 - 495*a**2 - 625*a. Determine k, given that d(k) = 0.
-22, -3, 1
Let q = 16 + -8. Solve -q - 2 + 2 - 7*h - 2*h**2 - h = 0 for h.
-2
Suppose w + 3*r + 6 = 0, 37*r = 5*w + 35*r - 4. Factor -13/2*i**2 - 1/2*i + w.
-i*(13*i + 1)/2
Suppose -3*t = 2*u - 6*t - 102, -143 = -3*u + 2*t. Determine p, given that 21*p**3 + 27*p + u*p**2 + 3*p**4 - 483 + 483 = 0.
-3, -1, 0
Let l = 58 - 113. Let i = -53 - l. Let -49/4*g**3 - 17/4*g + 1/2 + 9/2*g**4 + 23/2*g**i = 0. Calculate g.
2/9, 1/2, 1
Let u = 128521/105 + -1224. Let z(f) be the third derivative of 0*f**4 - 1/420*f**6 + 0 + 0*f - u*f**5 + 1/735*f**7 + 0*f**3 + 7*f**2. Factor z(n).
2*n**2*(n - 2)*(n + 1)/7
Let h(d) be the third derivative of -25*d**2 + 1/3*d**3 + 0*d + 0 - 1/24*d**4 - 1/60*d**5. Factor h(n).
-(n - 1)*(n + 2)
Let t(i) be the second derivative of 0*i**3 + 0*i**4 + 1/420*i**7 + 0 - 3/2*i**2 + 0*i**6 + 0*i**5 - 5*i. Let z(q) be the first derivative of t(q). Factor z(o).
o**4/2
Let f(x) = -4*x**3 - 100*x**2 + 1147*x - 1058. Let k(a) = 22*a**3 + 502*a**2 - 5734*a + 5290. Let h(s) = -16*f(s) - 3*k(s). Factor h(r).
-2*(r - 23)**2*(r - 1)
Let o(z) be the second derivative of 0 + 1/15*z**3 - 1/5*z**2 - 1/50*z**5 + 1/30*z**4 + 12*z. Let o(w) = 0. What is w?
-1, 1
Let t(y) = -y**3 - 7*y**2 - 32*y - 58. Let r be t(-3). Let f(x) be the first derivative of -1/9*x**3 - 10 + 0*x + 1/6*x**r. Let f(u) = 0. What is u?
0, 1
Solve 3/2*t**3 + 0 - 6*t - 9/2*t**2 = 0 for t.
-1, 0, 4
Let r(w) be the third derivative of w**5/120 - w**4/48 + 181*w**2. Factor r(n).
n*(n - 1)/2
Let m(n) be the third derivative of n**6/150 + 13*n**5/75 + 23*n**4/30 + 22*n**3/15 + 379*n**2. Let m(f) = 0. What is f?
-11, -1
Let j(f) be the first derivative of 4 + 11/7*f**3 + 12/7*f + 9/28*f**4 + 18/7*f**2. Suppose j(t) = 0. What is t?
-2, -1, -2/3
Let m(t) be the third derivative of 0 + 33*t**2 + 1/60*t**5 - t**3 - 5/24*t**4 + 0*t. Factor m(z).
(z - 6)*(z + 1)
Find c such that -112/11*c**4 - 4/11*c - 114/11*c**3 + 0 - 38/11*c**2 - 32/11*c**5 = 0.
-2, -1, -1/4, 0
Let q = 22804/56985 - 2/11397. Factor -7/5*z**2 - q + 9/5*z.
-(z - 1)*(7*z - 2)/5
Let f(r) be the third derivative of 89*r**6/600 - 44*r**5/75 + 17*r**4/24 + r**3/15 - 88*r**2. Find o, given that f(o) = 0.
-2/89, 1
Suppose -10*z + 24 + 76 = 0. Suppose 4*t = 2*q + 2*t - z, -5 = 5*t. Factor -2/3*d**q + 0 - 2/3*d**3 + 0*d + 2/3*d**2 + 2/3*d**5.
2*d**2*(d - 1)**2*(d + 1)/3
Let a(k) be the second derivative of k**6/30 + 8*k**5/15 + 8*k**4/3 + k**2 - 28*k. Let q(i) be the first derivative of a(i). Suppose q(p) = 0. What is p?
-4, 0
Factor -5*d - 65*d**2 + 5*d**3 + 0*d**3 + 478 - 413.
5*(d - 13)*(d - 1)*(d + 1)
Let a(g) = -g**2 - 15*g - 13. Suppose -2*f - 2*l - 30 = 0, 29 = -2*f + l - 2*l. Let h be a(f). Suppose -6*p**2 - h - 4 + 2 + 2*p + 7 = 0. Calculate p.
-2/3, 1
Let w(r) = -7*r**4 + 7*r**2 + 6. Let i(o) = -8*o**4 + 8*o**2 + 7. Let y be 20/12*3 + -1. Let b be (-8)/y - -3*3. Let q(a) = b*w(a) - 6*i(a). Factor q(n).
-n**2*(n - 1)*(n + 1)
Let v(l) = -l**2 + 21*l - 31. Let g be v(17). Factor -37*c + 140*c**2 + 25*c - g*c - 48*c**3 - 47*c + 16.
-4*(c - 2)*(3*c - 2)*(4*c - 1)
Let w(x) be the first derivative of -3*x**4/4 + 5*x**3 + 42*x**2 - 96*x - 295. Let w(o) = 0. What is o?
-4, 1, 8
Let h(g) be the second derivative of -g**6/50 + 9*g**5/100 + g**4/5 + 3*g - 50. Factor h(j).
-3*j**2*(j - 4)*(j + 1)/5
Let r(a) be the third derivative of 3*a**5/8 - 11*a**4/2 - 3*a**3 + 384*a**2. Factor r(w).
3*(w - 6)*(15*w + 2)/2
What is i in 5/2*i - 5/4*i**2 + 0 = 0?
0, 2
Let u(g) = g**2 + 14*g + 16. Let v be u(-1). Let l = 168 - 500/3. Factor 0*w + l*w**2 + 2/3*w**v + 0.
2*w**2*(w + 2)/3
Factor 4/3*f**3 + 0 - 2/3*f**4 + 0*f**2 + 0*f.
-2*f**3*(f - 2)/3
Let m(j) = j**2 - 7*j - 5. Let l be m(8). Determine w so that -51 + 9*w**2 + 5*w**l - 8*w**3 - 9*w + 54 = 0.
1
Let x be ((-6403)/(-342) - 19)*(-16)/10. Let -x - 2/9*n + 2/9*n**2 = 0. Calculate n.
-1, 2
Let o(c) be the first derivative of -2*c**3/9 - 2*c**2 + 32*c/3 - 418. Factor o(w).
-2*(w - 2)*(w + 8)/3
Let o(g) be the first derivative of -3*g**5/20 - 7*g**4/8 + 7*g**3/12 + 5*g**2/4 - 43. Find r, given that o(r) = 0.
-5, -2/3, 0, 1
Let s(q) be the second derivative of -q**6/240 + q**4/48 - q**2/16 - 16*q. Find g, given that s(g) = 0.
-1, 1
Suppose 0 = 3*o + 5*s + 21, o - 3*s = 9 - 2. Let a be (-598)/(-207) + 3*o/27. Solve -2/3*h**2 - a*h - 8/