et v(l) be the second derivative of 0 + 1/21*l**3 - 1/2*l**2 + 1/84*l**4 + 2*l - 1/35*l**5. Let t(p) be the first derivative of v(p). What is r in t(r) = 0?
-1/3, 1/2
Let z(i) = i**2 - 14*i - 28. Let n be z(17). Factor -24*j - 7 + n + 4*j**2 + 20.
4*(j - 3)**2
Let x(h) = -h**2 + 4*h + 23. Let o be x(7). Suppose k - 5 + o = 0. Factor -1/4*t**k + 1 + 0*t - 3/4*t**2.
-(t - 1)*(t + 2)**2/4
Let j(n) be the first derivative of -5*n**7/42 + n**6/6 + n**5/4 - 5*n**4/12 - 7*n + 6. Let a(k) be the first derivative of j(k). Factor a(q).
-5*q**2*(q - 1)**2*(q + 1)
Let k be 5*(-4 - -3) + 5. Let z(t) be the third derivative of 0*t**4 + 1/240*t**6 + 0*t + 0 - 1/60*t**5 + k*t**3 - 5*t**2. Factor z(b).
b**2*(b - 2)/2
Let m(n) = 23*n - 228. Let b be m(10). Factor 0*f + 2/5*f**3 + 0 - 4/5*f**b + 2/5*f**4.
2*f**2*(f - 1)*(f + 2)/5
Let -25/3*c**3 - 5/3*c**2 + 0 - 5*c**5 - 35/3*c**4 + 0*c = 0. What is c?
-1, -1/3, 0
Determine h, given that 1/3 - 1/12*h**2 + 1/4*h = 0.
-1, 4
Factor -5*i**2 + 13*i**4 - 15*i**3 - 24*i**4 + 16*i**4 + 10*i - 2*i**5 + 7*i**5.
5*i*(i - 1)**2*(i + 1)*(i + 2)
Factor t**4 - 6 - 74*t**2 - 10*t**3 + 120*t - 3*t**4 + 30*t**3 - 66.
-2*(t - 3)**2*(t - 2)**2
Let -8*f**3 - 4*f**2 - 13*f**3 - 15*f + 24*f**2 + 16*f**3 = 0. What is f?
0, 1, 3
Factor -49/2*z + 35*z**2 - 12 + 3/2*z**3.
(z - 1)*(z + 24)*(3*z + 1)/2
Factor -92/5*z**4 + 256/5*z**3 + 64/5*z - 288/5*z**2 + 12/5*z**5 + 64/5.
4*(z - 2)**4*(3*z + 1)/5
Suppose -10*d = -11*d + 11. Let r(a) be the second derivative of 2/21*a**3 - d*a + 0 + 0*a**2 + 1/42*a**4. Factor r(w).
2*w*(w + 2)/7
Suppose -129*c**2 - 3888 + 9/2*c**4 + 2052*c + 3/4*c**5 - 261/4*c**3 = 0. Calculate c.
-9, 4
Let z = 5/52 + 2/13. Let s be (((800/(-140))/(-4))/((-4)/(-7)))/10. Suppose -1/8 + s*b**2 - 1/8*b**4 - 1/8*b**5 - 1/8*b + z*b**3 = 0. Calculate b.
-1, 1
Let u be 3/(-9) + -3 + 76/12. Determine b so that 2*b - 2*b**u - 15*b**2 + 7*b**3 + 8*b = 0.
0, 1, 2
Suppose -2*h - v = -19, 4*h = 8*h - 4*v - 32. Let u be ((-2)/(-24))/(1/h). Suppose 3/4*y**2 + u*y + 0 = 0. Calculate y.
-1, 0
Suppose -5*l + 16 = 3*x - 2, l = 4*x - 1. Let o = -65 + 65. Determine b, given that -3 + 3*b**2 + 3*b**3 + o + b - l*b - b = 0.
-1, 1
Let o(q) be the first derivative of q**3/5 - 78*q**2/5 + 153*q/5 - 360. Find h such that o(h) = 0.
1, 51
Let u(g) be the first derivative of g**6/14 - 6*g**5/35 - 3*g**4/14 + 4*g**3/7 + 3*g**2/14 - 6*g/7 + 42. Solve u(j) = 0.
-1, 1, 2
Suppose 2*j - 72 = -4*j. Factor 73*a**2 - 4*a**4 + 56*a**3 + 8*a**4 + j*a**4 + 9 + 42*a.
(a + 1)**2*(4*a + 3)**2
Let o be 2 - -13 - 4/(12/9). Suppose -10*s**4 + 16*s + o*s**2 + 19*s**4 + 6 - 11*s**4 = 0. What is s?
-1, 3
Let m(y) be the third derivative of -2*y**7/7 + y**6/30 + 62*y**5/15 - 2*y**4/3 - 16*y**3/3 - 2*y**2 - 2. Find x such that m(x) = 0.
-2, -1/3, 2/5, 2
Let 0*b - 3/7*b**4 + 6/7*b**2 + 0 + 17/7*b**3 = 0. What is b?
-1/3, 0, 6
Let z(h) be the third derivative of 0*h**3 - 5/8*h**4 - 1/12*h**5 + 0*h + 11*h**2 + 0. Determine f so that z(f) = 0.
-3, 0
Let t(r) be the first derivative of -1/7*r**2 + 6/35*r**5 - 1/2*r**4 - 12 + 0*r + 10/21*r**3. Let t(y) = 0. What is y?
0, 1/3, 1
Let g = 83 + -67. Let t be (6/10)/(6/g). Factor -t + 8/5*q - 2/5*q**2.
-2*(q - 2)**2/5
Let l be (-4592)/(-154) - 4/(-22). Factor -35 + 10*t**2 - 7*t**2 + 2*t**2 + l*t.
5*(t - 1)*(t + 7)
Solve -9 + 6 - 25*t - 2*t**2 + 19 + 39*t = 0.
-1, 8
Suppose c - 4*y = -9, y + 48 = -c + 54. Factor -2/11*i**c + 14/11*i**2 + 18/11 - 30/11*i.
-2*(i - 3)**2*(i - 1)/11
Let y(x) = -x + x**3 + 5*x + 2*x - 8*x - 1. Let h be y(2). Let -18/11*p**h - 4/11 + 0*p**2 + 14/11*p = 0. What is p?
-1, 1/3, 2/3
Let m(u) = -12*u + 516. Let h be m(43). Factor -1/7*o**2 - 1/7*o + h.
-o*(o + 1)/7
Let a(k) be the first derivative of -k**7/1680 + k**5/240 - k**3/3 - 2. Let d(g) be the third derivative of a(g). Find q such that d(q) = 0.
-1, 0, 1
Let h(v) = 20*v + 58. Let o(z) = 7*z + 19. Let g(d) = -3*h(d) + 8*o(d). Let w be g(-6). Suppose -2/3*q**w - 2/9*q + 0 + 8/9*q**3 = 0. What is q?
-1/4, 0, 1
Factor 23 - 22*c - 137 - 19*c - 9*c + 5*c**2 - 6.
5*(c - 12)*(c + 2)
Let q(z) be the second derivative of 2/3*z**4 + 0*z**6 - 2/21*z**7 + 0*z**3 + 0*z**2 + 0 + 31*z + 3/5*z**5. Factor q(m).
-4*m**2*(m - 2)*(m + 1)**2
Let x(a) be the second derivative of -24/5*a**2 + 0 + 4/5*a**3 + 7/20*a**4 - 17*a + 3/100*a**5. Solve x(s) = 0.
-4, 1
Let u(l) = -2*l + 10. Let c be u(4). Let j be (-20)/(-45) - (-2 + c)/2. Factor -j*x**2 + 2/9*x**3 + 0 + 2/9*x.
2*x*(x - 1)**2/9
Suppose 0 = i - 3, -i = 5*x - 0*i - 43. Suppose 6*y = x*y - 13*y. Factor -3/8*m**5 - 3/2*m**4 + y - 3/8*m - 9/4*m**3 - 3/2*m**2.
-3*m*(m + 1)**4/8
Let z(c) be the third derivative of -c**6/540 + 5*c**5/54 - 47*c**4/108 + 23*c**3/27 - 62*c**2. Suppose z(s) = 0. What is s?
1, 23
What is a in 11/4*a**3 + 5/4*a**2 + 0*a + 7/4*a**4 + 1/4*a**5 + 0 = 0?
-5, -1, 0
Let x(g) be the second derivative of -g**7/15120 - g**6/2160 - g**5/720 - 5*g**4/6 - 6*g. Let v(w) be the third derivative of x(w). Factor v(p).
-(p + 1)**2/6
Let d(y) = -4*y**2 + 6*y - 6. Let n(w) = -5*w**2 + 5*w - 6. Let g be ((-6 - -2) + 6)*-3. Let l(f) = g*d(f) + 4*n(f). Suppose l(u) = 0. What is u?
1, 3
Let m(b) be the second derivative of b**6/120 + b**5/40 + b**4/48 + 59*b - 1. Factor m(x).
x**2*(x + 1)**2/4
Let m = 5875/46 + -810/23. Let g = -92 + m. Suppose -g*i + 1/4*i**4 + 0*i**2 + 1/2*i**3 - 1/4 = 0. What is i?
-1, 1
Let z(y) be the third derivative of y**5/150 + y**4/4 + 12*y**3/5 + 2*y**2 - 6*y. Factor z(b).
2*(b + 3)*(b + 12)/5
Suppose 445*n - 435*n = 0. Factor 32/9*s + 2/9*s**3 - 16/9*s**2 + n.
2*s*(s - 4)**2/9
Let b be (-44)/(-16) + 3/(-4). Let i(t) = 6*t**2. Let y be i(1). Determine g, given that y*g**2 + 8*g**2 + 8*g + 3 - b + 2*g**2 = 0.
-1/4
Let n(d) = -5*d**4 - 16*d**3 - d**2 + 21*d - 1. Let l(h) = -h**3 - h**2 + h - 1. Let q(g) = -l(g) + n(g). Factor q(j).
-5*j*(j - 1)*(j + 2)**2
Factor -3/2 - 1/8*u**2 - 7/8*u.
-(u + 3)*(u + 4)/8
Let t = 64 - 72. Let o(y) = -20*y**2 + 48. Let s(h) = 7*h**2 - 16. Let c(r) = t*s(r) - 3*o(r). Find p, given that c(p) = 0.
-2, 2
Factor -185*b**2 - 347*b**2 - 548*b**3 + 564*b**3 - 408*b.
4*b*(b - 34)*(4*b + 3)
Suppose 3*p + 12 = -3*k + 2*k, 0 = -3*k - 3*p - 6. Let g(t) be the first derivative of 7/10*t**4 - 16/5*t**2 + 8/5*t + 2/3*t**k - 5. Factor g(z).
2*(z - 1)*(z + 2)*(7*z - 2)/5
Let l(k) be the second derivative of -k**6/6 - k**5 - 5*k**4/12 + 5*k**3 - 249*k. Solve l(g) = 0.
-3, -2, 0, 1
Suppose -4*m = -0*w + 2*w - 12, 0 = 4*w - 3*m - 13. Suppose 1 = w*b - 7. Factor b*x**3 + 20*x + 7*x**2 + 8 - 3*x**2 - 10*x**3.
-4*(x - 2)*(x + 1)*(2*x + 1)
Let i(q) be the third derivative of 0 + 19*q**2 + 7/3*q**4 + 0*q - 1/30*q**5 - 196/3*q**3. Suppose i(f) = 0. Calculate f.
14
Let v(h) = -h**4 - 5*h**2 - 9*h + 3. Let p(t) = -2*t**4 + 2*t**3 - 14*t**2 - 26*t + 8. Let m(g) = 3*p(g) - 8*v(g). What is f in m(f) = 0?
-3, -1, 0, 1
Let d(q) = q**3. Let c(j) = 4*j**4 - 16*j**3 + 148*j**2 - 240*j + 144. Let r(y) = y + 1. Let w be r(0). Let i(g) = w*c(g) - 24*d(g). Factor i(z).
4*(z - 3)**2*(z - 2)**2
Suppose h - 2 = -0*h. Factor -s**h + 79 + 10*s - 4*s**2 - 79.
-5*s*(s - 2)
Let j be 840/(-14)*146/14. Let y = -624 - j. Solve -3/7 - 3*w**4 + y*w**5 + 24/7*w**2 - 6/7*w - 6/7*w**3 = 0.
-1, -1/4, 1
Let b be ((-968)/(-55) - 18)/((-8)/15). Factor -3/2 + b*l**2 + 3/4*l.
3*(l - 1)*(l + 2)/4
Let z be 8 + ((-4)/(-2) - 30/6). Solve 59*m**z - m - 38*m**4 - 2*m**2 - 45*m**5 + 0*m**2 + 30*m**3 - 3*m = 0 for m.
-2/7, 0, 1
Let u(v) be the first derivative of -2*v**5/45 + v**4/18 + 14*v**3/27 - v**2/9 - 4*v/3 - 189. What is b in u(b) = 0?
-2, -1, 1, 3
Let m be (-16)/(-12)*5/30*-9 + 5. Suppose 0*h**2 + 1/4*h**m + 0 - 1/4*h = 0. What is h?
-1, 0, 1
Let c = 349/248 + -32/31. Factor -3/2*t**4 + 3/2*t - 3 - 3/8*t**5 - c*t**3 + 15/4*t**2.
-3*(t - 1)**2*(t + 2)**3/8
Let b(r) be the second derivative of -r**4/114 - 2*r**3/19 + 16*r**2/19 + 74*r. Suppose b(x) = 0. What is x?
-8, 2
Let u = 10/273 + 1588/1365. Determine n, given that -8/5 + 2/5*n**2 + u*n = 0.
-4, 1
Suppose -2*n + 3 = -q - 12, 5*q - 65 = -4*n. Let g = 12 - n. Factor 0*h**g + 2/3*h - 2/3*h**3 + 0.
-2*h*(h - 1)*(h + 1)/3
Let j(y) = -y**2 + 5*y - 1. Let i be (-3 - -3)/4 - -4. Let r be j(i). Determine q, given that -q - q + 2*q - r*q**2 - 3*q = 0.
-1, 0
What is m in -12 + 57*m