
5*g**2*(g - 1)*(4*g + 1)/2
Let l be 1232/121 + (-2)/11. Factor l*y**3 - 48*y**4 - 26*y**3 - y**5 - 19*y**5.
-4*y**3*(y + 2)*(5*y + 2)
Let q(b) be the first derivative of -b**6/3 - 4*b**5/5 + 6*b**4 + 28*b**3/3 - 11*b**2 - 24*b - 205. Determine g, given that q(g) = 0.
-4, -1, 1, 3
Let j = -14998/3 - -5032. Factor 2/3*o**2 + 28/3*o + j.
2*(o + 7)**2/3
Let f(a) be the second derivative of -a**7/189 + 83*a**6/135 - 235*a**5/9 + 447*a**4 - 1539*a**3 + 2187*a**2 - 376*a. Let f(j) = 0. What is j?
1, 27
Let y(s) be the second derivative of 0*s**3 + 7/20*s**4 + 0 + 0*s**2 + 28*s - 3/100*s**5. Factor y(t).
-3*t**2*(t - 7)/5
Let w(u) be the second derivative of u**6/70 - 36*u**5/35 + 207*u**4/14 + 1944*u**3/7 + 19683*u**2/14 - 92*u + 2. Factor w(k).
3*(k - 27)**2*(k + 3)**2/7
Let z(s) be the first derivative of 2*s**3/27 + 8*s**2/9 + 8*s/3 + 318. Factor z(v).
2*(v + 2)*(v + 6)/9
Let d(m) be the third derivative of -1/3*m**3 + 0 - 1/8*m**4 - 1/60*m**5 + 0*m + 5*m**2. Factor d(f).
-(f + 1)*(f + 2)
Suppose -7*n = 2*n + 9*n - 4*n. Factor 4/3*x**2 - 10/3*x**5 - 16/3*x**4 - 2/3*x**3 + n + 0*x.
-2*x**2*(x + 1)**2*(5*x - 2)/3
Factor 12*b - 11*b**2 - 9/2 - 1/2*b**4 + 4*b**3.
-(b - 3)**2*(b - 1)**2/2
Let l be (-17)/15 + 1 + 8/60. Let r(s) be the first derivative of s**4 + l*s - 8/3*s**3 + 2*s**2 + 9. Factor r(k).
4*k*(k - 1)**2
Let s(n) be the second derivative of n**7/3360 - n**6/240 + 3*n**5/160 + n**4/2 + 13*n. Let z(f) be the third derivative of s(f). Factor z(r).
3*(r - 3)*(r - 1)/4
Let v(y) be the first derivative of 1 - 2*y**3 - y - 1/5*y**5 + 2*y**2 + y**4. Find z, given that v(z) = 0.
1
Let y(w) = 73*w + 1. Let l be y(4). Let p = l - 2047/7. Find x such that 2/7 - p*x + 2/7*x**2 = 0.
1
Let k(n) be the second derivative of 1/180*n**5 - 1/54*n**3 - 1/18*n**2 + n + 1/108*n**4 + 0. Factor k(g).
(g - 1)*(g + 1)**2/9
Let -18*p**5 - 12*p**3 + 58*p**4 - 9*p**5 - 10*p**4 + 6*p**5 = 0. Calculate p.
0, 2/7, 2
Let i(q) be the first derivative of 1/3*q + 1/24*q**4 - 1/12*q**2 - 1/9*q**3 + 16. Find f such that i(f) = 0.
-1, 1, 2
Let f be 20/3 + 46 + -50. Determine g so that 34/3*g**3 - f*g - 7*g**4 + 20/3*g**2 + 0 = 0.
-2/3, 0, 2/7, 2
Let q be (-12)/(-9) + (-2)/(-3). Suppose 8 = 2*k - 0*k - 2*o, 2*k - 5*o = 11. Determine f so that 2*f + f + f - 2 - k*f**2 + f**q = 0.
1
Suppose 3*k = -4*r + 7 + 9, -4*k - r + 17 = 0. Let j(y) be the third derivative of 0*y**3 - 1/80*y**5 + 0 - 1/32*y**k + y**2 + 0*y. What is o in j(o) = 0?
-1, 0
Let u be 3/(-3) - (-5 + 2). Suppose 21*c**u + 2*c + c**4 - 10*c**2 - 5*c**2 - 9*c**2 = 0. What is c?
-2, 0, 1
Let s(d) be the third derivative of d**6/60 + d**5/30 - 4*d**4/3 + 20*d**3/3 + 55*d**2. Determine n so that s(n) = 0.
-5, 2
Let i(n) be the second derivative of n**3 + 0 + 13/30*n**5 - 4/3*n**4 + 0*n**2 - 2/45*n**6 - 14*n. Solve i(v) = 0 for v.
0, 1/2, 3
Let h(x) = -x + 1. Let c be h(-7). Let k be (-10)/c*(-4 + 0). Factor 4*l**5 - 10*l + k*l**4 + 10*l + l**3.
l**3*(l + 1)*(4*l + 1)
Suppose -2*q + 1 = -2*z + 3, 0 = 5*z + 2*q - 5. Let y be 0*((-4)/(-6) - z). Let -9 - 15*h + 82*h**2 - 89*h**2 - h**3 + y*h = 0. What is h?
-3, -1
Let o(u) be the first derivative of u**4/15 + u**3/5 + 11*u + 10. Let n(x) be the first derivative of o(x). Determine s, given that n(s) = 0.
-3/2, 0
Factor -3*i**4 - 3*i**3 + i - i**3 + 5*i**4 + i**3.
i*(i - 1)**2*(2*i + 1)
Solve 3/10*p**4 - 9/10 - 22/5*p - 29/5*p**2 - 2*p**3 = 0.
-1, -1/3, 9
Let f be (4 + 8/(-3))*3. Factor -6*h**2 + h**2 - f*h + 39*h.
-5*h*(h - 7)
Find n, given that -n**2 + 591*n**3 + 2*n + 8*n**2 - 593*n**3 - 4 - n**2 - 2*n**4 = 0.
-2, -1, 1
Let b be (2/2)/(((-6)/(-20))/3). Suppose -x - 4*f - 10 = -2*f, -3*x - 2*f - b = 0. Factor 2/9*u**3 - 4/9*u + 2/9*u**2 + x.
2*u*(u - 1)*(u + 2)/9
Factor 23/2*c**3 - 10*c**4 + 0 + 0*c - 3*c**2.
-c**2*(4*c - 3)*(5*c - 2)/2
Factor 2*f**3 - 255*f + 3*f**2 + 450 - 7*f**3 + 23*f**3 - 13*f**3 + 17*f**2.
5*(f - 3)**2*(f + 10)
Determine g so that -1/5 - 3150*g**2 - 503/10*g + 7938/5*g**3 = 0.
-1/126, 2
Suppose -4*o + 7*o + 1 = 5*y, 0 = -2*o - 5*y + 16. Let l = 427/78 - 21/26. Find i such that 32/3*i**4 + 4/3*i**2 + 22/3*i**o + l*i**5 + 0*i + 0 = 0.
-1, -2/7, 0
Solve 8/7*v**2 + 0 + 0*v + 2/7*v**3 = 0.
-4, 0
Let n(b) be the first derivative of 2*b**5/45 + b**4/9 - 2*b**3/9 - 4*b**2/9 + 8*b/9 + 24. Determine k so that n(k) = 0.
-2, 1
Let i(w) be the first derivative of w**6/2 + 6*w**5/5 - 81*w**4 - 670*w**3 - 2175*w**2/2 + 4500*w + 466. Solve i(f) = 0 for f.
-5, 1, 12
Let n(d) be the third derivative of 0 - 1/50*d**5 + 3*d**2 + 1/5*d**3 - 1/560*d**8 + 0*d + 1/50*d**6 + 0*d**7 - 3/40*d**4. Determine j, given that n(j) = 0.
-2, -1, 1
Let g(s) be the third derivative of -s**6/30 - 7*s**5/15 - 11*s**4/6 - 10*s**3/3 - 2*s**2 - 33*s. Find q, given that g(q) = 0.
-5, -1
Let l be -1 + (-10)/(-14) - (-80)/840*3. Determine o, given that 0*o - 4/9*o**3 + 0 + 2/9*o**5 - 2/9*o**4 + l*o**2 = 0.
-1, 0, 2
Let u(l) be the first derivative of -l**4/3 + 26*l**3/9 + 23*l**2/3 + 16*l/3 + 37. Solve u(x) = 0 for x.
-1, -1/2, 8
Suppose -12*x + 13*x + 69 = 0. Let s = 74 + x. Factor 0*j - 4/5*j**2 - 16/5*j**4 - 14/5*j**3 + 0 - 6/5*j**s.
-2*j**2*(j + 1)**2*(3*j + 2)/5
Let l(o) = o**2 - 2*o - 1. Let g(z) = 2*z**2 + 42*z - 579. Let x(p) = g(p) - 3*l(p). Factor x(m).
-(m - 24)**2
Suppose -3*m = -10*f + 35, 7*m = -2*f + 3*m - 16. Find i, given that 16/5*i**2 - 16/5*i**4 + 0 - 18/5*i**3 + f*i**5 + 8/5*i = 0.
-1, -2/5, 0, 1, 2
Let v(y) be the third derivative of y**6/180 - 2*y**5/27 + y**4/4 - 10*y**3/27 - 161*y**2. Solve v(g) = 0 for g.
2/3, 1, 5
Suppose 2/3*t**2 + 4*t + 0 = 0. Calculate t.
-6, 0
Let z be -2*(-2 + -2*(-20)/16). Let m be (-3)/(-6)*(-1 - z). Factor 2/7 + m*j - 2/7*j**2.
-2*(j - 1)*(j + 1)/7
Let m(n) be the third derivative of 0*n + 0 - 1/12*n**4 + 0*n**3 - 32*n**2 - 1/120*n**5. Factor m(h).
-h*(h + 4)/2
Let z(t) be the third derivative of -t**6/30 + 14*t**5/15 - 49*t**4/6 - 238*t**2. Let z(m) = 0. Calculate m.
0, 7
Let m(x) be the second derivative of -5*x**8/336 - 2*x**7/21 - 7*x**6/60 - x**5/15 - 17*x**4/6 + 19*x. Let q(l) be the third derivative of m(l). Factor q(s).
-4*(s + 2)*(5*s + 1)**2
Suppose -h + 5*z = 6, -4*z = -4*h - z + 10. Let d(m) be the first derivative of 0*m - 2/3*m**3 - 7 + 0*m**2 - 1/4*m**h. Solve d(p) = 0.
-2, 0
Factor 0 + 6/7*f**2 - 2/7*f**4 - 4/7*f**3 + 0*f.
-2*f**2*(f - 1)*(f + 3)/7
Let r be (-18)/(-8) - 7/28. Let v(g) be the first derivative of 32/3*g**2 + r - 27/2*g**4 - 8/3*g - 10*g**3. Determine a, given that v(a) = 0.
-1, 2/9
Let r(w) be the first derivative of -2/27*w**3 + 0*w - 1/9*w**4 - 16 + 1/9*w**2. Factor r(j).
-2*j*(j + 1)*(2*j - 1)/9
Let i(n) = n**3 + 4*n**2 + n - 3. Let h be i(-2). Suppose o + h*o - 8 = 0. Factor -9/7*j**3 + 2/7 - 5/7*j - 16/7*j**o.
-(j + 1)**2*(9*j - 2)/7
Let a(g) = -5*g**2 - 267*g - 61. Let m be a(-53). Factor 9*j**2 + 3/5*j**3 + 75 + m*j.
3*(j + 5)**3/5
Factor -129/7*t + 30/7 - 27/7*t**2.
-3*(t + 5)*(9*t - 2)/7
Let v(r) = -r**2 - 10*r + 2. Let b be v(-8). Let z = -16 + b. Determine f so that 22*f**z - 27*f**2 + 10 - 2*f - 3*f = 0.
-2, 1
Let x = -1901/42 - -275/6. Let x*z**2 - 8*z + 28 = 0. Calculate z.
7
Suppose -28*d + 20 = -24*d. Factor 5*i**d + 15*i**3 + 1 - 15*i**4 - 1 + 40*i**2 - 45*i**2.
5*i**2*(i - 1)**3
Let u(v) be the second derivative of -6/5*v**5 + 6*v**2 - 2/15*v**6 - 2/3*v**4 + v + 2/21*v**7 + 10/3*v**3 + 3. Suppose u(m) = 0. Calculate m.
-1, 1, 3
Suppose -40 = -7*o + 3*o. Let b be 4/o*(-10)/(-8). What is m in -m + b*m**2 + 1/2 = 0?
1
What is y in 1/7 + 22/7*y**2 + 8/7*y + 4/7*y**5 + 4*y**3 + 17/7*y**4 = 0?
-1, -1/4
Let x(g) be the third derivative of g**5/90 - 26*g**4/3 + 2704*g**3 + 576*g**2. Factor x(n).
2*(n - 156)**2/3
Let k(p) be the first derivative of p**4/6 - 8*p**3/9 + p**2 - 402. Factor k(v).
2*v*(v - 3)*(v - 1)/3
Let m(c) = 11 + 3*c**3 - 5*c**2 + 21*c + 11*c**2 + 2*c**2 - 4*c**4. Let s(d) = d**4 - d**3 + d**2 - d - 1. Let x(v) = 4*m(v) + 12*s(v). Factor x(n).
-4*(n - 4)*(n + 1)**2*(n + 2)
Let x = -60 + 62. Suppose w - 2*w + 8 = 0. What is f in 0*f + 6*f**x - w*f**2 + 2 + 3*f - 10*f**2 + 7*f**3 = 0?
-2/7, 1
Let c be -2*(-16)/(-40)*-15. Let r(b) be the second derivative of 0*b**2 - 1/48*b**4 - 1/12*b**3 - c*b + 0. Factor r(l).
-l*(l + 2)/4
Suppose 4*n = 4*f + 3 + 5, f - 3*n + 12 = 0. Determine t so that 