**2 - 1/75*f**6 + 2/15*f**3 + 1/30*f**4 + 0. Let c(a) = 0. Calculate a.
-2, -1, 0, 1
Suppose 5*l = 2*l + 5*l. Let j(u) be the third derivative of l*u**3 + 1/228*u**4 + 1/190*u**5 + 1/1995*u**7 + 0 + 0*u + 4*u**2 + 1/380*u**6. Factor j(z).
2*z*(z + 1)**3/19
Let b(d) = -d + 20. Let h be b(16). Suppose 2*z - 8 = -h*c, -2*c + 2*z + 4 = -0*c. Determine i so that -68*i**2 - i**3 - 12*i + 32*i**c + 15*i**4 - 8*i**3 = 0.
-1, -2/5, 0, 2
Let g(c) = -c**5 - c + 2. Let w(z) = -2*z**5 - z**3 - 2*z + 5. Let y(k) = -5*g(k) + 2*w(k). Suppose y(f) = 0. Calculate f.
-1, 0, 1
Let m(p) be the first derivative of -p**8/168 - 3*p**7/35 - p**6/4 + 5*p**5/6 + 23*p**2 + 56. Let z(a) be the second derivative of m(a). Factor z(h).
-2*h**2*(h - 1)*(h + 5)**2
Let s(z) be the first derivative of -3/2*z**2 - 1/4*z**4 - z**3 + 8 - z. Determine c so that s(c) = 0.
-1
Let k = 57 + -52. Let m be (-3)/(9/k) + 2. Factor t + 0*t**2 - m*t**3 - 2/3.
-(t - 1)**2*(t + 2)/3
Solve -3*x**2 + 8/5*x**3 - 8/5*x - 1/5*x**4 + 16/5 = 0.
-1, 1, 4
Let u(v) be the third derivative of v**7/70 + 3*v**6/40 + 4*v**2 - 7. Factor u(a).
3*a**3*(a + 3)
Suppose -15 = 3*z, 7*u + 7 = 3*u - 3*z. Find h, given that 2/7 - 4/7*h**3 + 4/7*h + 0*h**u - 2/7*h**4 = 0.
-1, 1
Let o(i) be the second derivative of -i**7/105 + i**5/10 + i**4/6 + 9*i**2/2 - 50*i. Let a(u) be the first derivative of o(u). Factor a(f).
-2*f*(f - 2)*(f + 1)**2
Let w = 1978/21 - 657/7. Factor 2/3*s - 2/3*s**3 + 0*s**2 + 1/3*s**4 - w.
(s - 1)**3*(s + 1)/3
Let d(h) be the second derivative of h**7/252 + h**6/90 + h**5/120 + 114*h. Factor d(t).
t**3*(t + 1)**2/6
Let c(d) be the first derivative of d**5/5 - 5*d**4 + 22*d**3/3 + 390*d**2 + 1521*d + 70. Factor c(r).
(r - 13)**2*(r + 3)**2
What is o in 1/2*o**4 - o**2 + 1/2 + 0*o + 0*o**3 = 0?
-1, 1
Let w(c) be the second derivative of -5*c**4/48 + 65*c**3/24 + 35*c**2/4 - 160*c. Solve w(a) = 0 for a.
-1, 14
Let x = -2058 + 10292/5. Solve -8/5 + 6/5*g**2 + 0*g + x*g**3 = 0 for g.
-2, 1
Suppose -2*l + 7 = -1. Let b be 87 + -80 + -2*(-10)/(-4). Determine s so that -2/3*s**l - 2/3*s**b + 0 + 0*s + 4/3*s**3 = 0.
0, 1
Let t(i) be the third derivative of i**7/70 + i**6/5 - 9*i**5/20 - 4*i**2 - 2*i. Factor t(v).
3*v**2*(v - 1)*(v + 9)
Solve 0 + 7/5*j**2 + j**3 + 1/5*j**4 + 3/5*j = 0 for j.
-3, -1, 0
Suppose 5*q = -0*n - n + 7, 0 = 3*n + q - 7. Let x be 13 + -11 + n*1/(-3). Let -8/3 + x*v**3 - 2/3*v**4 - 8/3*v + 2*v**2 = 0. What is v?
-1, 2
Let b(p) be the third derivative of p**8/180 + 2*p**7/105 + p**6/90 - p**5/45 + 3*p**3/2 - 24*p**2. Let y(z) be the first derivative of b(z). Factor y(k).
4*k*(k + 1)**2*(7*k - 2)/3
Let l(x) be the second derivative of -x**7/10080 - x**6/5760 + 29*x**4/12 - 18*x. Let v(g) be the third derivative of l(g). Factor v(d).
-d*(2*d + 1)/8
Let y = -2/3417 - -43288/10251. Let b = y - 257/63. Factor -b*a**2 + 3/7*a + 0.
-a*(a - 3)/7
Let b be (15 + (-705)/45)*-1*6. Let x(o) be the third derivative of -1/160*o**6 + 0*o - 3/80*o**5 + 1/32*o**b + 0 + o**2 + 1/4*o**3 + 1/280*o**7. Factor x(m).
3*(m - 2)*(m - 1)*(m + 1)**2/4
Let t = 8857/4 + -2214. Factor 0 - 1/4*b + 0*b**2 + t*b**3.
b*(b - 1)*(b + 1)/4
What is s in -4/7*s**2 - 24/7*s - 36/7 = 0?
-3
Let a(i) = -8*i**3 + 4*i + 1. Let h(d) be the first derivative of 7*d**4/4 - 5*d**2/2 - 2*d + 6. Let q(t) = 4*a(t) + 5*h(t). Let q(v) = 0. Calculate v.
-1, 2
Let j be (-5)/2 - 7139/(-2662). Let i(b) be the first derivative of -2/33*b**3 + 0*b - j*b**4 + 2/11*b**5 + 0*b**2 - 13. Factor i(z).
2*z**2*(z - 1)*(5*z + 1)/11
Suppose -33*x + 88*x = 28*x. Let 1/7*v**2 + x + 3/7*v = 0. What is v?
-3, 0
Suppose 52 = -19*h + 52. Factor 0 - 12/5*c**3 + h*c + 14/5*c**2 - 2/5*c**4.
-2*c**2*(c - 1)*(c + 7)/5
Suppose -64*p**3 + 2*p**3 - 6*p**5 + 22*p**2 + 74*p**4 - 41*p**3 + 45*p**3 - 32*p**3 = 0. What is p?
0, 1/3, 1, 11
Let r(z) be the second derivative of 20*z**4/3 - 60*z**3 + 405*z**2/2 + 3*z + 5. Let r(u) = 0. What is u?
9/4
Let s be ((-3)/9)/(1/(-6)). Factor 2*j**2 - 24 - 42 + 4*j + 2*j**s + 42.
4*(j - 2)*(j + 3)
Let h(j) be the third derivative of j**5/40 + 17*j**4/16 - 19*j**3/2 + 528*j**2. Suppose h(l) = 0. Calculate l.
-19, 2
Let d = 61/17 - 166/51. Let o(l) be the second derivative of -d*l**3 + 0 + 6*l + 1/24*l**4 + l**2. What is f in o(f) = 0?
2
Let j(z) be the third derivative of z**10/10080 - z**9/2520 - z**8/2240 + z**7/420 + z**4/24 + z**2. Let w(o) be the second derivative of j(o). Factor w(q).
3*q**2*(q - 2)*(q - 1)*(q + 1)
Determine j, given that -22*j**3 - 9520*j - 5287 - 5463 - 6 - 274*j**2 + 20*j**3 + 1508 = 0.
-68, -1
Let y(t) = -t**5 - 6*t**3 + t**2 + 3. Let j(d) = 2*d**5 - d**4 + 11*d**3 - 2*d**2 - 5. Let v(q) = 3*j(q) + 5*y(q). Factor v(g).
g**2*(g - 1)**3
Let x be -3*(-4)/(60/385). Let o = x - 77. Suppose -2/5*v**2 + o + 2/5*v = 0. Calculate v.
0, 1
Let k(a) be the third derivative of a**7/1575 - a**5/450 - 135*a**2. Let k(r) = 0. What is r?
-1, 0, 1
Let o(j) be the third derivative of j**6/420 - 4*j**5/105 - 19*j**4/84 - 10*j**3/21 - 12*j**2 + 6. Find f, given that o(f) = 0.
-1, 10
Let f(s) be the third derivative of s**6/40 + 7*s**5/20 + 11*s**4/8 + 5*s**3/2 + 41*s**2. Factor f(k).
3*(k + 1)**2*(k + 5)
Let k(l) be the second derivative of 0*l**2 - 2*l - 1/462*l**7 + 0 - 1/66*l**4 - 1/44*l**5 - 2/165*l**6 + 0*l**3. Solve k(t) = 0.
-2, -1, 0
Determine i so that -82*i + 2*i**4 + 18*i + 34*i**3 - 98*i**3 + 22*i**3 + 72*i**2 + 18*i**3 = 0.
0, 2, 8
Let d(l) be the first derivative of -2 - 1/6*l**4 - 16*l**2 + 6*l - 8/3*l**3. Let x(b) be the first derivative of d(b). Let x(u) = 0. What is u?
-4
Let u(c) = -12*c**2 - 4*c - 16. Let y(o) = -8*o**2 + 3*o - 5. Let v(w) = -4*w**2 + w - 3. Let t(p) = 5*v(p) - 2*y(p). Let d(f) = 16*t(f) - 5*u(f). Factor d(m).
-4*m*(m - 1)
Let b(j) be the third derivative of 0*j - 2*j**2 + 0*j**3 + 0 - 1/160*j**5 + 5/64*j**4. Factor b(m).
-3*m*(m - 5)/8
Let d(w) = -w**3. Let u(g) = 42*g**3 + 45*g**2 + 10*g. Let x(b) = 3*d(b) - u(b). Factor x(s).
-5*s*(3*s + 1)*(3*s + 2)
Let 26 + 2*r + 28 + 0*r**2 - r**2 + 9*r + 42*r = 0. Calculate r.
-1, 54
Let o be 27/9 - 3*2. Let z be o/(2 - (-7)/(-2)). Suppose -121 - 2*t**3 + 2*t**z + 121 = 0. What is t?
0, 1
Solve -24*k**2 - 354*k**3 + 370*k**3 - 16*k + 6*k**4 - 2*k**4 + 20 = 0.
-5, -1, 1
Let h = -16833 - -117833/7. Factor -2/7*n**2 + 2/7*n + 0 - 2/7*n**3 + h*n**4.
2*n*(n - 1)**2*(n + 1)/7
Let x(m) be the third derivative of 9*m**6/80 - 73*m**5/20 + 167*m**4/16 - 15*m**3/2 - 10*m**2 + 4*m. Find g, given that x(g) = 0.
2/9, 1, 15
Let k be 1/(-1)*(-5)/105*492/41. Solve 0*t**2 + k*t**5 + 0*t**3 + 0 - 4/7*t**4 + 0*t = 0.
0, 1
Suppose 13*t = 28*t. Find y such that 0*y**2 + 0*y - 2/5*y**3 + t - 1/5*y**4 = 0.
-2, 0
Let z = -25373/7 - -3625. Determine y so that 2/7*y**2 - z*y**3 + 0 + 4/7*y = 0.
-1, 0, 2
Let x = -27619 - -27621. Let 7/4*f**3 + 35/2*f + 47/4*f**x - 6 = 0. Calculate f.
-4, -3, 2/7
Let p = -22 + 22. Suppose 4*i - i + d - 1 = p, -3*d - 11 = 2*i. Solve -5*c**i + 5*c**2 - 3 + 3*c**2 = 0.
-1, 1
Let j(p) = p + 20. Let v be j(4). Solve 0*q**3 + 5*q**2 - 26*q**2 + 19*q**2 - 16*q + 2*q**3 + v = 0.
-3, 2
Let w(f) = -f**2 + 13*f + 4. Let b be 1/((2/(-2))/(-13)). Let k be w(b). Factor -33*j - j**3 + 30*j + k*j**3.
3*j*(j - 1)*(j + 1)
Suppose -3*c = -0*c - 21. Suppose -5*j = -2*b - 48, 0 = -c*j + 2*j - 5*b + 20. Find m, given that -31*m**4 + 12*m**4 + j*m**2 + 15*m**4 - 4 = 0.
-1, 1
Find i, given that 4*i - 36 + 2*i**3 + 36*i**2 - 11*i + 11*i - 6*i**3 = 0.
-1, 1, 9
Factor 99*h - 150 + 45*h + 80*h**2 + 22 - 12*h**3.
-4*(h - 8)*(h + 2)*(3*h - 2)
Suppose -57*a + 168 = -3. Suppose -2/9*k**4 + 4/9*k**a - 8/9 - 8/9*k + 2/3*k**2 = 0. Calculate k.
-1, 2
Suppose -t - 5 = -2*n, 20 = 3*n - 3*t - t. Suppose n = -5*p + 4 + 6. Factor -2/9*k**p + 0*k + 0.
-2*k**2/9
Factor 0*s**2 + 0 - 4/3*s + 1/3*s**4 + s**3.
s*(s - 1)*(s + 2)**2/3
Let s(c) be the third derivative of -c**6/24 + c**5/2 + 35*c**4/24 - 80*c**2. What is g in s(g) = 0?
-1, 0, 7
Let c(z) be the second derivative of 2/7*z**2 - 3/7*z**3 + 2/35*z**5 + 1/14*z**4 - 10*z + 0. Suppose c(j) = 0. Calculate j.
-2, 1/4, 1
Let p(r) be the second derivative of 9*r**7/1400 + 3*r**6/100 + 3*r**5/50 + r**4/15 + 5*r**3/6 - 2*r. Let y(m) be the second derivative of p(m). Factor y(a).
(3*a + 2)**3/5
Factor -7/3*p**2 - 8/3*p + 0 + 1/3*p**3.
p*(p - 