*b**2 + 3 + 0*b + 2/15*b**3 - 1/10*b**4. Let y(c) = 0. Calculate c.
0, 1
Let f(u) be the first derivative of u**6/2160 + u**5/90 + u**4/9 - 7*u**3/3 + 7. Let y(k) be the third derivative of f(k). Factor y(x).
(x + 4)**2/6
Let i(g) = -7*g**2 + 4*g + 4. Let b be -3*(3 - (-5)/(-3)). Let z(v) = 6*v**2 - 3*v - 3. Let k(a) = b*z(a) - 3*i(a). Factor k(u).
-3*u**2
Suppose 5*r - 17 - 3 = 0. Let p = r - 2. Factor 0 + 0*f**5 - 2*f**4 - 2*f - 2*f**5 - f**2 + 4*f**3 + 5*f**2 - p.
-2*(f - 1)**2*(f + 1)**3
Factor 0 + 4/3*q**3 + 0*q**2 - 4/3*q.
4*q*(q - 1)*(q + 1)/3
Let o(l) be the second derivative of -l**5 + 55*l**4/12 - 25*l**3/6 - 5*l**2 + 4*l. Factor o(f).
-5*(f - 2)*(f - 1)*(4*f + 1)
Let f = 143/2 + -71. Let l(g) be the first derivative of f*g**6 + 0*g + 0*g**3 - 2/5*g**5 + 0*g**2 + 1 + 0*g**4. Factor l(d).
d**4*(3*d - 2)
Let c(p) be the second derivative of 3*p**5/35 + p**4/4 + p**3/7 - 3*p**2/14 - 5*p. Find w such that c(w) = 0.
-1, 1/4
Let m(x) be the second derivative of -x**9/22680 + x**8/10080 - x**4/4 - 4*x. Let w(b) be the third derivative of m(b). Find f, given that w(f) = 0.
0, 1
Let k(p) be the first derivative of -p**4 - 20*p**3/3 + 12*p**2 + 8. Factor k(f).
-4*f*(f - 1)*(f + 6)
Let m(i) be the second derivative of -i**5/150 - i**4/20 - 2*i**3/15 - i**2/2 + 3*i. Let v(y) be the first derivative of m(y). Let v(o) = 0. What is o?
-2, -1
Let s(u) = 3*u**3 - 17*u**2 - 3*u + 3. Let c(j) = -j**3 + 9*j**2 + j - 1. Let l(k) = 7*c(k) + 4*s(k). Determine i so that l(i) = 0.
-1, 1
Let j(f) = 5*f**3 - 2*f**2 + f + 4. Suppose 0*q - 2*q = 8. Let g(o) = 4*o**3 - 2*o**2 + o + 3. Let v(x) = q*g(x) + 3*j(x). What is h in v(h) = 0?
0, 1
Suppose -2*q + 5 = -3*f + 2, 2*q + 4*f + 4 = 0. Let c be (-40)/28 - (q - 2). Solve -2/7*n**2 - 6/7*n - c = 0 for n.
-2, -1
Let g(q) be the third derivative of -1/45*q**5 + 0*q + 0*q**3 - 3*q**2 + 1/180*q**6 + 0 + 1/36*q**4. Solve g(x) = 0.
0, 1
Let p(q) be the third derivative of 1/945*q**7 + 0 - 2*q**2 + 5/108*q**4 - 2/27*q**3 - 1/540*q**6 + 0*q - 1/90*q**5. Factor p(f).
2*(f - 1)**3*(f + 2)/9
Let t(g) be the third derivative of g**5/12 - 5*g**4/24 - 5*g**3/3 + 39*g**2. Factor t(o).
5*(o - 2)*(o + 1)
Let r(h) be the first derivative of 0*h - 2/5*h**5 + 0*h**2 - 8/3*h**3 - 1 + 2*h**4. Determine z so that r(z) = 0.
0, 2
Let m(q) be the third derivative of 3*q**6/160 + q**5/16 + q**4/32 - q**3/8 - 2*q**2. Factor m(f).
3*(f + 1)**2*(3*f - 1)/4
Suppose -3*o + 14 = m, -2*m + 33 - 13 = 4*o. Let y = 6 - o. Factor -f**5 + 5*f**4 - 6*f**3 - 6*f**4 + 5*f**4 - f + 4*f**y.
-f*(f - 1)**4
Let g = -149/10 + 15. Let z(u) be the second derivative of -2/3*u**3 + 0 + g*u**5 - 1/6*u**4 + u + 0*u**2. Let z(i) = 0. What is i?
-1, 0, 2
Let x be 66/(-45)*-5 + -8 + 1. Factor x*g**2 - g + 2/3.
(g - 2)*(g - 1)/3
Find s, given that -4/3*s**3 + 4/3*s - 8/3*s**2 + 8/3 = 0.
-2, -1, 1
Let c be (6/2)/((-144)/(-32)). Factor -c*n - 5/3*n**2 + 1.
-(n + 1)*(5*n - 3)/3
Factor 0 - 2/3*g**2 + 0*g - 1/3*g**3.
-g**2*(g + 2)/3
Let j = -20 - -22. Factor 2*c**4 + 10*c**3 - 7*c**3 - 5*c**4 - c**j + c**5.
c**2*(c - 1)**3
Let l(f) be the second derivative of f**7/14 - f**6/10 - 3*f**5/20 + f**4/4 - f. Find n, given that l(n) = 0.
-1, 0, 1
Let k = -5 + 7. Let w = k + 1. Let -c + 6*c**w + 3/2*c**2 + 0 + 7/2*c**4 = 0. Calculate c.
-1, 0, 2/7
Let s(t) be the first derivative of 2*t**5/15 - t**4/6 - 8*t**3/9 + 4*t**2/3 + 33. Find g such that s(g) = 0.
-2, 0, 1, 2
Let b(c) = -c + 1. Let h be b(-5). Let a(r) be the third derivative of 0*r + 1/160*r**h + 1/280*r**7 + 3*r**2 + 0*r**3 + 0 - 1/80*r**5 - 1/32*r**4. Factor a(f).
3*f*(f - 1)*(f + 1)**2/4
Let m be 0 + (-2)/(4 - 2). Let n be -11*(-3)/27 + m. Determine j so that -2/9*j**2 + 0 - n*j = 0.
-1, 0
Let f = -346 + 2424/7. Let -f*h - 6/7*h**2 + 8/7*h**3 + 0 = 0. What is h?
-1/4, 0, 1
Let o(t) = -t**3 + 2*t**2 + 5*t - 3. Let m be o(3). Suppose -4*s + 3*s - m = 5*k, -2*s = 3*k + 6. Factor 1/4*x**3 + k*x + 0 + 1/4*x**2.
x**2*(x + 1)/4
Let y(o) be the first derivative of o**8/280 - o**7/105 - o**6/270 + o**5/45 + o**4/36 + o**3 - 4. Let t(z) be the third derivative of y(z). Factor t(g).
2*(g - 1)**2*(3*g + 1)**2/3
Let i(y) = y**3 + y**2 - y - 1. Let f(u) = 4*u**4 + 5*u**3 - 5*u**2 + u + 1. Let p(a) = -f(a) - i(a). Suppose p(o) = 0. What is o?
-2, 0, 1/2
Factor -1/3*t**5 + 0 - 1/3*t**4 + 0*t + 0*t**2 + 2/3*t**3.
-t**3*(t - 1)*(t + 2)/3
Let w = -2/29 + 35/87. Suppose 0*q + 1/3*q**2 - w = 0. What is q?
-1, 1
Let o(w) = -3*w**4 - 4*w**3 + w**2 - 2*w. Let l(p) = -7*p**4 - 9*p**3 + 3*p**2 - 5*p. Let d(y) = 2*l(y) - 5*o(y). Determine b so that d(b) = 0.
-1, 0
Suppose 5/2*i - 1/2*i**4 + 3/2*i**2 + 1 - 1/2*i**3 = 0. Calculate i.
-1, 2
Factor 0*x + 2/3*x**2 + 0.
2*x**2/3
Factor 0*x**2 + 3/4*x**3 + 0 - 3/4*x.
3*x*(x - 1)*(x + 1)/4
Let h(v) be the second derivative of -v**9/5040 + v**7/420 - v**5/40 - v**4/6 - 2*v. Let a(t) be the third derivative of h(t). Factor a(i).
-3*(i - 1)**2*(i + 1)**2
Let i(u) be the first derivative of -2/3*u**3 - 3 - 2*u**2 - 2*u. Suppose i(w) = 0. Calculate w.
-1
Suppose 0 = 22*z + 52 - 96. Solve -3/4*i**z - 7/4*i**3 + 0 + 5/4*i**5 + 1/2*i + 3/4*i**4 = 0 for i.
-1, 0, 2/5, 1
Let c(j) be the third derivative of j**5/12 + 5*j**4/12 + 5*j**3/6 + 16*j**2. Let c(h) = 0. What is h?
-1
Suppose -4*h = -w + 14, 0*w + 4*w - 3*h - 17 = 0. Let 2/3*z**5 + 4/3*z + 0 - 2/3*z**w + 2/3*z**4 - 2*z**3 = 0. Calculate z.
-2, -1, 0, 1
Suppose -4*x + 10 = 4*o - 2, -2*o = -4*x - 24. Let r be o/4*(-2)/(-3). Factor -4*g**2 - 3*g - r - 3*g + g**2 - 2.
-3*(g + 1)**2
Suppose -30*h = -33*h. Factor 2/3*t**3 + 2/9*t**5 + h*t - 2/3*t**4 - 2/9*t**2 + 0.
2*t**2*(t - 1)**3/9
Suppose -1 = 2*i - 11. Suppose 0 = -3*l + i*l. Find q such that l*q + q**3 - 4/3 + 7/3*q**2 = 0.
-2, -1, 2/3
Let n(g) be the second derivative of g**6/15 - g**4/2 + 2*g**3/3 + 19*g. Factor n(l).
2*l*(l - 1)**2*(l + 2)
Let q(o) = 33*o**3 - 57*o + 3. Let a(f) = f**2 - 2*f - 7. Let u be a(5). Let h(d) = -1 + 14*d + 0 + 0 - u*d**3 + 0*d. Let c(v) = -21*h(v) - 5*q(v). Factor c(l).
3*(l - 1)**2*(l + 2)
Let q(i) be the second derivative of -6*i + 0 + 1/2*i**2 + 1/24*i**4 - 1/4*i**3. Let q(t) = 0. Calculate t.
1, 2
Let b(x) be the first derivative of 1/30*x**4 + 0*x**2 - 4 - 2/15*x**3 + 3*x. Let k(o) be the first derivative of b(o). Factor k(u).
2*u*(u - 2)/5
Factor 2/7*v**3 + 32/7*v + 0 - 16/7*v**2.
2*v*(v - 4)**2/7
Let t(s) be the second derivative of -s**4/4 + s**3/6 + s**2 - 16*s. Factor t(m).
-(m - 1)*(3*m + 2)
Let c = -1/291 + 589/2037. Factor 0 + 0*a**3 + 4/7*a**4 - 2/7*a**5 - 4/7*a**2 + c*a.
-2*a*(a - 1)**3*(a + 1)/7
Let j(f) = -4 - 2*f + 5*f**3 - 2*f + 3 + f**2 + 5*f. Let b(s) = -24*s**3 - 4*s**2 - 4*s + 4. Let g(w) = 3*b(w) + 14*j(w). Suppose g(c) = 0. What is c?
-1, 1
Let f = 2 - -1. Let a(l) be the second derivative of 0*l**2 + 0 - 1/3*l**f - 1/6*l**4 - l. Factor a(h).
-2*h*(h + 1)
Let g(q) be the second derivative of -q**6/120 - q**5/20 - q**4/8 - q**3/6 + 3*q**2/2 - 2*q. Let u(l) be the first derivative of g(l). What is x in u(x) = 0?
-1
Let l = -13 + 14. Let t(f) = -4*f + 4*f + f**4 + f**3. Let k(p) = -p**5 + 4*p**4 + 4*p**3 - p**2. Let d(j) = l*k(j) - 3*t(j). Factor d(q).
-q**2*(q - 1)**2*(q + 1)
Suppose 18 = -40*v + 43*v. Determine h, given that -v*h**4 + 6*h**5 - 2*h - 4*h**3 + 52/9*h**2 + 2/9 = 0.
-1, 1/3, 1
Suppose -4*a = 5*a - 4*a. What is r in 1/2*r - 3/4*r**2 + a - 2*r**3 - 3/4*r**4 = 0?
-2, -1, 0, 1/3
Determine y, given that -3 - 21*y + 17 + 5 - 1 + 3*y**3 = 0.
-3, 1, 2
Suppose -3/4*i**3 + 1/2 + 5/4*i**4 + 3/4*i - 7/4*i**2 = 0. Calculate i.
-1, -2/5, 1
Let h(z) be the third derivative of -z**6/180 + 4*z**5/45 - 52*z**2. Factor h(b).
-2*b**2*(b - 8)/3
Let m(s) be the third derivative of -s**9/1008 - 3*s**8/560 - 3*s**7/280 - s**6/120 + s**3/3 - 3*s**2. Let a(z) be the first derivative of m(z). Factor a(c).
-3*c**2*(c + 1)**3
Let t(r) = -2*r**3 + r**2 - 1. Let n be t(-1). Find l such that l**5 - l**2 - n*l**2 - 4*l**4 - 2*l + 7*l**4 + l**3 = 0.
-2, -1, 0, 1
Let v(c) = -10*c**3 - 9*c**2 + c - 5. Let t = -2 + 0. Let r(k) = -5*k**3 - 5*k**2 - 2. Let o(d) = t*v(d) + 5*r(d). Factor o(a).
-a*(a + 1)*(5*a + 2)
Let m be ((1/(-33))/(3/9))/(-6). Let c(f) be the second derivative of -1/165*f**6 + 0 + 0*f**3 + 0*f**5 + 0*f**2 - 3*f + m*f**4. Find p such that c(p) = 0.
-1, 0, 1
