et u(i) be the first derivative of i**4/20 - 2*i**3/15 + i**2/10 + 6. Factor u(h).
h*(h - 1)**2/5
Let z(l) be the first derivative of l**6/30 + 6*l**5/25 + 9*l**4/20 + 4*l**3/15 + 11. Solve z(c) = 0.
-4, -1, 0
Factor 5/6*v**2 - 5 + 25/6*v.
5*(v - 1)*(v + 6)/6
Let j(n) = -n**3 + 3*n**2 + 4*n + 3. Let c be j(4). Let h be (4 - c) + (-2)/2. Factor 2 + h*y - 3*y + 2*y**2 + 7*y.
2*(y + 1)**2
Find m such that 260 + 1022*m**2 - 35 - 1021*m**2 + 30*m = 0.
-15
Determine t so that 1 + 9/2*t**2 - 7/2*t - 5/2*t**3 + 1/2*t**4 = 0.
1, 2
Let b = -1475/9 + 165. Let -b*m**2 + 14/9*m + 2/9*m**3 - 2/3 = 0. What is m?
1, 3
Let k(s) be the first derivative of s**7/42 - s**6/15 - s**5/20 + s**4/6 - 3*s - 1. Let w(p) be the first derivative of k(p). Factor w(z).
z**2*(z - 2)*(z - 1)*(z + 1)
Solve 2/3 + 2*x + 2/3*x**3 + 2*x**2 = 0.
-1
Let s be ((-80)/56)/((-16)/2). Let f = s - -1/14. Factor 0 + 0*z + 1/4*z**2 + 1/2*z**3 + f*z**4.
z**2*(z + 1)**2/4
Let t(k) be the first derivative of -1/6*k**3 + 1 + 1/2*k**2 - 1/2*k. Let t(l) = 0. Calculate l.
1
Suppose -8 = 5*z - 23. Factor 3*u**z - u**2 - 2*u + 5*u**3 + u**4 - 6*u**4.
-u*(u - 1)**2*(5*u + 2)
Let x = 8 - 5. Let b(y) be the second derivative of -x*y + 1/4*y**2 + 0 - 1/20*y**6 + 1/12*y**4 - 1/20*y**5 - 1/84*y**7 + 1/4*y**3. Solve b(v) = 0 for v.
-1, 1
Let q be ((-3)/(-12))/(2/(-302)). Let o = 38 + q. Factor -1/4*c**2 + 1/2*c - o.
-(c - 1)**2/4
Let x be (8/26)/(5*24/780). Factor 0 - 10/9*f**x + 2/3*f + 2/9*f**3 + 2/9*f**4.
2*f*(f - 1)**2*(f + 3)/9
Factor 5*j**3 + 11*j**2 + 3*j**2 + 10*j**2 - 4 + j**4 - 21*j**2 - 5*j.
(j - 1)*(j + 1)**2*(j + 4)
Let f(c) be the second derivative of -c**5/10 + c**4/2 - c**3 + c**2 - c. Factor f(o).
-2*(o - 1)**3
Let m be -83 - -83 - 5/((-70)/4). Factor -2/7*d + m*d**3 + 0 + 0*d**2.
2*d*(d - 1)*(d + 1)/7
Let a be -6*4/8*-1. Factor -9*n**a + 4*n + 0*n - 2 + 5*n**3 + 2*n**4.
2*(n - 1)**3*(n + 1)
Let z(r) = r**3 - 15*r**2 + 15*r - 10. Let p be z(14). Factor 6*b - 45*b**2 + p - 175/2*b**3.
-(5*b + 2)**2*(7*b - 2)/2
Let o(d) = -4*d**4 + 12*d**3 + 19*d**2 - 107*d + 91. Let l(v) = -12*v**4 + 36*v**3 + 58*v**2 - 322*v + 274. Let g(b) = -5*l(b) + 14*o(b). Factor g(t).
4*(t - 2)**3*(t + 3)
Let a(m) be the first derivative of -1/6*m**6 + 0*m + 0*m**2 + 1/4*m**4 - 1/5*m**5 + 1/3*m**3 - 3. Factor a(b).
-b**2*(b - 1)*(b + 1)**2
Let i(y) be the third derivative of y**6/120 + 4*y**5/15 + 77*y**4/24 + 49*y**3/3 + 12*y**2 - y. Determine f, given that i(f) = 0.
-7, -2
Let u = -47/2 + 24. Find c such that 3*c + u*c**2 + 9/2 = 0.
-3
Solve 1/3*a + 0 + 2/3*a**2 + 1/3*a**3 = 0.
-1, 0
Let l(z) = 4*z**4 + 16*z**3 + 12*z**2 - 1. Let p(b) = -1. Let g(f) = -l(f) + p(f). Find q such that g(q) = 0.
-3, -1, 0
Let k(u) be the first derivative of u**6/27 - 2*u**5/15 + u**4/9 + 4*u**3/27 - u**2/3 + 2*u/9 - 18. Determine w so that k(w) = 0.
-1, 1
Let h(c) be the third derivative of c**2 + 1/24*c**4 + 0*c + 1/3*c**3 + 0 - 1/60*c**5. Determine f so that h(f) = 0.
-1, 2
Suppose r = 3*r - 2. Factor -r + h - 1/4*h**2.
-(h - 2)**2/4
Let w(q) be the first derivative of 2*q**5/55 - 3*q**4/11 + 6*q**3/11 - 4*q**2/11 + 39. Factor w(v).
2*v*(v - 4)*(v - 1)**2/11
Let m(d) = 4*d**2 - 6. Let s(a) = 13*a**2 + a - 19. Let t(w) = 7*m(w) - 2*s(w). Let t(h) = 0. What is h?
-1, 2
Factor 1/3*h**2 - 2/3 - 1/3*h.
(h - 2)*(h + 1)/3
Let d(w) be the second derivative of -w**5/50 - w**4/6 - w**3/5 + 9*w**2/5 + 2*w. Suppose d(b) = 0. Calculate b.
-3, 1
Solve 3*o**5 - 2*o**5 - 26*o**2 + 12*o**2 - 2*o - 9*o - 6*o**3 - 3 + o**4 = 0.
-1, 3
Suppose 2 = 3*y + 4*q, -q = -5*y - 4*q + 7. Let c(n) = n**3 + 13*n**2 + 11*n - 9. Let l be c(-12). Factor 2/7*u**l + 2/7*u - 4/7*u**y + 0.
2*u*(u - 1)**2/7
Let f(c) be the second derivative of -c**7/21 + c**6/15 + c. Let f(a) = 0. Calculate a.
0, 1
Let d(t) be the third derivative of -3*t**2 - 1/360*t**6 + 0*t + 1/36*t**4 + 0 - 1/180*t**5 + 0*t**3. Factor d(z).
-z*(z - 1)*(z + 2)/3
Let w(v) = -v**3 + 4*v**2 - 2*v - 2. Let y be w(3). Suppose -5*c + y + 14 = 0. Factor c*a**4 - 7*a**3 - 2 + 0 - a**2 + 4*a**2 + 3*a.
(a - 1)**3*(3*a + 2)
Let j(x) be the first derivative of x**7/63 + x**6/15 + x**5/10 + x**4/18 - x - 1. Let w(p) be the first derivative of j(p). Factor w(c).
2*c**2*(c + 1)**3/3
Let m(p) be the third derivative of p**8/168 - p**7/105 - p**6/12 - p**5/10 + 13*p**2. What is q in m(q) = 0?
-1, 0, 3
Suppose -2*o + 1 = -1. Let b = -11 - o. Let s(r) = 4*r**3 + 5*r**2 - 9*r - 5. Let w(j) = 10*j**3 + 12*j**2 - 22*j - 12. Let g(f) = b*s(f) + 5*w(f). Factor g(a).
2*a*(a - 1)*(a + 1)
Suppose 1200*l**4 + 185*l**2 - 93*l - 320*l**5 - 134*l**3 - 646*l**3 + 78*l = 0. Calculate l.
0, 1/4, 3
Let s(k) be the second derivative of 0 + 0*k**2 - 3*k + 1/120*k**6 - 3/80*k**5 + 1/16*k**4 - 1/24*k**3. Find z such that s(z) = 0.
0, 1
Factor 15*h**2 + 3*h**4 - 6*h**2 - 7*h**3 - 2*h**3 - 3*h.
3*h*(h - 1)**3
Let m be (-2)/(-6)*(12 + -3). Factor 2*g - g - m*g + 0*g + g**2.
g*(g - 2)
Suppose 10 = 5*v - 10. Suppose -3*p - v = -22. Determine a, given that -4 + 12*a + 7*a**2 + p + 3*a**2 = 0.
-1, -1/5
Let q(t) be the second derivative of -1/6*t**3 + 1/20*t**5 + 1/12*t**4 - 1/30*t**6 + 0*t**2 + 0 - 7*t. Factor q(n).
-n*(n - 1)**2*(n + 1)
Determine p, given that -12/5*p**2 - 3/5*p**5 + 11/5*p**4 - 6/5*p**3 + 0 + 8/5*p = 0.
-1, 0, 2/3, 2
Let o(b) be the second derivative of b**6/120 - b**5/40 - b**4/16 + b**3/6 - 4*b**2 + 2*b. Let n(w) be the first derivative of o(w). Factor n(z).
(z - 2)*(z + 1)*(2*z - 1)/2
Suppose 2*c + 0*i - 124 = -2*i, -5*c - 2*i = -316. Let u = c + -574/9. Factor 0 + 4/3*w**3 + u*w**5 - 8/9*w**4 - 8/9*w**2 + 2/9*w.
2*w*(w - 1)**4/9
Suppose -4*q + 23 = 5*i + 5, -5*i + 5*q = 0. Let v be i/7 + 52/14. Factor -z + 3*z - 3*z**4 - 2*z**3 - z**4 + v*z**2.
-2*z*(z - 1)*(z + 1)*(2*z + 1)
Let i(y) be the second derivative of y**7/420 - y**6/120 + y**4/24 - y**3/12 + 3*y**2/2 - 2*y. Let k(o) be the first derivative of i(o). Factor k(g).
(g - 1)**3*(g + 1)/2
Factor 16/11*n + 2/11*n**2 + 32/11.
2*(n + 4)**2/11
Let -6 - 14/3*u**2 + 10*u + 2/3*u**3 = 0. What is u?
1, 3
Suppose -3*l + 2*o + 8 = -5*l, 5*l - 4*o - 7 = 0. Let k(i) = -5*i**4 - i**3 - 3*i**2 + i. Let h(m) = m**4 + m**3. Let q(f) = l*k(f) - 4*h(f). Factor q(c).
c*(c - 1)**3
Let g(k) be the second derivative of k**6/40 - 3*k**5/80 - k**4/8 - 3*k. Factor g(t).
3*t**2*(t - 2)*(t + 1)/4
Suppose 2*c = -2*c + 12. Let x = -1 + c. Find b such that b**2 - 2 + 4*b - 5*b**x + 2*b**2 = 0.
1
Let x = 10 - 10. Suppose 0 = -u - x + 2. Factor 0 + 2/5*g**u + 1/5*g**3 + 1/5*g.
g*(g + 1)**2/5
Factor -12*h**2 - 7*h**4 - 3*h + 6*h**3 + 7*h + 6*h**3 + 3*h**4.
-4*h*(h - 1)**3
Let c(z) be the third derivative of -z**5/390 + z**4/78 - z**3/39 - 2*z**2. Factor c(r).
-2*(r - 1)**2/13
Let b = 2 - -4. Let w = -4 + b. Suppose -1/4*x**w + 0 + 1/4*x = 0. Calculate x.
0, 1
Suppose 3 = -s - 4*n - 3, 0 = 5*n + 10. Factor 4/9*j + 0*j**s - 2/9 - 4/9*j**3 + 2/9*j**4.
2*(j - 1)**3*(j + 1)/9
Let 4*t**2 + 6*t**3 + 5*t**3 - 2*t**2 = 0. What is t?
-2/11, 0
Let v(r) = -r + 3. Let u be v(1). Factor u*i**4 + 0*i + 4/7*i**3 + 10/7*i**5 + 0*i**2 + 0.
2*i**3*(i + 1)*(5*i + 2)/7
Factor 0 - 2/11*o + 2/11*o**2 - 2/11*o**4 + 2/11*o**3.
-2*o*(o - 1)**2*(o + 1)/11
Let w(r) be the second derivative of 0 + 0*r**2 + 4*r + 3/20*r**5 - 1/8*r**4 - 1/4*r**3. Suppose w(j) = 0. What is j?
-1/2, 0, 1
Let p(d) = 23*d - 179. Let y be p(8). Determine s, given that 0*s + 0*s**2 - 2/9*s**4 + 0*s**3 + 0 + 2/9*s**y = 0.
0, 1
Let z(q) = 7*q**2 - 5*q + 5. Let j(h) be the third derivative of -h**5/10 + h**4/6 - 2*h**3/3 + 3*h**2. Let p(s) = 5*j(s) + 4*z(s). Factor p(u).
-2*u**2
Factor -665 + 70*f + 2*f**2 + 3*f**2 + 910.
5*(f + 7)**2
Determine n, given that -3/2*n**4 + 0*n**2 + 3/2*n**3 + 0*n + 0 = 0.
0, 1
Let m(r) = -2*r**3 - 2*r**2 - 3*r. Let j(x) = 3*x**3 + 3*x**2 + 5*x. Let d(i) = -3*j(i) - 5*m(i). Factor d(y).
y**2*(y + 1)
Suppose -x = i + 2*i - 2, 2 = x - 3*i. Let j = x + 0. Let -6*u**3 + 10*u**3 - 4*u**5 + u**4 + j*u**2 - 3*u**2 = 0. Calculate u.
-1, 0, 1/4, 1
Let o be 82/(4 + 2/(-1)). Determine q so that 122*q**2 + 7*q + o*q**4 + 9*q**4 - 24*q + 8 + 180*q**3 - 55*q = 0.
-2, 1/5
Let -6*q - 3*q**3 + 9*q**3 + 4*q**3 - 4*q**3 - 3*q**4 + 3*q**2 = 0. Calculate q.
-1, 0, 1, 2
Let j(p) be the third derivative of 2*p**7/245 + p**6/210 - 3*p**5/35 - 3*p**4