6/900 - 2*y**5/225 - y**4/60 - 20*y**2. Factor f(t).
-2*t*(t + 1)*(t + 3)/15
Let l = -99 - -201/2. Factor l + 3/2*c - 3/2*c**3 - 3/2*c**2.
-3*(c - 1)*(c + 1)**2/2
Let y(r) = r**2. Let f(m) = 2 - 2 + 5*m**2. Let n = 8 + -19. Let b(s) = n*y(s) + 2*f(s). Factor b(d).
-d**2
Solve 2/5 - 2/5*g + 1/10*g**2 = 0.
2
Let x = -2 - -4. Let h = 9 - 7. Factor a**2 - a**3 - a**x - h + 3*a.
-(a - 1)**2*(a + 2)
Let c(b) be the second derivative of 3*b**5/4 - 55*b**4/12 + 5*b**3 + b. Factor c(i).
5*i*(i - 3)*(3*i - 2)
Suppose -4*h + 7 = -1. Let f(t) be the first derivative of -3 + 2/3*t**3 - h*t + t**2 - 1/2*t**4. Factor f(o).
-2*(o - 1)**2*(o + 1)
Let l(w) be the third derivative of -1/100*w**6 + 1/350*w**7 + 5*w**2 + 0 + 0*w + 0*w**3 + 1/100*w**5 + 0*w**4. Determine x so that l(x) = 0.
0, 1
Suppose -2 + 5*g**4 + 4 - 3*g**4 - 4*g**2 = 0. What is g?
-1, 1
Suppose 93 = 3*h - 3*q + 27, 0 = h + 3*q - 30. Find o such that -h*o**2 + 77*o**5 - 2*o**5 - 108*o**3 + o**4 - 88*o**4 - 3*o**4 = 0.
-2/5, 0, 2
Let d(z) be the second derivative of z**5/120 + z**4/16 + z**3/6 - 3*z**2/2 - 2*z. Let g(n) be the first derivative of d(n). Factor g(y).
(y + 1)*(y + 2)/2
Factor 6/17*d + 4/17 + 2/17*d**2.
2*(d + 1)*(d + 2)/17
Let h(t) = -6*t - 6. Let g be h(-1). Let 0*o**2 - 2/5*o**4 + g + 4/5*o**3 + 0*o = 0. What is o?
0, 2
Factor 1/2*x + 0*x**2 - 1/3 - 1/6*x**3.
-(x - 1)**2*(x + 2)/6
Let x = 1430/1059 - 6/353. Let -x*z**3 + 4/3*z + 0 - 2/3*z**4 + 2/3*z**2 = 0. Calculate z.
-2, -1, 0, 1
Let a(q) = -3*q + 4*q - 2*q + 1. Let i(z) = -2*z**3 - 2*z**2 + 3*z - 3. Let u(x) = -3*a(x) - i(x). Factor u(p).
2*p**2*(p + 1)
Suppose d - 3*b = 44, -2*d + 3*d + 2*b = 29. Let m be 13/d + (-13)/(-65). Solve -2/7*u**3 + 2/7*u - 4/7*u**2 + m = 0.
-2, -1, 1
Let m = 7 - 4. Let h(n) be the first derivative of 0*n**5 + 0*n**m + 0*n**2 + 1/24*n**6 - 1/16*n**4 - 1 + 0*n. Factor h(a).
a**3*(a - 1)*(a + 1)/4
Let p(d) = 3*d**2 + 180*d + 817. Let z(f) = -2*f**2 - 90*f - 408. Let q(w) = 3*p(w) + 7*z(w). Factor q(t).
-5*(t + 9)**2
Let v(w) be the second derivative of -w**6/160 - w**5/80 + w**4/16 - 3*w**2/2 - 4*w. Let f(m) be the first derivative of v(m). Determine k so that f(k) = 0.
-2, 0, 1
Let k(o) be the second derivative of -o**4/3 - 2*o**3/3 + 3*o. Factor k(x).
-4*x*(x + 1)
Suppose -2*j + 2 = -4. Determine l so that 1 + 3*l**2 + j*l - 4*l**2 - l + 2*l**2 = 0.
-1
Let -76/15*w**2 + 56/15*w + 10/3*w**3 - 16/15 + 2/15*w**5 - 16/15*w**4 = 0. What is w?
1, 2
Let c(d) be the third derivative of -1/20*d**6 + 0 + 4/15*d**5 + 0*d - 2/3*d**3 - 1/4*d**4 - 4*d**2. Factor c(w).
-2*(w - 2)*(w - 1)*(3*w + 1)
Let 0 - 12/7*o**2 - 3/7*o**4 + 11/7*o**3 + 4/7*o = 0. Calculate o.
0, 2/3, 1, 2
Suppose 5*a + 2*k - k = 5, -3*a + k + 11 = 0. Let u(m) = -m**3 - 8*m**2 - 9*m + 2. Let n be u(-7). Factor -4*p**3 - 10*p**2 - 2*p**a - n + 2*p**3 - 24*p.
-2*(p + 2)**3
Let q(d) = 2*d. Suppose -z - 4*z - 4*l = -26, 5*l = -5. Let m = z + -4. Let t(j) = -j**2 + 4*j + 1. Let r(i) = m*t(i) - 4*q(i). Factor r(b).
-2*(b - 1)*(b + 1)
Suppose w = -2*i - w + 10, 18 = 3*i + 4*w. Factor -2 + i + 0 - o**2.
-o**2
Let i be (-6)/(-10) - (-6)/(-10)*1. Solve 0*b**2 - 2/9*b**5 + i + 0*b**4 + 0*b**3 + 0*b = 0 for b.
0
Let r(w) be the first derivative of -3*w**4/4 + 5*w**3 - 9*w**2/2 - 27*w + 1. Factor r(k).
-3*(k - 3)**2*(k + 1)
Let c(g) be the first derivative of g**5/10 + g**4/8 - g**3/3 + 32. Factor c(f).
f**2*(f - 1)*(f + 2)/2
Let v(c) be the second derivative of c**6/15 + 3*c**5/5 + c**4/6 - 8*c**3 + 16*c**2 + 16*c. Find u such that v(u) = 0.
-4, 1
Let 0*n + 4/9*n**2 + 4/9*n**3 + 0 = 0. Calculate n.
-1, 0
Let t(z) be the second derivative of z**5/160 - z**4/96 - 6*z - 1. Solve t(m) = 0 for m.
0, 1
Let c(i) be the second derivative of 2*i + 2/15*i**6 + 0*i**2 - 2/21*i**7 + 0*i**5 + 0 + 0*i**3 + 0*i**4. Determine t so that c(t) = 0.
0, 1
Let v(y) = -51*y**5 + 73*y**4 - 9*y**3 - 8*y**2 + 5. Let k(q) = 152*q**5 - 220*q**4 + 28*q**3 + 24*q**2 - 16. Let r(u) = -5*k(u) - 16*v(u). Solve r(o) = 0.
-2/7, 0, 1/2, 1
Suppose q + 1 - 3 = 0. Suppose -9 = q*y - 29. What is o in 3*o**2 + y*o**2 + 4*o - 2 - 15*o**2 = 0?
1
Factor -10*l**3 - l**4 + 4*l**3 - 6*l**2 + 15*l**4 + 9*l - 5*l**4 - 3 - 3*l**5.
-3*(l - 1)**4*(l + 1)
Determine f so that -1/6*f**3 + 0*f - 1/6*f**2 + 1/6*f**4 + 1/6*f**5 + 0 = 0.
-1, 0, 1
What is a in a - 18*a**4 + 8*a**5 + 28*a**2 - 10*a**2 - 4*a**3 - 5*a = 0?
-1, 0, 1/4, 1, 2
Let b(s) = -2*s**2 + 11*s. Let u(c) = -6*c + 0*c**2 + 3*c**2 + c**2 - 3*c**2. Let d(i) = 6*b(i) + 11*u(i). Factor d(p).
-p**2
Let v(f) be the first derivative of f**3/3 + f**2/2 - f + 3. Let h(q) = -q**2 + 13*q - 19. Let j(s) = -h(s) + v(s). Determine c, given that j(c) = 0.
3
Let i = 22 - 85/4. Factor 0 - 3/4*q - 3/4*q**4 + i*q**3 + 3/4*q**2.
-3*q*(q - 1)**2*(q + 1)/4
Factor -3/5 + 3/5*v + 9/5*v**3 + 3*v**2.
3*(v + 1)**2*(3*v - 1)/5
Let o(n) be the first derivative of n**4/8 - n**3/2 - 9*n**2/4 - 5*n/2 + 8. Factor o(x).
(x - 5)*(x + 1)**2/2
Factor -1 + 11 + 2*v**2 - 8*v - 4.
2*(v - 3)*(v - 1)
Let t = -90 - -361/4. Find w, given that -t*w + 0 - 1/4*w**3 + 1/2*w**2 = 0.
0, 1
Suppose 2*j = 6*j - 28. Solve -2*o**4 + j*o**2 + 2*o + 7*o**4 + o**2 + 12*o**3 + o**2 = 0 for o.
-1, -2/5, 0
Suppose 0 = 4*q - 8 - 4. Factor 4/3 + 2*i + i**2 + 1/6*i**q.
(i + 2)**3/6
Let c(u) = -u - 1. Let m be c(5). Let r be (4/m)/(-1)*12. Determine s, given that -s + 2*s**3 - s - s**2 + 6*s**4 - r*s**4 + 3*s**2 = 0.
-1, 0, 1
Find o such that 12/7*o - 36/7*o**2 - 18/7*o**4 + 3/7*o**5 + 39/7*o**3 + 0 = 0.
0, 1, 2
What is l in 0 + 3/4*l**4 + 0*l + 3/4*l**3 - 3/4*l**5 - 3/4*l**2 = 0?
-1, 0, 1
Let q(f) = f**3 - 9*f**2 - 11*f + 14. Let u be q(10). Factor -4*m**5 - 4*m**3 - 4*m**u + 7*m**3 + 4*m**2 + m**3.
-4*m**2*(m - 1)*(m + 1)**2
Factor 20*r**2 + 6*r**4 + r**5 - 5*r + 14*r**4 - 30*r**3 - 6*r**5.
-5*r*(r - 1)**4
Suppose r - 3 = -0*r. Let t(z) be the third derivative of -1/30*z**4 + 0 + 0*z - z**2 + 1/15*z**r + 1/150*z**5. Determine l, given that t(l) = 0.
1
Let 1/2*y - 1/4*y**4 + 0 + 0*y**3 + 3/4*y**2 = 0. What is y?
-1, 0, 2
Let w = -4 - -4. Suppose 5*a - 20 = -w*a. Factor -119*p**a + 67*p**3 + 6*p**2 + 49*p**5 - 16*p + 21*p**2 - 4*p**2 - 4.
(p - 1)**3*(7*p + 2)**2
Suppose 4*r - 3*b + 27 = 26, -3*b = -9. Factor 4/3*i**r - 16/3*i + 4.
4*(i - 3)*(i - 1)/3
Suppose 10*g = 6 + 14. Let d(n) be the first derivative of 2 - 1/4*n + 1/4*n**g - 1/12*n**3. Let d(b) = 0. Calculate b.
1
Find y such that 2/9*y**2 + 2/9*y**4 + 0 - 4/9*y**3 + 0*y = 0.
0, 1
Let v(u) be the first derivative of -1/18*u**6 + 2 + 0*u**2 + 1/9*u**3 + 0*u - 1/4*u**4 + 1/5*u**5. Factor v(b).
-b**2*(b - 1)**3/3
Let z be ((-6)/8)/((-1)/20). Let y be 10/z + (-10)/(-21). Factor -2/7*x**2 + y*x - 8/7.
-2*(x - 2)**2/7
Let l(w) be the second derivative of w**5/4 + 5*w**4/6 - 50*w**3/3 + 60*w**2 - 56*w. Suppose l(n) = 0. Calculate n.
-6, 2
Suppose -17 = -3*w - 5*f, -2*w + 12 = 3*f + f. Let y(a) be the second derivative of 1/15*a**3 + 2*a + 0 + 0*a**2 + 1/30*a**w. Solve y(d) = 0.
-1, 0
Let q(v) be the third derivative of 0*v - 1/60*v**6 - 2/315*v**7 + 0*v**3 + 0*v**4 + 0 - 5*v**2 - 1/90*v**5. Factor q(a).
-2*a**2*(a + 1)*(2*a + 1)/3
Suppose h + 3*r - 4 = 0, -48 = -5*h + 2*r - 3*r. What is w in 8 + h*w**4 - 16*w**4 + 28*w**2 - 44*w + 22*w**3 + 22*w**3 - 30*w**4 = 0?
-1, 2/9, 1
Suppose -2*z - p = -0*z - 5, p - 1 = 0. Let 2*t - 6*t**3 - 9*t**z + 4 + 5*t**2 - 4 = 0. What is t?
-1, 0, 1/3
Factor 6/7*g**3 - 12/7*g**2 + 8/7*g - 1/7*g**4 + 0.
-g*(g - 2)**3/7
Suppose 4 = x - 1. Suppose x*o = 3*o. Factor 0 - 2/3*b**3 + 1/3*b**5 + 0*b**2 + o*b**4 + 1/3*b.
b*(b - 1)**2*(b + 1)**2/3
Solve -32/15*u - 10/3*u**2 - 8/15 - 14/15*u**4 - 2/15*u**5 - 38/15*u**3 = 0 for u.
-2, -1
Let n(o) = 4*o + 4. Let x be n(-1). Let z = 2790/4907 + 2/701. Factor -2/7*r**4 + 0 + 6/7*r**5 - z*r**3 + 0*r**2 + x*r.
2*r**3*(r - 1)*(3*r + 2)/7
Let k = -1/42 + 11/21. Factor -k + 1/2*o**3 - 1/2*o + 1/2*o**2.
(o - 1)*(o + 1)**2/2
Let d be (207/54)/23*3. Factor c - 3/2*c**3 + d*c**2 + 0.
-c*(c - 1)*(3*c + 2)/2
Let c(b) be the third derivative of 1/3*b**3 + 0*b**4 + 0*b + 0*b**5 + 0 - 3*b**2 + 1/1080*b**6. Let z(n) be the first derivative of c(n). Factor z(u).
u**2/3
Determine z so that 75*z**3 - 36*z - 102*z**2 - 21*z**4 + 5*z**3 + 7*z**4 = 0.
-2/7, 0, 3
Let o(q) = q**2 - 8*q + 12. Let z be o(6). Let z -