, 1
Let m be (18/10)/(18/60). Let s(r) = -8*r**3 - 8*r**2 + 8*r + 8. Let q(g) = 9*g**3 + 9*g**2 - 9*g - 9. Let c(h) = m*s(h) + 5*q(h). Factor c(u).
-3*(u - 1)*(u + 1)**2
Suppose -15*g**2 - 6 - g**3 - 8*g**3 - 3*g + 9 = 0. What is g?
-1, 1/3
Factor 2/13*x**3 - 6/13*x - 36/13 + 8/13*x**2.
2*(x - 2)*(x + 3)**2/13
Let l(x) be the first derivative of -3*x**5/10 - 3*x**4/2 - 5*x**3/2 - 3*x**2/2 - 5. Factor l(m).
-3*m*(m + 1)**2*(m + 2)/2
Let l(w) be the first derivative of 2*w**3/3 - 6*w**2 + 18*w + 16. Factor l(b).
2*(b - 3)**2
Factor -11*z - 17*z + 7*z - 24 + z + 4*z**3 + 8*z**2.
4*(z - 2)*(z + 1)*(z + 3)
Let r(t) be the third derivative of t**5/510 - t**3/51 - 2*t**2. Factor r(x).
2*(x - 1)*(x + 1)/17
Let r be (-60)/(-315)*7/6. Factor 0 + 0*m + 2/9*m**4 - r*m**2 + 0*m**3.
2*m**2*(m - 1)*(m + 1)/9
Let f(d) be the third derivative of -1/20*d**5 + 0 - 1/40*d**6 + 3*d**2 - 1/210*d**7 + 0*d - 1/24*d**4 + 0*d**3. Determine l, given that f(l) = 0.
-1, 0
Let x(p) = -p**2 + 6*p - 4. Let d be x(2). Suppose 2*a + 3*n - 7 - 6 = 0, 5*a = 3*n + 22. Solve 4/3*y**2 + 2/3*y - 4/3*y**d + 0 - 2/3*y**a + 0*y**3 = 0.
-1, 0, 1
Suppose -60 + 21 = -3*r. What is p in 12 + 13*p - 5*p + 3*p**5 + 3*p**2 - 3*p**4 + r*p - 15*p**3 + 3*p = 0?
-1, 2
Let b be (84/(-105))/((-2)/5). Factor -2/5*d**b - 4/5*d - 2/5.
-2*(d + 1)**2/5
Let x(g) = g**2 - g - 1. Let z be x(3). Let q(w) be the second derivative of 0*w**z + 1/24*w**4 - 1/60*w**6 + 0*w**3 + 0 + 0*w**2 + 2*w. What is a in q(a) = 0?
-1, 0, 1
Let c(n) be the first derivative of -3*n**4/4 + 3*n**2/2 + 5. Factor c(o).
-3*o*(o - 1)*(o + 1)
Let c(l) = 3*l**2 + 3*l + 9. Let o be 0 - (0/3 - 6). Let n(s) = -4*s**2 - 4*s - 10. Let p(v) = o*c(v) + 5*n(v). Let p(j) = 0. Calculate j.
-2, 1
Let m(o) = 9*o**3 - 27*o**2 + 8*o. Let x(z) = -28*z**3 + 82*z**2 - 24*z. Let d(j) = -14*m(j) - 5*x(j). Let d(i) = 0. Calculate i.
0, 2/7, 2
Let m(p) = p**2 - 2*p + 3. Let y be m(2). Solve -4 - 2 + 3 + 21*g**2 - y - 9*g**3 + 9*g - 15*g**4 = 0.
-1, 2/5, 1
Factor 1/4*d**2 - 3/8*d + 1/8*d**3 + 0.
d*(d - 1)*(d + 3)/8
Suppose -2*a = a + 2*j - 737, 0 = -a - j + 247. Let g = a - 2185/9. Find o, given that 2/9*o**3 + 0*o - 2/9*o**2 + 0 + g*o**4 - 2/9*o**5 = 0.
-1, 0, 1
Suppose 5*w - 12 = 2*k, 4*k - 4 = w - 10. Suppose 13*v - 4*v**4 + 0*v**3 - 8 + 15*v - 36*v**w + 20*v**3 = 0. Calculate v.
1, 2
Let p(z) be the second derivative of -3*z - 4*z**2 + 1/3*z**4 + 2/3*z**3 + 0. Factor p(q).
4*(q - 1)*(q + 2)
Factor 0*o**2 - 4*o**2 + o**2 - 3*o.
-3*o*(o + 1)
Let q = 77 + -74. Let j(l) be the first derivative of 2/21*l**q + 3/7*l**2 + 3 + 2/35*l**5 - 4/7*l - 3/14*l**4. Factor j(o).
2*(o - 2)*(o - 1)**2*(o + 1)/7
Let m(f) be the third derivative of f**6/210 + f**5/35 - 8*f**3/21 + 7*f**2 - 6*f. Let m(t) = 0. What is t?
-2, 1
Let g(j) be the second derivative of j**7/1260 + j**6/360 + j**4/6 - 3*j. Let q(h) be the third derivative of g(h). Factor q(c).
2*c*(c + 1)
Let 12*g**4 - 4*g - 11 + 8*g - 21*g**3 + 17*g + 2 - 3*g**2 = 0. What is g?
-1, 3/4, 1
Let a(x) be the second derivative of -x**4/24 - x**3/3 - x**2 + 4*x. Suppose a(s) = 0. What is s?
-2
Suppose -8 = 11*m - 13*m. Let d(r) be the first derivative of -m*r**5 - r**4 - 3 + 0*r**3 + 0*r**2 + 0*r - 25/6*r**6. Suppose d(p) = 0. Calculate p.
-2/5, 0
Let q(u) = 6*u**3 + 7*u**2 + 18*u - 5. Let h(f) = -3*f**3 - 3*f**2 - 9*f + 3. Let i(y) = -11*h(y) - 6*q(y). Let i(c) = 0. What is c?
-1
Suppose 2*s + 8 = 2*t, 0 = 2*t + 2*s + s + 12. Suppose t = v + v + 2*j - 10, -3*v + 4*j + 8 = 0. Factor 2*d**v - d**5 + 0*d**3 + 0*d**4 - d**3.
-d**3*(d - 1)**2
Let a(v) be the first derivative of -2*v**3/39 - 3*v**2/13 - 4*v/13 + 9. Factor a(k).
-2*(k + 1)*(k + 2)/13
Let f(v) be the third derivative of v**6/720 - v**4/48 + v**3/2 + v**2. Let o(p) be the first derivative of f(p). Suppose o(y) = 0. What is y?
-1, 1
Let l(y) be the first derivative of -y**5 + 25*y**4 - 250*y**3 + 1250*y**2 - 3125*y + 3. Factor l(j).
-5*(j - 5)**4
Let c be ((-2)/4)/((-3)/(-24)). Let i be (-72)/(-45) - c/10. Factor 5*f**i - 8*f**2 + 0*f**2 + 3*f.
-3*f*(f - 1)
Let u(i) be the second derivative of -i**7/1260 - i**6/120 - i**5/30 + 2*i**4/3 + 4*i. Let p(h) be the third derivative of u(h). Factor p(a).
-2*(a + 1)*(a + 2)
Suppose 5*y + 0*y - 20 = 0. Suppose o + 0*o = y. Factor -1/4*b**o - 3/4*b**2 + 1/4*b + 3/4*b**3 + 0.
-b*(b - 1)**3/4
Suppose -d**2 + 1/2*d**3 - 1/2*d**5 + 0 + d**4 + 0*d = 0. Calculate d.
-1, 0, 1, 2
Let l(u) = -u**2 + 2*u + 2. Let v(p) = p**2 + p + 1. Let g(n) = l(n) + 2*v(n). Factor g(y).
(y + 2)**2
Let t(v) be the first derivative of 5 + 1/5*v**3 + 0*v**2 - 12/5*v. Factor t(i).
3*(i - 2)*(i + 2)/5
Suppose 5*n + 10 = 3*k, -2*n + 28 = 5*k - 3*k. Let c = k - 8. Factor 2/9*o**c + 8/9 + 8/9*o.
2*(o + 2)**2/9
Suppose 4*s = -0*y + y + 15, -s = -y - 6. Factor 4 - 20*k**s + 8*k - 12*k**2 - 4 + 0.
-4*k*(k + 1)*(5*k - 2)
Let m be 4/14 - (-48)/28. Let a(s) be the second derivative of 0*s**m + 0*s**3 - 1/42*s**4 + 0 + s. Factor a(p).
-2*p**2/7
Let p(j) be the second derivative of j**3 - 8/15*j**6 - 6/5*j**5 + 0 + j - 1/2*j**2 - 1/12*j**4. Let p(z) = 0. Calculate z.
-1, 1/4
Solve -36 + 18 + 8*x + 2*x**2 + 24 = 0 for x.
-3, -1
Let x be 6*(2 - (-15)/(-9)) + 1. Factor 2/9 - 2/9*o**x - 2/3*o + 2/3*o**2.
-2*(o - 1)**3/9
Let a(s) be the second derivative of s**5/330 + s**4/33 + s**3/11 - 2*s**2 + 5*s. Let m(d) be the first derivative of a(d). Determine k so that m(k) = 0.
-3, -1
Let t be (-1)/7 + (4/7)/4. Factor 2/11*r - 2/11*r**3 + 2/11*r**2 - 2/11*r**4 + t.
-2*r*(r - 1)*(r + 1)**2/11
Suppose 3 + 3 = -3*s. Let r = s + 4. Suppose 3*b**5 + 10*b - 4*b**2 - 16*b**r - 1 - 10*b**4 - b**5 + 20*b**3 - 1 = 0. What is b?
1
Let z(h) = -h**2 + 4*h - 1. Let w(y) = -2*y**2 + 9*y - 2. Suppose c = -0*c + 5. Let i(a) = c*z(a) - 2*w(a). Suppose i(k) = 0. What is k?
1
Let j(i) be the second derivative of 5*i**4/12 - 5*i**3/3 + 5*i**2/2 + 25*i. Factor j(s).
5*(s - 1)**2
Let n = -19 - 0. Let y be n/114*(-3)/2. Factor -1/4*a**5 + 0*a + y*a**3 + 0 - 1/4*a**2 + 1/4*a**4.
-a**2*(a - 1)**2*(a + 1)/4
Solve 4*o**3 + 5*o**4 + 3*o**4 - 4*o**4 + 0*o**4 = 0 for o.
-1, 0
Suppose 3*w + 2 = 5*z - 1, -2*z - 6 = -3*w. Factor -1/4*k**4 + 1/4*k**z + 0*k**2 + 0*k + 0.
-k**3*(k - 1)/4
Let r(g) = -g**2 - 7*g - 4. Let t be r(-6). Let y(a) be the third derivative of a**t + 0*a + 0 + 1/36*a**4 - 1/60*a**5 + 0*a**3. Factor y(v).
-v*(3*v - 2)/3
Let z(d) = -d**3 + 3*d**2 + 2*d + 1. Let k be z(3). Suppose 4*q + k = 19. Factor 1/4*j**q + 0*j**2 + 0 + 0*j.
j**3/4
Let b(d) = d**3 - 3*d**2 - 3*d - 2. Let f be b(4). Let z be 2/11 - 9/(-132). Find n, given that 0 - z*n**f + 1/2*n**3 - 1/4*n**4 + 0*n = 0.
0, 1
Let c = 42 + -629/15. Let l(x) be the third derivative of x**2 + 1/150*x**5 + c*x**3 + 0*x + 0 + 1/30*x**4. Factor l(r).
2*(r + 1)**2/5
Let d(m) be the first derivative of -m**4 + 8*m**2 - 17. Suppose d(q) = 0. Calculate q.
-2, 0, 2
Let p(k) be the third derivative of 1/180*k**5 - 1/630*k**7 + 0*k**3 + 0*k**4 + 0*k + 0 + 0*k**6 - 6*k**2. Let p(v) = 0. Calculate v.
-1, 0, 1
Let n(l) = l - 1. Let h be n(3). Suppose 4*p = -3*k + 7*k, h*k = -4*p + 12. Factor 1/4*r**5 + 0*r**4 + 1/4*r - 1/2*r**3 + 0*r**k + 0.
r*(r - 1)**2*(r + 1)**2/4
Suppose 6*m**2 + 10/3*m + 4/3*m**4 + 14/3*m**3 + 2/3 = 0. Calculate m.
-1, -1/2
What is w in 2*w - w**2 + 6*w + 3*w**2 = 0?
-4, 0
Let c(r) be the third derivative of -r**8/16800 + r**7/3150 - r**6/1800 + r**4/12 - 2*r**2. Let q(z) be the second derivative of c(z). Factor q(f).
-2*f*(f - 1)**2/5
Solve -2/5*i**5 - 6/5*i**4 + 6/5*i + 4/5*i**2 + 2/5 - 4/5*i**3 = 0 for i.
-1, 1
Let a(z) be the first derivative of -z**6/39 - 6*z**5/65 - z**4/13 + 4*z**3/39 + 3*z**2/13 + 2*z/13 - 9. Factor a(m).
-2*(m - 1)*(m + 1)**4/13
Let b be (-9)/(-3) + (-14)/6. Let u(m) be the first derivative of 2/9*m**3 - b*m + 0*m**2 - 2. Factor u(l).
2*(l - 1)*(l + 1)/3
Let r(d) be the first derivative of -5*d**6/21 + 26*d**5/35 - 9*d**4/14 - 2*d**3/21 + 2*d**2/7 - 11. Factor r(q).
-2*q*(q - 1)**3*(5*q + 2)/7
Let a be (-7)/(-28)*(-1)/2*-2. Determine m so that -1/2*m**2 + 1/4 + 1/4*m**5 - 1/2*m**3 + 1/4*m**4 + a*m = 0.
-1, 1
Let a = -15 - -15. Factor 4/5*r**2 + a - 2/5*r.
2*r*(2*r - 1)/5
Suppose -7*o = -0*o - 3*o. Determine d, given that -5/2*d**2 + o - d**3 + 5/2*d**4 + d = 0.
-1, 0, 2/5, 1
Let j be (2 - 1) + 1 + 0. W