t y = -1/2 + 2. Let 0 + 0*a**2 - y*a**3 + 3/2*a = 0. What is a?
-1, 0, 1
Let m(u) = u**2 - 4*u - 1. Let j be m(4). Let t be ((-6)/4)/(j/2). Factor -c**3 + 0*c**t - 4*c**2 + 2*c**2.
-c**2*(c + 2)
Let p(d) be the third derivative of -3*d**7/350 + d**6/100 + 7*d**5/100 + d**4/20 - 14*d**2. Determine r, given that p(r) = 0.
-1, -1/3, 0, 2
Let u = -3131/11 - -285. Suppose 3 = 3*n - 3*s, 3*n + 4*s = -s + 11. Determine c, given that 0 + 2/11*c**3 + u*c**n + 2/11*c = 0.
-1, 0
Let j(u) = 5*u**3 - 5*u**2 - 6*u. Let g(c) = 14*c**3 - 14*c**2 - 17*c. Let b(t) = -4*g(t) + 11*j(t). Factor b(i).
-i*(i - 2)*(i + 1)
Let y(t) be the first derivative of -t**6/90 + t**4/12 - t**3/9 - 9*t - 2. Let x(p) be the first derivative of y(p). Let x(b) = 0. Calculate b.
-2, 0, 1
Let d be ((-3)/(-6))/((-1)/4). Let u be ((-1)/1)/(d/4). Determine t, given that t - t**u + 9 - 9 = 0.
0, 1
Let x(h) = -2*h**3 + 4*h**2 - 5*h - 3. Let n(z) = -2*z**3 + 4*z**2 - 6*z - 4. Let b = -9 + 5. Let w(q) = b*x(q) + 3*n(q). What is t in w(t) = 0?
0, 1
Let f(h) = h**3 + h**2 - h + 4. Let p be f(0). Let n = p + -1. Suppose -3*m**5 + 3*m + m - 12*m**4 - 6*m**5 + 5*m**n + 12*m**2 = 0. What is m?
-1, -2/3, 0, 1
Let i(c) be the first derivative of -1/15*c**3 + 2/5*c**2 + 2*c - 5 - 1/30*c**4. Let g(b) be the first derivative of i(b). Factor g(r).
-2*(r - 1)*(r + 2)/5
Let j(o) = -o**3 - 1. Let w(q) = -26*q**3 + 16*q**2 - 2*q + 6. Let z(i) = 12*j(i) + 2*w(i). Find x such that z(x) = 0.
0, 1/4
Let s = -9 - -16. Let f(w) = w**2 - 6*w - 4. Let x be f(s). Factor -r - x*r**3 - 4*r**4 + 3*r**4 - 2*r**2 - r**2.
-r*(r + 1)**3
Let b(j) = -j - 2. Let s be b(-9). Let n(u) be the third derivative of 0*u - 3*u**2 - 1/45*u**6 + 0 - 1/9*u**4 + 1/9*u**3 + 1/15*u**5 + 1/315*u**s. Factor n(t).
2*(t - 1)**4/3
Let w = 697/7 - 99. Solve -6/7*p + w + 2/7*p**2 = 0.
1, 2
Factor 9/2*r**2 + 6*r**3 - 6 - 6*r + 3/2*r**4.
3*(r - 1)*(r + 1)*(r + 2)**2/2
Let x be (-1 + 2 + -1 - -2) + 1. Let w(y) be the first derivative of -2*y + 1/3*y**x - 1/2*y**2 - 2. Solve w(z) = 0 for z.
-1, 2
Suppose 20 = 2*l + 3*l. Let o(i) be the first derivative of 1 - 2/15*i**3 + 1/10*i**2 + 0*i + 1/20*i**l. Factor o(u).
u*(u - 1)**2/5
Let k(w) be the first derivative of 1/3*w**3 + 0*w - 1/4*w**4 - 1/5*w**5 + 1/2*w**2 + 1. What is r in k(r) = 0?
-1, 0, 1
Let g be 2 + 1/((-4)/6). Let c = -47 - -49. Factor 0 - g*x**c + 0*x.
-x**2/2
Let n(t) be the third derivative of -t**8/84 + 2*t**7/105 + t**6/30 - t**5/15 + 15*t**2. Factor n(g).
-4*g**2*(g - 1)**2*(g + 1)
Let a(f) = -f**4 - f**3 - f + 1. Let c(k) = -8*k**4 - 7*k**3 + k**2 - 7*k + 7. Let u(z) = 14*a(z) - 2*c(z). Factor u(x).
2*x**2*(x - 1)*(x + 1)
Let g be -8 + 124/8 + -3. Solve 0 + 1/2*p + 12*p**3 - g*p**2 - 8*p**4 = 0 for p.
0, 1/4, 1
Find u, given that -6/7*u**2 - 4/7 - 2*u = 0.
-2, -1/3
Suppose -10 = -5*d - 2*i, 5*d - 5*i = d - 25. Factor 0*q + 0*q**2 + d + 0*q**3 - 1/3*q**4.
-q**4/3
Let k(l) = l**2 + l - 1. Let g(m) be the third derivative of -m**4/3 + 5*m**3/6 - m**2. Let n(v) = -2*g(v) - 6*k(v). Solve n(w) = 0.
2/3, 1
Factor 4 + 26/3*a - 10/3*a**2.
-2*(a - 3)*(5*a + 2)/3
Let r = 5 + 0. Find j, given that j + j**2 - 5*j + 1 - 3*j + r*j = 0.
1
Solve 10/3*y**2 - 8/3*y**3 - 4/3*y + 2/3*y**4 + 0 = 0 for y.
0, 1, 2
Let u be 1 + 6 + (-14)/7. Suppose -4*m**u + 18*m**3 - 6*m**4 + 15*m**2 - 9*m + 0*m**5 - 3*m**2 - 5*m**5 - 6 = 0. What is m?
-1, -2/3, 1
Suppose -22 = -4*t - 10. Let y(j) be the second derivative of 0 + 2*j**2 + 5/3*j**t + 2/3*j**4 + 1/10*j**5 - 3*j. Factor y(d).
2*(d + 1)**2*(d + 2)
Let t(h) be the third derivative of 0*h + 1/330*h**5 + 2*h**2 + 1/132*h**4 - 1/660*h**6 + 0 - 1/33*h**3. Factor t(y).
-2*(y - 1)**2*(y + 1)/11
Let a(q) = 3*q**2 - 4*q + 2. Let l be a(5). Let u be l/15 - (-1)/5. Factor -3*g**4 - 3*g**3 - g**2 + 4*g**u + g + 2*g**3.
g*(g - 1)**2*(g + 1)
Suppose -p + 8 = p. Suppose 10*r - 10*r**2 + 4*r**2 - 5*r**3 + 2*r**p + 3*r**3 - 4 = 0. What is r?
-2, 1
Let k(h) be the second derivative of -h**5/180 + h**4/27 - 2*h**3/27 - 3*h + 4. Determine m so that k(m) = 0.
0, 2
Let q(n) = 19*n**3 + 19*n**2 - 16*n - 11. Let t(o) = 7*o**2 - 3*o**3 + 13*o**3 + 9*o**2 - 6*o**2 - 8*o - 6. Let k(w) = 6*q(w) - 11*t(w). Factor k(j).
4*j*(j - 1)*(j + 2)
Let l = 80/3 - 388/15. Let -16/5*t**2 - 2/5*t + l - 2*t**3 = 0. What is t?
-1, 2/5
Suppose -22*x**2 + 25*x**2 - 3*x + 18 - 12*x = 0. Calculate x.
2, 3
Let p = -137 + 139. Suppose -5/6*q**p + 1/3*q + 0 = 0. Calculate q.
0, 2/5
Let d(l) be the first derivative of 1/3*l**3 - 1/2*l**2 - l + 1 + 1/4*l**4. Solve d(o) = 0 for o.
-1, 1
Let d(g) be the third derivative of 0 + 0*g + 5*g**2 + 1/80*g**5 + 1/12*g**4 + 1/6*g**3. Factor d(z).
(z + 2)*(3*z + 2)/4
Let 4*i**3 - 16 - 8*i**2 + 5*i**2 - 16*i + 4*i**2 + 3*i**2 = 0. What is i?
-2, -1, 2
Let n(u) be the third derivative of -u**6/40 - u**5/5 + 11*u**2. Let n(j) = 0. What is j?
-4, 0
Let b(d) be the third derivative of -d**5/210 - d**4/42 + d**3/7 - 4*d**2. Factor b(h).
-2*(h - 1)*(h + 3)/7
Let o(l) be the first derivative of 0*l**2 + 0*l**3 + 2*l + 1/42*l**4 + 1. Let m(r) be the first derivative of o(r). Find p such that m(p) = 0.
0
Let j be (-27)/(-63)*6/9. Find q such that -18/7 + 12/7*q - j*q**2 = 0.
3
Suppose 0 = -45*b + 41*b + 12. Let p(x) be the first derivative of -2/21*x**b + 0*x**2 + 0*x + 3. Suppose p(r) = 0. Calculate r.
0
Let c = 174 + -1912/11. Factor c*d**2 + 2/11*d + 0.
2*d*(d + 1)/11
Let d(s) = s**2 - 11*s - 8. Let r be d(12). Let n(p) be the first derivative of 0*p**2 + r + 1/4*p**3 + 0*p. Factor n(k).
3*k**2/4
Let n(i) be the third derivative of 1/30*i**5 - 1/12*i**4 + 0*i + 0 + 0*i**3 + 4*i**2. Factor n(r).
2*r*(r - 1)
Let i(f) = -f**4 + f - 1. Let c(g) = g**4 + 4*g**2 - 3*g + 1. Let s(b) = 2*c(b) + 6*i(b). Factor s(r).
-4*(r - 1)**2*(r + 1)**2
Let o = 151/3 + -743/15. Determine j so that -1/5*j**2 - o*j - 4/5 = 0.
-2
Let r(b) be the second derivative of -b**4/6 + 4*b**3/3 - 3*b**2 - 16*b. Let r(j) = 0. Calculate j.
1, 3
Let f be 1/(-7)*(2 - (5 + -1)). Suppose -2/7*g**2 + 2/7*g**3 - f*g + 2/7 = 0. Calculate g.
-1, 1
Determine h, given that -6*h**3 - 20 - 27 + 71 - 15*h**2 + 69*h - 27*h = 0.
-4, -1/2, 2
Let t = 578/9 + -64. Factor -2/9*q - t*q**2 + 2/9*q**3 + 2/9.
2*(q - 1)**2*(q + 1)/9
Factor -11 - 15 - 18*r + 15*r**2 - 10 + 102*r.
3*(r + 6)*(5*r - 2)
Let x be (-6)/(-20)*60/72. Factor -j**2 + 1/2*j + 3/4*j**4 - 1/2*j**3 + x.
(j - 1)**2*(j + 1)*(3*j + 1)/4
Suppose 2/3*k + 4/3 - 2/3*k**2 = 0. Calculate k.
-1, 2
Suppose -2*j - 3 = -7. Factor 3*g**2 - 3 + 3 + j*g + 91*g**4 - 92*g**4.
-g*(g - 2)*(g + 1)**2
Let g(q) be the third derivative of -q**6/120 - q**5/30 + q**4/6 + 4*q**3/3 - 6*q**2. Factor g(l).
-(l - 2)*(l + 2)**2
Suppose 0 = 3*t - 18 + 3. Let g = t - 2. Solve -3*w - 2 - 2*w**g - 4*w - 6*w**2 + w = 0 for w.
-1
Let v(c) be the first derivative of -14/3*c**3 - 2*c**2 - 2*c**5 + 0*c + 2 - 9/2*c**4 - 1/3*c**6. Let v(r) = 0. What is r?
-2, -1, 0
Let d(v) be the first derivative of v**7/35 + 3*v**6/40 - v**5/10 + v**2/2 + 8. Let s(n) be the second derivative of d(n). Let s(x) = 0. Calculate x.
-2, 0, 1/2
Let r(d) be the second derivative of d**9/45360 - d**7/7560 - d**4/6 + d. Let o(g) be the third derivative of r(g). Factor o(y).
y**2*(y - 1)*(y + 1)/3
Factor -8*h**2 + 3*h - 5 + 68*h**3 + 7*h + 1 - 66*h**3.
2*(h - 2)*(h - 1)**2
Let g be ((-1)/(1/3))/(15/(-20)). Let x(s) be the second derivative of s + 0 - 1/75*s**6 + 1/30*s**g + 0*s**2 - 1/15*s**3 + 1/50*s**5. Factor x(v).
-2*v*(v - 1)**2*(v + 1)/5
Let q = 23/76 - 1/19. Factor -q*c**3 - c**2 - c + 0.
-c*(c + 2)**2/4
What is j in 0 + 10/3*j - 5/3*j**2 = 0?
0, 2
Let x(g) = 6*g**2 + 10*g + 2. Let p = 1 + -2. Let a(w) be the second derivative of w**3/6 + w**2/2 + 14*w. Let h(y) = p*x(y) - 6*a(y). Factor h(l).
-2*(l + 2)*(3*l + 2)
Let l(b) be the second derivative of 0*b**3 + 0 - 2*b + 1/9*b**4 + 0*b**2 - 1/6*b**5 + 1/15*b**6. Solve l(q) = 0 for q.
0, 2/3, 1
Let v(r) be the third derivative of -1/60*r**5 + 0*r + 1/80*r**6 + 0*r**4 - 1/420*r**7 - 2*r**2 + 0 + 0*r**3. Let v(t) = 0. What is t?
0, 1, 2
Let r(x) be the second derivative of x**6/10 - 3*x**5/10 + x**3 - 3*x**2/2 + x - 10. Factor r(q).
3*(q - 1)**3*(q + 1)
Let v = 5 + -1. Suppose -y + 3*u + 8 = 0, -v*y + u + 0 = -10. Factor -1/2*a**y + 1/2 + 0*a.
-(a - 1)*(a + 1)/2
Determine x so that 3