3, -1, -1/2
Let t(g) = -3*g**3 + 2*g**2 - 9*g + 7. Let o be 4 - (4 + -3)*-3. Let h(l) = -l**3 + l**2 - 4*l + 3. Let j(i) = o*h(i) - 3*t(i). Factor j(x).
x*(x + 1)*(2*x - 1)
What is x in 1/2*x**3 + 0 - 3/2*x**2 + 0*x = 0?
0, 3
Let i = -32/13 - -263/91. Factor 3/7*s**2 - 3/7 + 3/7*s**3 - i*s.
3*(s - 1)*(s + 1)**2/7
Let i = -3 - -5. Let r = -2 + 4. Determine v so that -3*v**2 + 6*v**2 + r*v**3 - v**i - 1 - v - v**4 - v**5 = 0.
-1, 1
Let v(p) be the first derivative of p**5/40 + 3*p**4/32 + p**3/8 + p**2/16 + 21. Let v(d) = 0. Calculate d.
-1, 0
Factor -5*q**2 - 3*q**4 + 3*q**3 + 6*q**3 + 17*q**2.
-3*q**2*(q - 4)*(q + 1)
Let x(q) be the second derivative of -q**6/20 + 9*q**5/40 - 3*q**4/8 + q**3/4 - 3*q. Find v such that x(v) = 0.
0, 1
Let c be 77/22*6/7. Factor 0*r - 2/3*r**c - 1/3*r**4 - 1/3*r**2 + 0.
-r**2*(r + 1)**2/3
Let f(d) = -d**3 + d**2 + 2*d + 3. Let w be f(0). Let q(m) be the second derivative of 2/7*m**2 + 0 + w*m + 1/14*m**4 + 5/21*m**3. Factor q(o).
2*(o + 1)*(3*o + 2)/7
Let q(c) be the first derivative of c**3/3 - 4*c + 14. Factor q(d).
(d - 2)*(d + 2)
Suppose 0*l + l + 4*b - 6 = 0, 0 = -5*b. Suppose -5*z = -4 - l. Solve 2*i**2 + 0*i**z + 0*i**2 - 2 = 0 for i.
-1, 1
Let b(l) be the first derivative of 1/60*l**5 - 1/12*l**4 + 0*l - 1/2*l**2 - 3 + 1/6*l**3. Let h(d) be the second derivative of b(d). Factor h(k).
(k - 1)**2
Suppose 4*r + r + 1 = z, 2*r = -4*z + 4. Suppose 0 = -3*s - r*s + 9. Let -1/4*w**2 + 0 + 1/4*w**4 + 0*w**s + 0*w = 0. What is w?
-1, 0, 1
Let o(w) = w**2 + 5*w + 7. Let u be o(-5). Suppose 0 = -2*r + 5*c, 6*c = 5*r + u*c. Let 0*i**4 + 0*i**2 + 0*i + 0*i**3 + 2/7*i**5 + r = 0. Calculate i.
0
Factor -20/7*c + 40/7*c**4 - 8/7 + 12/7*c**5 + 0*c**2 + 40/7*c**3.
4*(c + 1)**4*(3*c - 2)/7
Let b(i) be the second derivative of -8/15*i**5 - 13/18*i**4 + 0 + 1/5*i**6 + 16/9*i**3 - 5*i + 4/3*i**2. Suppose b(z) = 0. Calculate z.
-1, -2/9, 1, 2
Let y be (4/10)/(12/15). Let u = -11 + 13. Suppose 0 + y*j**3 + 1/2*j**u + 0*j = 0. What is j?
-1, 0
Let d(h) be the third derivative of h**8/840 + h**7/105 + h**6/100 - 3*h**5/50 - 21*h**2. Factor d(i).
2*i**2*(i - 1)*(i + 3)**2/5
Let k(u) be the third derivative of -u**8/2352 + u**6/840 - 18*u**2. Factor k(g).
-g**3*(g - 1)*(g + 1)/7
Let g(j) be the third derivative of -j**7/210 - j**6/48 + 5*j**4/48 + j**3/6 - j**2. Suppose g(q) = 0. Calculate q.
-2, -1, -1/2, 1
Let y be 3 - (-1 + -3 + 3). Suppose -1/3*m**2 + 0 - 1/3*m**3 + 1/3*m**y + 1/3*m**5 + 0*m = 0. What is m?
-1, 0, 1
Let q(i) be the first derivative of i**5/70 + i**4/42 - i**3/21 - i**2/7 - 5*i - 4. Let x(n) be the first derivative of q(n). Solve x(l) = 0 for l.
-1, 1
Let m(j) be the third derivative of -j**8/112 - 4*j**7/35 - 2*j**6/5 - 5*j**2 + 4. Solve m(u) = 0.
-4, 0
Let x(i) = -4*i**3 + 7*i**2 + 35*i. Let t(u) = -u**3 + 2*u**2 + 9*u. Let r(l) = 22*t(l) - 6*x(l). Let r(m) = 0. Calculate m.
-3, 0, 2
Let a = 193/11568 - -1/241. Let m(r) be the third derivative of 0*r - 1/60*r**5 + 4*r**2 + a*r**4 + 0 + 1/240*r**6 + 0*r**3. Factor m(n).
n*(n - 1)**2/2
Suppose 7 - 2 = w. Determine l so that 7*l**2 - 8 - l - w*l**2 - l**3 + 5*l = 0.
-2, 2
Let a(k) be the first derivative of k**6/6 + 6*k**5/5 + 3*k**4 + 10*k**3/3 + 3*k**2/2 - 62. Solve a(p) = 0 for p.
-3, -1, 0
Let t(c) = -c**2 - c + 3. Let b be t(0). Suppose 0 = -5*r + 3*q + 15, 10 = -2*r - 0*r - 2*q. Factor r + 2/5*z**4 + 0*z + 0*z**b - 2/5*z**2.
2*z**2*(z - 1)*(z + 1)/5
Factor 0*w + 1/6*w**2 + 0.
w**2/6
Let p(a) be the third derivative of a**6/180 + a**5/20 + a**4/6 + a**3/3 - a**2. Let h(n) be the first derivative of p(n). Factor h(f).
2*(f + 1)*(f + 2)
Let s(a) = a**2 + a - 2. Let r = -29 - -27. Let g be s(r). What is k in 0*k + g - 1/2*k**2 + 1/2*k**3 = 0?
0, 1
Let m = 8 - 6. Determine v, given that -3*v + 0*v**3 + v**m - 3*v**3 + 5*v**2 = 0.
0, 1
Let z be (-376)/(-72) + -5 - 0. Factor z + 4/9*r - 4/9*r**3 - 2/9*r**4 + 0*r**2.
-2*(r - 1)*(r + 1)**3/9
Let f(w) be the first derivative of -8*w + 4/3*w**3 - 2*w**2 - 3. Solve f(l) = 0 for l.
-1, 2
Suppose 0 = 5*a + 20, -2*g - 3 = 3*a + 1. Factor 64/3*j**3 + 98/3*j**5 - 154/3*j**g + 0 + 0*j - 8/3*j**2.
2*j**2*(j - 1)*(7*j - 2)**2/3
Suppose 4*t + 0*p - 2*p = -2, 5*p = 15. Let i be (((-12)/21)/(-2))/t. Suppose -2/7*b - i*b**3 - 4/7*b**2 + 0 = 0. Calculate b.
-1, 0
Let d(h) = 19*h**2 - 19*h - 17. Let g(b) = -6*b**2 + 6*b + 6. Let k(s) = -2*d(s) - 7*g(s). Solve k(n) = 0.
-1, 2
Let h be (-13)/(-4) - -3*(-3)/36. Let m(c) be the first derivative of 0*c**2 + 0*c**h - 1 + 0*c**5 + 0*c - 1/3*c**6 + 1/2*c**4. Factor m(f).
-2*f**3*(f - 1)*(f + 1)
Let l(p) be the third derivative of 1/20*p**6 + 0*p**3 - 1/30*p**5 + 1/168*p**8 - 5*p**2 - 1/35*p**7 + 0 + 0*p**4 + 0*p. Suppose l(t) = 0. What is t?
0, 1
Let r(f) be the third derivative of f**7/70 + f**6/10 + f**5/4 + f**4/4 + 6*f**2. Find m, given that r(m) = 0.
-2, -1, 0
Let u(n) = 8*n**4 - 33*n**3 + 7*n**2 - 9*n. Let f(c) = 2*c**4 - 8*c**3 + 2*c**2 - 2*c. Let s(y) = 18*f(y) - 4*u(y). Solve s(h) = 0.
0, 1, 2
Let h(n) be the first derivative of -n + 1/3*n**3 + 7/30*n**4 - 3 - 2/5*n**2. Let v(f) be the first derivative of h(f). Factor v(r).
2*(r + 1)*(7*r - 2)/5
Suppose -3*w = 27 - 0. Let z(v) = 3*v**3 + 2*v. Let d(s) = -13*s**3 - s**2 - 9*s. Let c(y) = w*z(y) - 2*d(y). What is g in c(g) = 0?
0, 2
Let m(s) be the second derivative of s**4/42 + 2*s**3/21 + s**2/7 - 2*s. Find c such that m(c) = 0.
-1
Let n(v) = v**2 + v - 1. Let k(r) = 8*r + 15 + 25*r + 7*r**3 - r**3 + 21*r**2 - 2*r**3. Let u(y) = -k(y) + n(y). Find d, given that u(d) = 0.
-2, -1
Let l(p) be the third derivative of -p**8/840 - p**7/105 - 2*p**6/75 - 2*p**5/75 - 4*p**2. Factor l(g).
-2*g**2*(g + 1)*(g + 2)**2/5
Solve 24/5*b - 144/5 - 1/5*b**2 = 0 for b.
12
Let z(f) be the second derivative of 2*f**7/3 - 32*f**6/15 - 17*f**5/5 + 34*f**4/3 + 40*f**3/3 - 16*f**2 - 20*f. What is a in z(a) = 0?
-1, 2/7, 2
Let n(l) be the third derivative of 2*l**7/105 - l**6/15 + l**4/3 - 2*l**3/3 - l**2. Factor n(y).
4*(y - 1)**3*(y + 1)
Let o be 255/(-6)*42/(-15). Let q be (1 + 1)*17/o. Let -2/7*h**5 + 20/7*h**2 - 20/7*h**3 - 10/7*h + q + 10/7*h**4 = 0. What is h?
1
Let x(q) be the first derivative of 16*q**5/5 - 8*q**4 + 20*q**3/3 - 2*q**2 + 1. Factor x(i).
4*i*(i - 1)*(2*i - 1)**2
Let b(j) be the second derivative of 3/50*j**6 - 4/15*j**3 + 1/10*j**2 + 11/30*j**4 + 0 - 2*j - 6/25*j**5. Find c, given that b(c) = 0.
1/3, 1
Let j(b) be the first derivative of b**6/15 + 2*b**5/5 + 4*b**4/5 + 8*b**3/15 + 7. Find r, given that j(r) = 0.
-2, -1, 0
Let k = 44/477 - -1/53. Let t(d) be the first derivative of k*d**6 + 0*d**2 + 1/2*d**4 - 2/5*d**5 - 2/9*d**3 - 2 + 0*d. Factor t(c).
2*c**2*(c - 1)**3/3
Let k(d) = d**2 - 10*d - 9. Let r be k(11). Let r + 2*o - 2 + o**2 - 3*o**2 + 4 = 0. What is o?
-1, 2
Let z(k) be the first derivative of 0*k**5 + 7 + 0*k**3 + 0*k + 0*k**4 + 0*k**2 - 1/21*k**6. Factor z(o).
-2*o**5/7
Factor 1/3*z**3 + 5/3*z**2 + 0 + 2*z.
z*(z + 2)*(z + 3)/3
Let x(v) = 8*v**3 - v**2 - 2*v. Let r be 39/(-15) + (-4)/10. Let q(h) = -11*h**3 + 7*h**3 + 3*h - 2*h. Let z(k) = r*x(k) - 5*q(k). What is p in z(p) = 0?
-1/4, 0, 1
Let m(h) be the first derivative of -h**6/6 + h**4/4 - 1. Factor m(i).
-i**3*(i - 1)*(i + 1)
Let p(x) be the second derivative of x**4/20 - x**3/2 + 6*x**2/5 - 30*x. Factor p(j).
3*(j - 4)*(j - 1)/5
Let m(h) = 2*h + 27. Let q be m(-12). Suppose 4*p - 4 = 4*r, -2*r - 2 = q*p - 0*r. Factor -2/7*s**4 + 0 + p*s + 4/7*s**3 - 2/7*s**2.
-2*s**2*(s - 1)**2/7
Let k(v) be the third derivative of -v**7/210 + v**6/40 - v**5/20 + v**4/24 + 6*v**2. Suppose k(i) = 0. What is i?
0, 1
Suppose -6 = -3*g - 0. Let d be (-4)/(-8) - g/20. Factor -d*t**3 + 2/5*t + 2/5 - 2/5*t**2.
-2*(t - 1)*(t + 1)**2/5
Let j(f) = f**2 - 6*f - 1. Let m be j(6). Let z = 3 + m. Factor 4 - 20*b**2 - 2*b - z + 5*b.
-(4*b + 1)*(5*b - 2)
Let j(f) = 2*f + 12. Let k be j(-5). Find q, given that 0 - 2*q**4 - 1/2*q - q**3 + k*q**2 + 3/2*q**5 = 0.
-1, 0, 1/3, 1
Let c(u) be the first derivative of -u**7/63 + u**6/45 + u**5/30 - u**4/18 - 2*u + 3. Let b(t) be the first derivative of c(t). Let b(j) = 0. What is j?
-1, 0, 1
Let k = -210/11 - -1668/77. Factor -3/7*m**4 - 12/7*m - 3/7 - k*m**2 - 12/7*m**3.
-3*(m + 1)**4/7
Let o(c) = 3*c**2 - 9*c - 9. Let a(i) = i. Let x(z) = -15*a(z) - 