2*f - 1)/2
Factor 3/2*m**2 + 2 + 4*m.
(m + 2)*(3*m + 2)/2
Let m(o) = 4*o**4 + 12*o**3 + 10*o**2 + 4*o + 2. Let r(a) = -8*a**4 - 24*a**3 - 19*a**2 - 8*a - 5. Let d(l) = -5*m(l) - 2*r(l). Let d(y) = 0. What is y?
-1, 0
Let i be (-4)/12 - 1/(-3). Suppose 2*q = 0, -h + i + 2 = -3*q. Factor -4*g**h + 2*g**3 + 0 + 9*g - 5*g**2 - 3 + g**3.
3*(g - 1)**3
Determine r so that r**5 + r**3 - 2*r**4 - 1 + 1 = 0.
0, 1
Let q(a) be the first derivative of -a**6/4 + 9*a**5/10 - 9*a**4/8 + a**3/2 - 35. Find x, given that q(x) = 0.
0, 1
Let c(n) = -n**2 - 5*n - 4. Let i be c(-3). Factor 2*o**3 - 2*o**i + 7*o**2 + 0*o**2 - 2 - 3*o**2 - 2*o.
2*(o - 1)*(o + 1)**2
Let b(p) be the first derivative of -1/4*p**4 + 0*p - 1 - 1/10*p**5 - 1/6*p**3 + 0*p**2. Factor b(n).
-n**2*(n + 1)**2/2
Let s(u) be the third derivative of 7*u**6/200 - 37*u**5/100 + 19*u**4/20 - 4*u**3/5 + 3*u**2 - 6*u. Factor s(f).
3*(f - 4)*(f - 1)*(7*f - 2)/5
Let l(j) be the first derivative of 2*j**3/3 - 3*j**2 + 2*j - 1. Let h(u) = u - 1. Let r(o) = 2*h(o) + l(o). Suppose r(z) = 0. Calculate z.
0, 2
Suppose -3*g = g + 12. Let j(k) = -k**2 - 3*k. Let o be j(g). Solve o*s + 0 + 2/7*s**2 = 0 for s.
0
Suppose 0 = 2*m + 2*m - 20. Suppose 3*q - m*t - 6 = 0, -t + 9 - 3 = 3*q. Suppose -6*j**3 - 3 - j**4 + 0*j**5 - 2*j**4 + 3*j**5 + 3*j + 6*j**q = 0. Calculate j.
-1, 1
Let g(t) = 5*t**4 - 12*t**3 - 17*t**2 - 11. Suppose 3*w + 0 = -33. Let i(s) = 2*s**4 - 4*s**3 - 6*s**2 - 4. Let u(j) = w*i(j) + 4*g(j). Factor u(l).
-2*l**2*(l + 1)**2
Let l = -1 - -2. Let m be (-2 + l)*(-6)/3. Factor -m*h**5 + 3*h**5 - 3*h**5 + 2*h**3.
-2*h**3*(h - 1)*(h + 1)
Let j(h) be the first derivative of -7*h**5/90 + h**4/27 + 7*h**3/27 - 2*h**2/9 - h + 3. Let l(p) be the first derivative of j(p). Factor l(i).
-2*(i - 1)*(i + 1)*(7*i - 2)/9
Let w(y) be the third derivative of 0 + 1/105*y**7 + 0*y**5 + 5*y**2 + 0*y + 0*y**4 - 1/60*y**6 + 0*y**3. Factor w(i).
2*i**3*(i - 1)
Let c = 710/531 + -2/531. Factor 2/9*s**4 + 8/9*s**3 + 8/9*s + 2/9 + c*s**2.
2*(s + 1)**4/9
Suppose 0 = -0*g - 9*g. Factor g - 1/2*h - 1/2*h**4 + 1/2*h**3 + 1/2*h**2.
-h*(h - 1)**2*(h + 1)/2
Let c(s) = -s**2 + 7*s + 11. Let i be c(9). Let n be i/((-7)/(-2))*-1. What is v in -34 + 3*v + n*v**2 + 34 - 5*v = 0?
0, 1
Let w = 8 - 6. Suppose 4 - 3 + 2 + 5*r**w + r**3 + 7*r = 0. Calculate r.
-3, -1
Let m(s) be the second derivative of -s**9/3780 + s**7/630 + s**4/2 + 5*s. Let j(f) be the third derivative of m(f). Determine d, given that j(d) = 0.
-1, 0, 1
Factor -2/7*k - 3/7*k**2 + 0 - 1/7*k**3.
-k*(k + 1)*(k + 2)/7
Suppose -15 = -2*j + 3*i, -3*i + 5 - 29 = -5*j. Let x be 3 - (3/j + -3). Factor 5 - x + 3*b**2 + 3*b.
3*b*(b + 1)
Let o be (-140)/(-45) + -3 - 0. Let v(q) be the second derivative of 5/18*q**3 - 1/3*q**2 + 0 - o*q**4 - q + 1/60*q**5. Solve v(c) = 0.
1, 2
Let i = 436681/180 + -2426. Let b(j) be the third derivative of 0 + 0*j + 0*j**3 + i*j**5 - 1/72*j**4 - 3*j**2. Let b(q) = 0. What is q?
0, 1
Suppose 2 - 5 = -y. Suppose 4*g = y*g. Find l such that 0*l + 14*l**5 - 2*l**2 + 6*l**3 - 24*l**4 + g*l + 6*l**2 = 0.
-2/7, 0, 1
Let m = -25/33 - -12/11. Suppose 0 - m*w + 1/3*w**2 = 0. What is w?
0, 1
Let -4/9*j**3 - 2/9*j**4 - 2/9*j**2 + 0 + 0*j = 0. What is j?
-1, 0
Let b be (-10)/60 + (-22)/(-24). Factor -1/4*f - b*f**2 + 1/2 + 1/4*f**3 + 1/4*f**4.
(f - 1)**2*(f + 1)*(f + 2)/4
Let j be (2 - 1) + (-9 - -10). Let z = 6/11 - 1/22. Factor -1/2 + 0*u**j + u + z*u**4 - u**3.
(u - 1)**3*(u + 1)/2
Let q(o) be the first derivative of 0*o**3 + 0*o + 4 + 1/108*o**4 - 1/2*o**2 - 1/270*o**5. Let c(z) be the second derivative of q(z). Let c(a) = 0. Calculate a.
0, 1
Let d(i) = -4*i**3 + 2*i + 2. Let p(n) = n**3 - n**2 - n - 1. Let q = 7 + -9. Let v(s) = q*p(s) - d(s). Factor v(m).
2*m**2*(m + 1)
Let h(l) = -4*l**2 - 5*l - 1. Let u be (-1 - -7)/((-2)/4). Let r(q) = -10*q**2 - 12*q - 2. Let x be 2 + 2 - 6/(-6). Let k(g) = u*h(g) + x*r(g). Factor k(b).
-2*(b - 1)*(b + 1)
Let o(x) be the third derivative of x**6/20 - 3*x**5/20 + x**3/2 + 5*x**2. Let o(g) = 0. Calculate g.
-1/2, 1
Find h such that 0*h - 8/3*h**4 + 0 + 4/3*h**5 - 4/3*h**3 + 8/3*h**2 = 0.
-1, 0, 1, 2
Let i(v) be the first derivative of -v**4/48 + v**3/12 - v**2/8 - v + 4. Let k(l) be the first derivative of i(l). Factor k(u).
-(u - 1)**2/4
Let q be (-2)/(-7) + 8/168. Suppose 0 = -f + 2*f - 2. Find a such that -1/6*a + 1/6*a**4 - 1/6*a**5 + q*a**3 + 1/6 - 1/3*a**f = 0.
-1, 1
Suppose -4*b = -5*b. Let o(a) be the third derivative of 1/672*a**8 + 1/48*a**4 - 1/120*a**6 + 0 + 0*a**3 + 0*a**7 + 0*a - 2*a**2 + b*a**5. Factor o(u).
u*(u - 1)**2*(u + 1)**2/2
Suppose -7 - 18 = -5*n. Determine k, given that k**n + 4*k**4 + 0*k**5 - 4*k - 2*k**2 + 3*k**3 - 2*k**2 = 0.
-2, -1, 0, 1
Let u(c) be the first derivative of 4/9*c - 40/27*c**3 + 2 + 11/18*c**4 + 7/9*c**2. Factor u(d).
2*(d - 1)**2*(11*d + 2)/9
Let w be 130/42 + 3/2*-2. Let g(j) be the third derivative of 4/21*j**3 + 0 + j**2 + 1/60*j**6 + 0*j - 19/210*j**5 + w*j**4. Determine l so that g(l) = 0.
-2/7, 1, 2
Let x be 2/12 + 1/(-6). Solve -1/5*v + x - 1/5*v**2 = 0 for v.
-1, 0
Factor -1/5*i**3 + 0*i + 0 + 2/5*i**2.
-i**2*(i - 2)/5
Let y = 38/143 + 6/13. Suppose -8/11*m - 2/11*m**2 - y = 0. Calculate m.
-2
Let q(d) be the first derivative of -1 + 8/9*d**3 + 5/3*d**2 + 2/3*d. Factor q(m).
2*(m + 1)*(4*m + 1)/3
Let v = 2248/7 - 318. Let -36/7*d**3 - 4/7*d + 18/7*d**4 + 0 + v*d**2 = 0. Calculate d.
0, 1/3, 2/3, 1
Suppose -n = 3*n - 4*w, 5*n + 2*w = 0. Determine a so that n - 1/4*a**2 - 1/2*a = 0.
-2, 0
Let p be (71 - 57)*2/35. Suppose -1/5*r**2 - 4/5*r**3 + p*r + 1/5 = 0. Calculate r.
-1, -1/4, 1
Suppose 4*g**3 + 5 - 8*g**2 + 6 - 4*g - 3 = 0. What is g?
-1, 1, 2
Factor -43*o**5 - 36*o**3 + 37*o**5 - 6*o**2 + 11*o**2 + 7*o**2 + 27*o**4.
-3*o**2*(o - 2)**2*(2*o - 1)
Let x(z) = -2*z**2 + 21*z + 70. Let g be x(13). Let 0 - 1/5*h**g + 1/5*h + 0*h**3 + 2/5*h**2 - 2/5*h**4 = 0. Calculate h.
-1, 0, 1
Let u(p) be the third derivative of -p**5/20 - p**4/4 - p**3/2 - 17*p**2. Factor u(y).
-3*(y + 1)**2
Factor 2*r**2 + 66 - 5*r - r - 62.
2*(r - 2)*(r - 1)
Let n(c) be the first derivative of -c**3/9 + 6. Let n(v) = 0. What is v?
0
Suppose 4*i + 2*j = -46, 3*j - 10 = j. Let n be (-4)/i*35/15. What is z in -n*z**3 + 0 + 2/3*z**2 + 0*z - 4/3*z**4 = 0?
-1, 0, 1/2
Let z(c) be the first derivative of 1/3*c**6 + 0*c**2 + 0*c - 7/10*c**5 + 2 + 1/4*c**4 + 1/6*c**3. Determine h, given that z(h) = 0.
-1/4, 0, 1
Let c = 60/17 + -198/85. Factor c*l**2 + 4/5 - 9/5*l - 1/5*l**3.
-(l - 4)*(l - 1)**2/5
Let d be 0/1 - 1/(-5). Factor 4/5*k - 3/5*k**2 + d*k**4 + 4/5 - 2/5*k**3.
(k - 2)**2*(k + 1)**2/5
Let m(s) be the second derivative of s**7/98 - 2*s**6/35 + 3*s**5/35 + s**4/14 - 5*s**3/14 + 3*s**2/7 + 45*s. Factor m(l).
3*(l - 2)*(l - 1)**3*(l + 1)/7
Let g(r) be the first derivative of r**4/5 + 16*r**3/15 - 12. Factor g(v).
4*v**2*(v + 4)/5
Let j be 28/42*(-9)/(-4). Let b(d) be the first derivative of 6/5*d**5 - j*d**4 + 1 + 0*d + 2/3*d**3 - 1/3*d**6 + 0*d**2. Suppose b(v) = 0. Calculate v.
0, 1
Let h(s) be the second derivative of 2*s**5/5 - s**4/3 - 4*s**3/3 + 2*s**2 - 6*s. Factor h(n).
4*(n - 1)*(n + 1)*(2*n - 1)
Let p(i) be the first derivative of 4*i**6/3 + 18*i**5/5 - i**4 - 6*i**3 - 2*i**2 + 12. Find g, given that p(g) = 0.
-2, -1, -1/4, 0, 1
Let a(t) be the second derivative of 3/10*t**5 + 1/2*t**4 + 0 + 1/3*t**3 + 0*t**2 + t + 1/15*t**6. Factor a(p).
2*p*(p + 1)**3
Let g(o) = -17*o**3 - o**2 + o - 1. Let h be g(1). Let c be 2/6 - 48/h. Let -c - 2 + 7 - 4*s + 2*s**2 = 0. What is s?
1
Let u(y) = -2*y**4 - 6*y**3 + 6*y**2 - 6*y - 4. Let a(q) = q**4 + q + 1. Let o = 14 - 10. Let r = 8 - o. Let w(d) = r*a(d) + u(d). Factor w(v).
2*v*(v - 1)**3
Let b = -207/4 - -52. Factor 1/4*i**3 - 1/4 + 1/4*i**2 - b*i.
(i - 1)*(i + 1)**2/4
Let i = 509/427 + -3/61. Let 0 + 16/7*j**2 + 6/7*j**3 - 18/7*j**4 - i*j = 0. What is j?
-1, 0, 2/3
Let z be (-392)/(-84) - 4*1. Find h such that -1/3*h**2 + 1/3*h**4 + z*h**3 + 0 - 2/3*h = 0.
-2, -1, 0, 1
Let n = -398 + 400. Factor 0*x - 1/2*x**n + 0 - 1/2*x**3.
-x**2*(x + 1)/2
Let o(g) = -2*g**3 + 6*g**2 + 16*g - 16. Let c(n) = 3*n**3 - 13*n**2 - 32*n + 32. Let y(z) = -2*c(z) - 5*o(z). Suppose y(q) = 0. What is q?
-2, 1, 2
Let i(j) = -j**2 + 21*j + 49. Let o be i(23). Determine q, give