2.
-3*(i - 1)*(i + 3)/2
Let g(d) be the first derivative of -d**6/3 + 8*d**5/5 - 3*d**4 + 8*d**3/3 - d**2 - 7. Find w, given that g(w) = 0.
0, 1
Find y, given that 4*y + y**4 - 4*y**5 + 19*y**4 + 4 + 40*y**2 - 40*y**3 - 24*y = 0.
1
Suppose 3*w - 4*w + 3 = 2*y, 4 = -4*w. Find t, given that 0*t - 4/11*t**3 + 2/11*t**4 + 0 + 2/11*t**y = 0.
0, 1
Let i(x) be the third derivative of 3*x**6/40 + 13*x**5/20 + 5*x**4/3 + 2*x**3 + 2*x**2. Factor i(q).
(q + 3)*(3*q + 2)**2
Factor 19*a + 128*a**2 + 96*a**3 + 4*a**5 + 2*a + 43*a + 32*a**4.
4*a*(a + 2)**4
Find l such that 60*l**4 - 11*l**5 + 10*l**5 - 85*l**2 - 10 + 40*l**4 - 10*l**3 + 55*l - 39*l**5 = 0.
-1, 1/2, 2
Let r be (0 + -9)*(-7)/7. Let u(p) = -p**3 + 8*p**2 + 10*p - 6. Let v be u(r). Solve 0 - 4/5*s**v + 2/5*s**4 + 0*s + 2/5*s**2 = 0 for s.
0, 1
Let x be (-23)/(-3) + (-9)/(-27). Let g(l) be the first derivative of 28*l**2 - 98/3*l**3 + 2 - x*l. Factor g(m).
-2*(7*m - 2)**2
Let x(j) be the second derivative of -j**4/24 + 5*j**3/6 - 25*j**2/4 + 12*j. Find u such that x(u) = 0.
5
Let t be 2 + -2 + 4 + 34/(-9). Factor -4/9*p**2 + 4/9 + 2/9*p**3 - t*p.
2*(p - 2)*(p - 1)*(p + 1)/9
Suppose 0*y = -2*b + y + 170, 0 = -3*b + 4*y + 245. Let h = b + -607/7. Determine v so that 0*v + 0 - 4/7*v**3 + h*v**2 + 2/7*v**4 = 0.
0, 1
Let r(u) be the third derivative of -u**5/40 - 7*u**4/16 - 19*u**2. Find c, given that r(c) = 0.
-7, 0
Let d(c) be the third derivative of -c**7/1260 + c**6/270 - c**5/180 + c**3/6 - 2*c**2. Let l(q) be the first derivative of d(q). Solve l(x) = 0 for x.
0, 1
Let z(h) be the first derivative of -h**8/10920 - h**7/1820 - h**6/1170 - h**3/3 + 3. Let b(p) be the third derivative of z(p). Factor b(l).
-2*l**2*(l + 1)*(l + 2)/13
Let a(g) be the first derivative of g**6/10 + 3*g**5/5 + 21*g**4/20 - g**3/5 - 12*g**2/5 - 12*g/5 - 11. What is w in a(w) = 0?
-2, -1, 1
Suppose 0 - 2/5*d**5 + 0*d**3 + 0*d**2 + 0*d - 2/5*d**4 = 0. Calculate d.
-1, 0
Solve 4/3*s - 4/3*s**2 + 0 = 0 for s.
0, 1
Let u(v) be the first derivative of -2*v**3/39 - 4*v**2/13 - 8*v/13 + 4. Factor u(x).
-2*(x + 2)**2/13
Let g = -8 + 16. Factor -16*n**2 - g + 5*n - 7*n**3 + 2*n**3 - 6*n**2 - 33*n.
-(n + 2)**2*(5*n + 2)
Let j = 197/33 - 51/11. Factor 0*d - j*d**2 + 2*d**3 - 2/3*d**4 + 0.
-2*d**2*(d - 2)*(d - 1)/3
Let d(p) = -p**2 - 3*p. Suppose -3 = -z - q - 0*q, -3*q + 15 = 0. Let v be d(z). Factor a**v - a**3 + 0*a + a - 1 + a**2 - a**2.
-(a - 1)**2*(a + 1)
Suppose 5*w + 36 = 2*d, -2*d + w = 2*d - 36. Suppose -3*y + d = y. Factor 6*c - 4*c + c**y + 1 + 0.
(c + 1)**2
Suppose u - 3*u = -c, 0 = 4*u - 8. Factor -3*j**3 - 2 + j**3 + 4*j**3 + 4*j - 6*j**3 + 2*j**c.
2*(j - 1)**3*(j + 1)
Let t(b) be the first derivative of b**4/22 + 27. Factor t(n).
2*n**3/11
Let p(z) = -3*z**5 + 12*z**4 - 18*z**2 - 3*z. Let n(a) = -4*a**5 + 13*a**4 + a**3 - 19*a**2 - 4*a - 1. Let g(b) = 6*n(b) - 7*p(b). Determine x so that g(x) = 0.
-2, -1, 1
Let p(u) be the second derivative of u**9/52920 + u**8/11760 + u**7/8820 - u**4/4 + 3*u. Let y(s) be the third derivative of p(s). Factor y(o).
2*o**2*(o + 1)**2/7
Let m(d) = d**3 + 5*d**2 + 6*d + 8. Let o be m(-4). Let r(s) be the first derivative of -2/3*s**2 + 1/3*s**4 - 2/15*s**5 + 2/3*s + o*s**3 + 1. Factor r(n).
-2*(n - 1)**3*(n + 1)/3
Let j = 6 - 7. Let n = j + 3. Factor 4*w**n + 1 + w**2 + 2*w - 4*w**2.
(w + 1)**2
Let x = 130 + -908/7. Factor 0*c**3 + 0*c + x*c**2 + 0 - 2/7*c**4.
-2*c**2*(c - 1)*(c + 1)/7
Suppose 2*m - 3*m = -8. Factor -m*x**2 - 48*x**3 - 20*x**4 + 5*x**2 - 13*x**2.
-4*x**2*(x + 2)*(5*x + 2)
Let p(k) = -35*k - 68. Let o be p(-2). Suppose 0*r - 2*r**5 + 0 + o*r**3 - 4/7*r**4 + 4/7*r**2 = 0. What is r?
-1, -2/7, 0, 1
Let d(b) be the first derivative of -b**8/1512 + 2*b**7/945 - b**6/540 - 3*b**2/2 - 2. Let o(s) be the second derivative of d(s). Determine g so that o(g) = 0.
0, 1
Suppose 6*j + 2*j = 16. Factor -4/5 + 2/5*z**j - 2/5*z.
2*(z - 2)*(z + 1)/5
Let s be (-168)/36*(-6)/7. Suppose -2/5*y**3 - 1/5*y**5 - 1/5 + 3/5*y**s - 2/5*y**2 + 3/5*y = 0. What is y?
-1, 1
Let p = 2437/4 - 609. Let r(s) = s**3 + 4*s**2 - 5*s + 5. Let j be r(-5). Let 0*l - 1/4*l**2 + p*l**3 - 1/4*l**j + 1/4*l**4 + 0 = 0. What is l?
-1, 0, 1
Suppose 80/11*j + 64/11 - 2/11*j**4 - 4/11*j**3 + 24/11*j**2 = 0. Calculate j.
-2, 4
Let f(t) be the third derivative of -t**8/84 + t**6/10 - 2*t**5/15 - 29*t**2. Factor f(w).
-4*w**2*(w - 1)**2*(w + 2)
Let 0 + 102/7*c**2 - 134/7*c**3 - 18/7*c - 8/7*c**5 + 58/7*c**4 = 0. What is c?
0, 1/4, 1, 3
Let z(q) be the first derivative of 2*q**3 - 1 + 2/3*q**5 + 0*q + 2/3*q**2 + 2*q**4. Factor z(o).
2*o*(o + 1)**2*(5*o + 2)/3
Let t(j) be the second derivative of -j**7/231 - 4*j**6/165 + j**5/10 - j**4/11 - 18*j. Factor t(p).
-2*p**2*(p - 1)**2*(p + 6)/11
Let c be (2 + -2)/(-28 + 33). Find m, given that c - 4/5*m**5 + 0*m + 4/5*m**2 + 2*m**3 + 2/5*m**4 = 0.
-1, -1/2, 0, 2
Let r = -277 + 1113/4. Factor r*o - 1/2 + 7/4*o**2.
(o + 1)*(7*o - 2)/4
Let w be (-429)/1050 + 3/7. Let x(f) be the second derivative of -2*f + 1/15*f**3 + 1/15*f**4 + 0 + 0*f**2 + w*f**5. Suppose x(i) = 0. Calculate i.
-1, 0
Let n(c) be the first derivative of 0*c + 3 - 2/9*c**2 + 2/27*c**3. Factor n(h).
2*h*(h - 2)/9
Let x(n) be the third derivative of n**8/1008 + n**7/315 - 4*n**2. Factor x(s).
s**4*(s + 2)/3
Suppose 0 = -4*c - 5 + 17. Let h(g) be the first derivative of 1/2*g**c - 1 + g**2 + 1/2*g. Let h(f) = 0. What is f?
-1, -1/3
Let h(y) be the third derivative of y**7/1575 - y**6/300 + y**5/150 - y**4/180 + 14*y**2. Factor h(m).
2*m*(m - 1)**3/15
Let g = 3 + 0. Let 3*v**2 + g*v + v + v**3 - v**2 - 3*v = 0. What is v?
-1, 0
Let o(y) = -4*y - 49. Let j be o(-13). Find u such that -3/2 - 3/2*u**2 - j*u = 0.
-1
Let i(h) = -2*h**3 + 4*h**2 + 7*h - 4. Let t(o) = -3*o**3 + 6*o**2 + 10*o - 6. Let l(z) = 7*i(z) - 5*t(z). Factor l(a).
(a - 2)*(a - 1)*(a + 1)
Let a be (1 - 79)*(-24)/36. Let q be a/30 + (-18)/(-27). Determine x, given that q*x + 12/5 + 3/5*x**2 = 0.
-2
Let t(m) be the second derivative of 0 - 1/30*m**4 + 9*m + 2/15*m**3 + 3/5*m**2. What is s in t(s) = 0?
-1, 3
Suppose 0 = s - 0*s + 14. Let a be (-1)/(-2) + 7/s. Let 0*g + a - 4/5*g**2 + 6/5*g**3 - 2/5*g**4 = 0. Calculate g.
0, 1, 2
Let o(i) be the third derivative of 6*i**2 - 1/20*i**5 - 1/6*i**3 + 0 + 1/8*i**4 + 1/120*i**6 + 0*i. Solve o(v) = 0.
1
What is g in -100/3*g**3 - 28*g**2 - 2/3*g + 14/3 + 2*g**5 - 26/3*g**4 = 0?
-1, 1/3, 7
Let f(x) be the second derivative of x**6/15 + x**5/5 - 2*x**3/3 - x**2 + 6*x. What is s in f(s) = 0?
-1, 1
Suppose -2*c + 9 = 1. Factor -14 - 280*k**3 + 17*k + 18*k + 12*k**2 + 45*k - 2 - 196*k**c.
-4*(k + 1)**2*(7*k - 2)**2
Let s be 0 + (-35)/(-20) + 2/8. Let r be (-4)/(-6) + 0 - 0. Find h, given that 0*h**2 + 4/3 - r*h**3 + s*h = 0.
-1, 2
Let g = 7 - 5. Find s such that 3*s**g + s**2 + 2*s**2 - s**3 - 5*s**2 = 0.
0, 1
Let x = -90 - -992/11. Factor x*v**2 + 2/11*v + 0.
2*v*(v + 1)/11
Let j(d) = 3*d**2 + d. Let u(w) = w**3 + w**2 - w. Let v be u(1). Let g(z) = -z**3 - z**2 - z. Let q(h) = v*j(h) + g(h). Let q(a) = 0. Calculate a.
0, 2
Let w = 6937/24 + -289. Let v(k) be the second derivative of 1/4*k**2 + w*k**6 + 0 + 2*k - 1/8*k**3 + 3/80*k**5 - 7/48*k**4. Factor v(s).
(s - 1)*(s + 1)**2*(5*s - 2)/4
Let d(p) = -p. Let r be d(-3). Suppose 9 + 0 = r*l. Solve 2/3*w**2 + 2/3*w - 2/3 - 2/3*w**l = 0.
-1, 1
Let y be (-30)/(-8) - 1/(-4). Let q(h) = -h**2 + 6*h - 4. Let v be q(y). Factor -v*l - 2 - 4*l**3 + 5*l + l + 4*l**2 - 2*l**4 + 2*l**5.
2*(l - 1)**3*(l + 1)**2
Let y(o) = -4*o - 58. Let b be y(-15). Let j(i) be the third derivative of 0 + 4*i**b + 1/8*i**4 + 1/4*i**3 + 0*i + 1/40*i**5. Factor j(s).
3*(s + 1)**2/2
Let x(i) be the third derivative of -i**6/150 + 6*i**2. Factor x(r).
-4*r**3/5
Suppose -35 = -p - 4*p - 5*y, p - 2*y + 5 = 0. Suppose q - q**p - q + 3*q**5 - 2*q**2 + 4*q**4 = 0. Calculate q.
-1, 0, 2/3
Let q(j) = j**3 - 7*j**2 + 12*j - 7. Let p be q(5). Let a(c) be the first derivative of 1/12*c**4 + 4/3*c - 1/3*c**p + 1 + 0*c**2. Find v, given that a(v) = 0.
-1, 2
Solve -23*r**2 - r - 8*r + 8*r**2 + 0*r = 0.
-3/5, 0
Let r(f) be the first derivative of 4 + 3/16*f**4 - 1/4*f**3 + 3/20*f**5 + 0*f - 1/8*f**6 + 0*f**2. Find y, given that r(y) = 0.
-1, 0, 1
Let y(n) be the second derivative of 1/9*n**3 + 0*n**2 - 1/18*n**4 