**2.
-2*r**2*(r - 1)**2
Determine n so that -5/2 - 9*n**2 + 4*n**3 + 8*n - 1/2*n**4 = 0.
1, 5
Suppose 3 - 4 = -b. Let n(l) be the first derivative of l**4 + b - 2/5*l**5 + 0*l + 0*l**2 - 2/3*l**3. Factor n(r).
-2*r**2*(r - 1)**2
Let f be 2/(-2)*0 - -2. Let s(p) be the second derivative of 0*p**f + 2/5*p**5 + 2/9*p**3 + 0 + 1/2*p**4 - 3*p + 1/9*p**6. Factor s(h).
2*h*(h + 1)**2*(5*h + 2)/3
Suppose -3*m + m + 4*m = 0. Let y(k) be the second derivative of 0*k**2 + k - 1/30*k**5 + 1/36*k**4 + 1/9*k**3 + m - 1/90*k**6. Factor y(r).
-r*(r - 1)*(r + 1)*(r + 2)/3
Let r(t) be the first derivative of -t**5/80 - t**4/48 + t**3/24 + t**2/8 - 3*t + 2. Let a(l) be the first derivative of r(l). Suppose a(y) = 0. Calculate y.
-1, 1
Suppose -5*t + 5*f = 20, -t - 2*f + 8 = t. Suppose 0*i + 2 = -4*m - i, -4*m + 5*i + 10 = t. Let m + 0*l + 1/3*l**3 + 0*l**2 = 0. What is l?
0
Suppose y = -5*a - 6, 2*a - 4 = 2*y - 16. Factor 3/2*s**2 + 0*s + 0 - 3*s**3 + 3/2*s**y.
3*s**2*(s - 1)**2/2
Let h(a) be the third derivative of -5*a**8/336 + a**7/42 + a**6/12 - a**5/6 - 5*a**4/24 + 5*a**3/6 + 27*a**2. Suppose h(s) = 0. Calculate s.
-1, 1
Let s(z) be the third derivative of 0*z - 3*z**2 + 1/84*z**4 - 1/105*z**5 + 0 + 0*z**3 + 1/420*z**6. Suppose s(t) = 0. Calculate t.
0, 1
Let w be -4 + 35/5 + (-1)/1. Find r such that 14/9*r**w - 8/9 + 8/3*r = 0.
-2, 2/7
Suppose 1 = -14*u + 1. Factor s**3 + 0 + u*s - 1/4*s**4 - s**2.
-s**2*(s - 2)**2/4
Let y be ((-6)/(-12))/((-20)/(-6) - 3). Suppose -1/4 - y*w**2 - w - w**3 - 1/4*w**4 = 0. Calculate w.
-1
Factor 0 + 2/5*h**3 + 0*h + 0*h**2.
2*h**3/5
Let k be 21/28 + 1/(160/(-102)). Let o(w) be the second derivative of 1/2*w**4 + 0 + 0*w**2 + 1/2*w**3 - k*w**5 - 9/40*w**6 + 4*w. Suppose o(g) = 0. What is g?
-2/3, 0, 1
Factor -137*b + 89*b - 32 + 4*b**5 + 44*b**3 + 5*b**2 + 3*b**2 + 24*b**4.
4*(b - 1)*(b + 1)*(b + 2)**3
Let m(p) be the first derivative of p**5/100 + p**4/20 + 3*p**2/2 + 2. Let r(a) be the second derivative of m(a). Determine i so that r(i) = 0.
-2, 0
Let l(c) be the second derivative of -c**8/2520 + 2*c**3/3 - c. Let y(q) be the second derivative of l(q). Let y(w) = 0. Calculate w.
0
Let i = 1163/72 + -129/8. Let b(p) be the third derivative of 0*p**3 - 1/180*p**5 + 0*p - 2*p**2 + i*p**4 + 0. Factor b(a).
-a*(a - 2)/3
Let c(x) be the third derivative of -1/150*x**5 + 0 - 3*x**2 + 0*x + 1/15*x**3 - 1/600*x**6 + 1/120*x**4. Let c(u) = 0. Calculate u.
-2, -1, 1
Let y(o) be the second derivative of -o**7/735 + o**6/420 + o**5/105 + o**2 + 7*o. Let a(u) be the first derivative of y(u). Find g, given that a(g) = 0.
-1, 0, 2
Factor 1 + 6*x - x + 3*x - 2*x**2 - 7.
-2*(x - 3)*(x - 1)
Suppose 2/5 + 4/5*i + 2/5*i**2 = 0. What is i?
-1
Let a(k) = -3*k**2 - 6*k + 9. Let v(r) = 3*r**2 + 7*r - 10. Let j = 18 + -14. Let f(n) = j*a(n) + 3*v(n). Solve f(c) = 0 for c.
-2, 1
Let y(u) = 10*u**4 + 22*u**3 - 50*u**2 + 36*u + 6. Let q(c) = -9*c**4 - 21*c**3 + 49*c**2 - 34*c - 5. Let b(s) = -6*q(s) - 5*y(s). Factor b(m).
4*m*(m - 1)**2*(m + 6)
Let p(s) be the second derivative of s**8/20160 + s**7/7560 + s**4/2 + 3*s. Let n(b) be the third derivative of p(b). Solve n(j) = 0.
-1, 0
Factor -4*t**4 - t**5 + 4*t**4 + t**3 - 3*t**2 + t**4 + 2*t**2.
-t**2*(t - 1)**2*(t + 1)
Let d(n) be the second derivative of 5*n**7/168 + 17*n**6/120 + 21*n**5/80 + 11*n**4/48 + n**3/12 + 2*n. Determine w so that d(w) = 0.
-1, -2/5, 0
Let m(t) be the second derivative of 4/27*t**3 + 4*t + 0 + 1/9*t**4 - 8/9*t**2 - 1/18*t**5 + 1/135*t**6. Factor m(z).
2*(z - 2)**3*(z + 1)/9
Let x(o) = -13*o + 56. Let k be x(4). Let 65/3*b**3 - 2/3 + 20/3*b**2 - 5/3*b + 14*b**k = 0. What is b?
-1, -1/2, -1/3, 2/7
Let c = 165 - 1153/7. Factor 8/7*y + 8/7*y**3 - c*y**4 - 12/7*y**2 - 2/7.
-2*(y - 1)**4/7
Let t(b) = 20*b**5 - 66*b**4 - 34*b**3 + 74*b**2 + 25*b + 3. Let l(j) = j**4 - j**2 + j + 1. Let n(u) = -22*l(u) + 2*t(u). Determine q, given that n(q) = 0.
-1, -2/5, 1/4, 1, 4
Let p be (((-3)/4)/1)/(11/(-44)). Let 3*j**2 - 21/5*j + 9/5 - 3/5*j**p = 0. What is j?
1, 3
Let g(y) = 8*y**3 + 41*y**2 + 15*y. Let s(j) = 2*j**3 + 10*j**2 + 4*j. Let f(a) = 2*g(a) - 9*s(a). Let f(x) = 0. What is x?
-3, -1, 0
Let 2*y**4 - y**4 + 4*y - y**4 - 3*y**3 + y**4 = 0. Calculate y.
-1, 0, 2
Let t(y) = 6*y + 4 - 16*y**3 + 6 - 4 + 2*y**2. Let s(z) = -z**4 + z**3 - z**2 - z - 1. Let g(x) = -6*s(x) - t(x). Suppose g(u) = 0. What is u?
-1, -2/3, 0
Let y(c) be the second derivative of -1/36*c**3 - 1/36*c**4 - 4*c + 1/6*c**2 + 1/120*c**5 + 0. Solve y(j) = 0.
-1, 1, 2
What is x in x**4 + x**2 + 205*x - 205*x - 2*x**3 = 0?
0, 1
Let u be -152 - -4*(-3)/(-6). Let g be (-24)/30*u/4. What is p in 4 + 30*p**3 + 2 + 2*p**5 - 15*p - g*p**4 - 2*p**5 + 9*p**5 = 0?
-2/3, 1
Let a be ((-6)/(-4))/((-3)/(-10)). Let t be (-2)/8 + a/20. Suppose -2/9*g**2 + t*g + 0 + 2/9*g**3 = 0. Calculate g.
0, 1
Let v(u) = u**5 - 21*u**4 - 16*u**3 - 5*u**2 + 5. Let y(x) = -4 - 8*x**3 + 4 - 2*x**2 - 10*x**4 + 2. Let l(b) = 2*v(b) - 5*y(b). Solve l(z) = 0.
-2, 0
Let l(r) be the third derivative of -r**10/75600 - r**9/7560 - r**8/2520 - r**5/12 + 4*r**2. Let b(f) be the third derivative of l(f). Solve b(z) = 0 for z.
-2, 0
Let t(q) = -5*q**2 - 9*q + 5. Let g(c) = 2*c**2 + 4*c - 2. Let p(f) = 9*g(f) + 4*t(f). Factor p(j).
-2*(j - 1)*(j + 1)
Suppose 4*y + 5 = 13. Factor -8*t**2 + 4*t**2 - 2*t**2 + 2*t**y.
-4*t**2
Let n(m) be the second derivative of 0 - m + 0*m**4 + 0*m**2 + 1/3*m**3 - 1/10*m**5. Factor n(j).
-2*j*(j - 1)*(j + 1)
Let h(d) be the first derivative of -2 + 23/9*d**3 + 4/3*d + 7/12*d**4 + 10/3*d**2. Factor h(y).
(y + 1)*(y + 2)*(7*y + 2)/3
Let t(h) be the third derivative of -h**8/6720 - h**7/560 - h**6/120 - h**5/15 + 5*h**2. Let s(x) be the third derivative of t(x). Let s(p) = 0. What is p?
-2, -1
Let t = -78/5 - -47/3. Let a(m) be the second derivative of -t*m**3 + 0 + 1/30*m**4 - 3*m + 0*m**2. What is c in a(c) = 0?
0, 1
Let d(s) = s - 2. Let q be d(5). Let f be (-13)/(-26)*(q - -1). Factor 0*p - 1/2*p**f + 0 + 1/2*p**3.
p**2*(p - 1)/2
Let j(g) = -4*g**2 - g**2 + 6 + 0*g - 5*g. Let n(z) = -z**2 - z + 1. Let d(l) = -j(l) + 6*n(l). Factor d(b).
-b*(b + 1)
Let x be 10/(-45) - (-32)/(-18). Let k be 22/(-6) + 3 - x. Solve k - 2/3*f**2 - 2/3*f = 0 for f.
-2, 1
Factor 16 + 52*z + 17*z**2 - z**2 - 4.
4*(z + 3)*(4*z + 1)
Factor 7/2*n**3 + 0 - 2*n + 3/2*n**2.
n*(n + 1)*(7*n - 4)/2
Find l such that 1/5*l**3 + 6/5*l**2 + 8/5*l + 0 = 0.
-4, -2, 0
Let y be (2 + -2)/(2/(-2)). Let c(b) be the second derivative of 0 + 1/27*b**3 + 1/54*b**4 - b + y*b**2. Factor c(g).
2*g*(g + 1)/9
Let v(w) be the first derivative of -w**6/21 + 6*w**5/35 - 3*w**4/14 + 2*w**3/21 - 4. Factor v(u).
-2*u**2*(u - 1)**3/7
Determine u, given that -1/2*u**2 - 3/2*u**4 + 1/2*u**5 + 3/2*u**3 + 0*u + 0 = 0.
0, 1
Let a = 11 + -9. What is n in 5/2*n**3 - 2*n**5 + 0 - 1/2*n + 3/2*n**a - 3/2*n**4 = 0?
-1, 0, 1/4, 1
Factor -4*o**3 + o**4 - 6 + o**2 + 6 + 2*o**3.
o**2*(o - 1)**2
Let o(g) = -g - 6. Let k be o(-11). Suppose 0 = -k*z + 4*z + 2. Factor -3/2*j**z + 1/2*j**3 + 3/2*j - 1/2.
(j - 1)**3/2
Let l(b) be the second derivative of -b**6/75 + b**4/10 - 2*b**3/15 - 2*b. Solve l(a) = 0.
-2, 0, 1
Let q be ((-38)/(-6))/(-1) + 3. Let r = q - -4. Solve r*v**4 + 2/3 - 4/3*v**2 + 0*v**3 + 0*v = 0 for v.
-1, 1
Let c(i) = 5*i**4 + i**3 - i**2 - 5*i - 4. Let s(q) = 3*q + q**2 + 11 + 2*q**2 - 14*q**4 + 11*q - 3*q**3. Let a(m) = -11*c(m) - 4*s(m). Factor a(b).
b*(b - 1)*(b + 1)**2
Let o(r) be the third derivative of -r**10/50400 - r**9/60480 + r**8/6720 + r**7/5040 + r**5/30 + r**2. Let t(c) be the third derivative of o(c). Factor t(l).
-l*(l - 1)*(l + 1)*(3*l + 1)
Let p(g) be the third derivative of g**6/480 + g**5/80 + g**4/48 + 10*g**2. Factor p(b).
b*(b + 1)*(b + 2)/4
Let p = -6 + 9. Factor -8*s**2 - 21*s**p - 19*s**2 - 4*s - 2*s.
-3*s*(s + 1)*(7*s + 2)
Let c = -25 + 27. Let w(q) be the second derivative of 0*q**3 - c*q - 1/10*q**5 + 0*q**2 + 0 + 0*q**4. Factor w(b).
-2*b**3
Suppose 5 = y + 1. Let r(v) be the third derivative of 0*v - 2*v**2 + 2/15*v**3 - 1/60*v**y - 1/150*v**5 + 0. Factor r(q).
-2*(q - 1)*(q + 2)/5
Let d(n) be the first derivative of n**5/20 - n**3/4 - n**2/4 - 4. Find t, given that d(t) = 0.
-1, 0, 2
Suppose 0 = -6*j + 10*j - 24. Let c be (j/44)/(3/4). Suppose c*a**2 + 6/11*a**