et q(i) be the second derivative of 1/20*i**5 - 3*i - 1/12*i**3 + 0 - 1/4*i**2 - 1/60*i**6 + 1/12*i**4 - 1/84*i**7. Factor q(v).
-(v - 1)**2*(v + 1)**3/2
Determine u, given that 0*u**5 - 3*u**2 - 3*u**5 - 9*u**3 + 0*u**2 - 9*u**4 = 0.
-1, 0
Let y(m) = -m. Let j(h) = -225*h**2 - 62*h - 4. Let w(u) = -j(u) + 2*y(u). Let w(i) = 0. What is i?
-2/15
Suppose -40*z**2 - 6*z**3 - 3 - 10*z**3 - 32*z - 2*z**4 + 3 = 0. What is z?
-4, -2, 0
Suppose -6 = 2*n + 2*o, 3*n - 7*o + 5*o - 16 = 0. Factor 2/3*i - 2/3*i**3 + 2/3*i**n - 2/3.
-2*(i - 1)**2*(i + 1)/3
Solve -12/5*m**3 + 2/5*m**2 + 0*m + 18/5*m**4 + 0 - 8/5*m**5 = 0 for m.
0, 1/4, 1
Let m(a) = -a**2 - a + 4. Let w be m(5). Let p = w - -44. Factor 0*u - 3*u - p - 2*u**2 + 6*u + 9*u.
-2*(u - 3)**2
Let u(d) be the second derivative of d**7/231 + d**6/55 - 7*d**5/110 - 5*d**4/22 + 6*d**3/11 + 2*d + 9. Suppose u(g) = 0. What is g?
-3, 0, 1, 2
Let v(y) = -y**3 + 5*y**2 - y - 4. Let b be v(2). Let n be ((-16)/b)/(24/(-16)). Factor n*f - 10/9*f**2 + 8/9.
-2*(f - 2)*(5*f + 2)/9
Let y(b) be the second derivative of -29*b**4/14 + 31*b**3/7 - 6*b**2/7 + 52*b. Factor y(v).
-6*(v - 1)*(29*v - 2)/7
Let r(i) be the third derivative of 1/150*i**6 + 1/75*i**5 - 1/20*i**4 + 1/15*i**3 + 0 - 1/175*i**7 - i**2 + 1/840*i**8 + 0*i. Solve r(f) = 0.
-1, 1
Let v(f) = 4*f - 1. Let t be v(1). Let i be (2/(-36))/(t/(-12)). Factor 0 - 2/9*o + i*o**2.
2*o*(o - 1)/9
Factor -3/7*p**2 + 3/7*p**3 + 0*p + 0.
3*p**2*(p - 1)/7
Let d(l) be the second derivative of l**6/6 + 7*l**5/20 - 13*l**4/20 - 19*l**3/30 - l**2/5 + 9*l. Factor d(g).
(g - 1)*(g + 2)*(5*g + 1)**2/5
Let m(b) be the third derivative of -b**5/20 - b**4/2 - 3*b**3/2 + b**2. Solve m(s) = 0.
-3, -1
Let s = 58 - 288/5. Solve 0 + s*o**2 - 2/5*o = 0.
0, 1
Let u(d) = -d**4 + d**3 + d**2 - d - 1. Let i(p) = -p**5 - 2*p**4 + 3*p**3 + 2*p**2 - 2*p - 2. Let s(h) = i(h) - 2*u(h). Factor s(g).
-g**3*(g - 1)*(g + 1)
Let u(j) be the first derivative of j**6/3 + 2*j**5 - 80*j**3/3 - 80*j**2 - 96*j - 4. Determine f, given that u(f) = 0.
-2, 3
Let i be (2/(-2) - -1)*1. Let q(d) be the third derivative of d**2 + 1/60*d**5 + i + 0*d**3 - 1/24*d**4 + 0*d. Factor q(u).
u*(u - 1)
Let l(t) be the third derivative of -t**8/5880 + t**6/630 - t**4/84 - t**3/2 + t**2. Let k(q) be the first derivative of l(q). Factor k(v).
-2*(v - 1)**2*(v + 1)**2/7
Factor 11*c + 0*c - 2*c**2 - 10*c + 5*c.
-2*c*(c - 3)
Let y be (-3 - 33)*(-1)/(-2). Let w be 6/27 + (-32)/y. Factor 2/7*a**w - 4/7*a + 2/7.
2*(a - 1)**2/7
Let j(v) be the first derivative of -v**5 + 5*v**4/4 + 5*v**3/3 - 5*v**2/2 - 14. Solve j(d) = 0 for d.
-1, 0, 1
Let p(w) = -3*w**3 - 4*w**2 + 3*w + 4. Let h(l) = -6*l**3 - 9*l**2 + 6*l + 9. Let x(q) = 3*h(q) - 7*p(q). What is k in x(k) = 0?
-1, -1/3, 1
Let t = -57 - -61. Let g be ((-42)/8)/((-45)/168). Factor 0 - 8/5*y - 48/5*y**2 + g*y**t - 42/5*y**3.
2*y*(y - 1)*(7*y + 2)**2/5
Factor 2/9*j**2 + 2/9 - 4/9*j.
2*(j - 1)**2/9
Let n be 115/(-20) + 3 + 3. Factor -1/4*u**2 - n*u**5 + 0*u + 1/4*u**4 + 0 + 1/4*u**3.
-u**2*(u - 1)**2*(u + 1)/4
Let b(g) be the first derivative of g**4/20 + g**3/10 + 2*g + 4. Let k(j) be the first derivative of b(j). Factor k(w).
3*w*(w + 1)/5
Let t be 6/8 - 590/3304. Factor 16/7 + t*a**2 + 16/7*a.
4*(a + 2)**2/7
Let c(k) be the second derivative of -k**7/5670 - k**6/3240 - k**4/6 - 4*k. Let z(o) be the third derivative of c(o). Factor z(a).
-2*a*(2*a + 1)/9
Let g(x) be the third derivative of -x**5/60 - x**4/24 - x**3/6 + x**2. Suppose -2*w - 2 = 2. Let u(h) = 3*h**2 - h + 4. Let v(t) = w*g(t) - u(t). Factor v(m).
-(m - 2)*(m - 1)
Let v(i) = 101*i - 101*i + 7*i**2. Let p be (-14)/2 - (0 + -1). Let s(c) = 6*c**2. Let t(w) = p*s(w) + 5*v(w). Factor t(b).
-b**2
Let g = -563/33 - -52/3. Let a(n) be the first derivative of -8/11*n + 12/11*n**2 - 2 - 26/33*n**3 - 2/55*n**5 + g*n**4. Solve a(w) = 0.
1, 2
Let o(z) be the third derivative of -z**8/3528 - 2*z**7/2205 - z**6/1260 - 2*z**2. Factor o(i).
-2*i**3*(i + 1)**2/21
Let b be 28/(-10)*34/(-119). Let n(s) be the first derivative of -3 - 3/5*s**2 + 2/15*s**3 + b*s. Factor n(p).
2*(p - 2)*(p - 1)/5
Let s(a) = 9*a + 2 - 5 + a**2 - 11*a. Let w be s(3). Factor 4/9*q**3 - 2/9*q**4 + 2/9 - 4/9*q + w*q**2.
-2*(q - 1)**3*(q + 1)/9
Let k(c) be the second derivative of 0*c**5 + 0*c**4 + 0 + 0*c**3 - 2*c + 0*c**2 - 1/75*c**6. Factor k(m).
-2*m**4/5
Find i such that -4/13 + 2/13*i**2 + 6/13*i**3 + 2/13*i**4 - 6/13*i = 0.
-2, -1, 1
Let q be 2*-6*40/(-96). Find k, given that 0 - 2/3*k**4 + 2/3*k**3 + 0*k - 2/3*k**q + 2/3*k**2 = 0.
-1, 0, 1
Let k(y) = -3*y**3 + 12*y**2 + 12*y. Let m(x) = 0*x**2 + 5*x - x**2 - 6*x. Let n(g) = k(g) + 12*m(g). Factor n(a).
-3*a**3
Suppose -5 = 5*f + 6*v - v, f - 2*v - 2 = 0. Factor 0 - 1/2*s**3 + 1/2*s**2 + f*s.
-s**2*(s - 1)/2
Let a = 1 - -2. Let y(d) be the third derivative of 0*d**5 + 0*d**a + 0 + 1/12*d**4 + d**2 - 1/60*d**6 + 0*d. Factor y(f).
-2*f*(f - 1)*(f + 1)
Let s = 2472/7 - 353. Factor -s*f**3 - 2/7*f + 3/7*f**2 + 0.
-f*(f - 2)*(f - 1)/7
Suppose -5*w = 6*a - 5*a + 17, -a + 23 = -5*w. Factor -6*k**3 - 4*k**4 - 3*k - 2*k**4 - 3*k**5 - a*k**4 + 6*k**2 + 3 + 12*k.
-3*(k - 1)*(k + 1)**4
Suppose 2*a - 4 = 5*n, 2*n + 2 + 2 = 2*a. Let d(k) be the second derivative of -1/18*k**3 - 1/36*k**4 + n - k + 0*k**2. Find v such that d(v) = 0.
-1, 0
Let k be 938/105 + (-24)/(-9) + -2. Factor -12/5*j**2 + 1/5*j - 64/5*j**4 + 0 + k*j**3.
-j*(4*j - 1)**3/5
Let t(f) be the third derivative of -2*f**2 + 0*f**3 + 0 - 1/24*f**4 + 1/120*f**5 + 0*f. Determine q so that t(q) = 0.
0, 2
Let x(w) be the second derivative of -w**4/48 - w**3/4 - 9*w**2/8 + 5*w. Suppose x(q) = 0. Calculate q.
-3
Let c be (2/6)/((-14)/(-21)). Factor 1/4*o**4 + 1/4 - 1/4*o**5 - 1/4*o + 1/2*o**3 - c*o**2.
-(o - 1)**3*(o + 1)**2/4
What is w in -2/7*w**5 - 10/7*w**2 + 0 + 10/7*w**4 + 12/7*w - 10/7*w**3 = 0?
-1, 0, 1, 2, 3
Suppose b = -1 + 4. Suppose 3*n - n - 8 = -v, -n - b = -3*v. Factor 7*o**2 - n*o - 5*o**2 + o.
2*o*(o - 1)
Let q(b) be the second derivative of b**7/420 + b**6/180 - b**5/60 - b**4/12 - b**3/2 + 3*b. Let p(h) be the second derivative of q(h). Factor p(l).
2*(l - 1)*(l + 1)**2
Let a(k) be the second derivative of k**5/120 + k**4/24 + k**3/12 + 5*k**2/2 - 4*k. Let i(z) be the first derivative of a(z). Factor i(x).
(x + 1)**2/2
Let q(v) be the second derivative of -v**9/560 - v**8/1120 - 2*v**4/3 + 2*v. Let g(h) be the third derivative of q(h). Factor g(j).
-3*j**3*(9*j + 2)
Let g(k) be the third derivative of -k**7/420 - k**6/120 + k**5/120 + k**4/24 - 3*k**2. Solve g(t) = 0 for t.
-2, -1, 0, 1
Suppose 3/4*r**4 + 0 - 3/4*r**2 + 0*r**3 + 0*r = 0. What is r?
-1, 0, 1
Let o(x) be the third derivative of 0 + 0*x**4 - 1/8*x**3 + 0*x + 1/80*x**5 - 5*x**2. Factor o(s).
3*(s - 1)*(s + 1)/4
Find i, given that -52*i**2 - 1 + 48*i**3 + 123*i**4 - 3 + 24*i - 139*i**4 = 0.
1/2, 1
Let p(d) be the third derivative of d**9/7560 + d**8/3360 - d**4/6 - 2*d**2. Let x(t) be the second derivative of p(t). Factor x(h).
2*h**3*(h + 1)
Let u = 5 + -17. Let h = u + 17. Suppose c**2 - c**2 + c**h = 0. What is c?
0
Let i be 1/14*70/600. Let y(m) be the third derivative of 0*m - 1/2*m**4 - i*m**6 - 1/10*m**5 + 0 - 4/3*m**3 - 3*m**2. Let y(a) = 0. Calculate a.
-2
Let o(b) be the first derivative of b**6/9 - 2*b**5/15 - b**4/6 + 2*b**3/9 - 10. Factor o(s).
2*s**2*(s - 1)**2*(s + 1)/3
Suppose 2*r + 3*k - 5*k = -56, -4*r + 2*k = 110. Let w be 3 + 0 - (-45)/r. Factor w - 49/3*g**3 + 8*g + 7*g**2.
-(g - 1)*(7*g + 2)**2/3
Suppose 4*j - 6*k = -3*k + 63, 0 = 2*j + 5*k + 1. Let q be (j/(-2))/(-3 + 2). Suppose 4*m - q*m + 0*m**2 + m**2 = 0. Calculate m.
0, 2
Solve 2*j - 4*j - 2 - 8*j**3 + 2*j**2 + 11*j**3 - j**3 = 0 for j.
-1, 1
Let g(a) = -a**5 + a**3 - a. Let r(x) = -10*x**5 - 5*x**4 + 20*x**3 + 25*x**2 + 5*x. Let b(n) = -5*g(n) + r(n). Factor b(s).
-5*s*(s - 2)*(s + 1)**3
Let j = -7 + 11. Suppose 0 = -7*v + j*v. Factor 2 + 2*o**2 + v - 3 - o**4.
-(o - 1)**2*(o + 1)**2
Suppose -5*s = -5*i + 25, 19 = i + i - 5*s. Let -2/3 - l - 1/3*l**i = 0. Calculate l.
-2, -1
Let q(f) = 2*f**2 - f. Let i(u) = -3*u**2. Let w(n) = i(n) + 3*q(n). Factor w(t).
3*t*(t - 1)
Let y(m) be the third derivative of -m**6/90 + m**5/60 + m**4/12 - m**3/3 + 2*m**2. Let p(o) be the first derivative of y(o). Factor