 - l**4/90 + 8*l**2. Suppose r(z) = 0. What is z?
-2, 0
Let a(n) be the third derivative of 1/112*n**8 + 0 + 1/5*n**5 + 6*n**2 + 0*n**3 + 0*n + 1/8*n**4 + 2/35*n**7 + 3/20*n**6. Factor a(q).
3*q*(q + 1)**4
Suppose 6 = -0*i - 2*i. Let f be 32/12*i/(-2). Solve -3 + f*x**2 - 2*x**3 + 2*x + 0*x - 1 = 0.
-1, 1, 2
Determine w so that 15*w**5 + 45*w**4 + 115/3*w**3 - 20/3 - 5*w**2 - 20*w = 0.
-1, -2/3, 2/3
Let y be (1 - 1)/(-2 - -3). Factor 0*p**4 + 0*p**2 + y + p**3 - 1/2*p**5 - 1/2*p.
-p*(p - 1)**2*(p + 1)**2/2
Let h(g) = g**3 - 6*g + 1. Let z(l) = -l**3 + 5*l. Let d(s) = -4*h(s) - 6*z(s). Let d(r) = 0. What is r?
-1, 2
Factor -250 - 5/2*c**2 - 50*c.
-5*(c + 10)**2/2
Let k be ((4 - 2)*-2)/1. Let n(g) = -g**3 - 5*g**2 + 5*g + 1. Let c(m) = -m**3 - 4*m**2 + 5*m. Let b(t) = k*c(t) + 3*n(t). Factor b(u).
(u - 1)**2*(u + 3)
Let y be 0*(-1 + 3/6). Suppose 5*r + y*r = 0. Factor 0 - 1/2*d**2 + r*d.
-d**2/2
Let f(r) be the third derivative of 1/40*r**5 + 1/90*r**6 + 0*r - 1/24*r**4 - r**2 + 0 - 1/3*r**3. Let s(y) be the first derivative of f(y). Factor s(w).
(w + 1)*(4*w - 1)
Let l(u) = 4*u**2 + 12*u + 8. Let n(m) = 20*m**2 + 60*m + 40. Let g(k) = 14*l(k) - 3*n(k). Factor g(b).
-4*(b + 1)*(b + 2)
Let i = -135 - -137. Factor 0 - 9/4*o**i - 1/2*o.
-o*(9*o + 2)/4
Let r(n) = -n**3 - n - 1. Let b(u) = u**5 - 4*u**3 - 3*u - 3. Let f(h) = 2*b(h) - 6*r(h). Factor f(m).
2*m**3*(m - 1)*(m + 1)
Suppose p = -3*b - b - 6, 2*b = p - 12. Factor -p*g**3 + g**2 + g**4 + 7*g**3 - g**2.
g**3*(g + 1)
Let i be (-6)/4 - (-21)/(-6). Let p be (-1)/(i/2 - -2). Find f such that -14*f**2 - f + 5*f**p - 2*f = 0.
-1/3, 0
Let y(s) = -s**3 - 3*s**2 + 3*s + 12. Let w be y(-2). Factor -3/2*x**3 + 0 + 3*x - 3/2*x**w.
-3*x*(x - 1)*(x + 2)/2
Let g(y) be the third derivative of 1/330*y**6 + 1/330*y**5 + 0 - 5*y**2 + 1/1155*y**7 + 0*y**3 + 0*y**4 + 0*y. Factor g(b).
2*b**2*(b + 1)**2/11
Let a(b) = -3*b**5 - 15*b**3 - 6*b**2 + 6*b + 6. Let w(o) = o**5 + o**4 + o**3 - o**2 + o - 1. Let h(y) = a(y) + 6*w(y). Factor h(t).
3*t*(t - 1)**2*(t + 2)**2
Let y(f) be the third derivative of -f**6/120 + f**5/45 + f**4/72 - f**3/9 - 5*f**2. What is a in y(a) = 0?
-2/3, 1
Factor -4/7*n**3 - 4/7*n**4 + 8/7*n**5 + 0 + 0*n**2 + 0*n.
4*n**3*(n - 1)*(2*n + 1)/7
Let x(j) be the third derivative of j**7/3780 - j**6/540 + j**5/180 + j**4/24 + 3*j**2. Let n(u) be the second derivative of x(u). Let n(t) = 0. Calculate t.
1
Let u be (0 + -5)*1/(-1). Factor -1 - i - u*i**4 - 5*i**3 + 2*i**3 + 3*i**5 + i**3 + 6*i**2.
(i - 1)**3*(i + 1)*(3*i + 1)
Let k be 864/840 - 12/(-21). Factor -k - 16/5*p - 2/5*p**3 - 2*p**2.
-2*(p + 1)*(p + 2)**2/5
Let a(p) be the second derivative of -p**4/42 + 4*p**3/21 - 4*p**2/7 - 10*p. Factor a(j).
-2*(j - 2)**2/7
Let o(h) = -h**2 - 6*h. Let l be o(-6). Let f(s) be the first derivative of l*s - s**2 + 2 - 4/5*s**5 + 1/2*s**4 + 4/3*s**3. Solve f(a) = 0.
-1, 0, 1/2, 1
Let x(n) = n**4 + n**3 - n**2 + 3*n + 2. Let p be -7 + -2 + 4/(-2). Let s(i) = -6*i**4 - 4*i**3 + 4*i**2 - 16*i - 11. Let y(q) = p*x(q) - 2*s(q). Factor y(m).
m*(m - 1)**3
Let c(g) = -2*g + 18. Let n be c(8). Let f(m) be the first derivative of m**n + 1 - 10/3*m**3 + 2*m**4 + 0*m. Find p such that f(p) = 0.
0, 1/4, 1
Let o(t) be the third derivative of t**8/336 - t**7/42 + t**6/40 + 3*t**5/20 + 5*t**2. Factor o(u).
u**2*(u - 3)**2*(u + 1)
Let f(r) be the first derivative of -r**7/21 - 2*r**6/15 - r**5/10 - 3*r + 2. Let a(i) be the first derivative of f(i). Find u, given that a(u) = 0.
-1, 0
Let g(b) be the second derivative of b**4/12 + 5*b**3/6 + 3*b**2 + 8*b. Find y, given that g(y) = 0.
-3, -2
Let s be (-12)/150*(-5)/6. Let b(o) be the second derivative of 1/3*o**2 + 0*o**4 + 0 - s*o**5 - 1/45*o**6 + 2/9*o**3 + 2*o. What is g in b(g) = 0?
-1, 1
Let p be 6 + 7/((-14)/(-12)) + -10. Factor -1/5*v + 0 + 0*v**p + 1/5*v**3.
v*(v - 1)*(v + 1)/5
Let i(t) be the first derivative of -3*t**4/8 + 5*t**3/3 - t**2 - 4*t + 52. Find s, given that i(s) = 0.
-2/3, 2
Let r = 222 - 222. Solve 1/2*o**3 - 1/2*o + 0 + r*o**2 = 0.
-1, 0, 1
Let m be -11*3/18*-3. Let u(w) be the first derivative of -m*w**2 - 49/24*w**6 + 143/16*w**4 - 7/6*w**3 - 2*w - 7/5*w**5 - 1. Find x such that u(x) = 0.
-2, -2/7, 1
Let h(a) be the second derivative of a**6/120 + a**5/20 + a**4/8 + 2*a**3/3 - 3*a. Let g(i) be the second derivative of h(i). Factor g(q).
3*(q + 1)**2
Let l be -2 + 4 - 0/(-6). Let x(f) be the second derivative of 1/8*f**l - 1/12*f**3 + 0 + 1/48*f**4 - f. Solve x(o) = 0.
1
Let c(y) = -y + 3. Let z be (0/(1 + -3))/2. Let l be c(z). Solve 2/3*g**l + g**4 + 0*g**2 + 0 + 0*g = 0 for g.
-2/3, 0
Let p(w) = -w**3 - 29*w**2 - 32*w - 110. Let v be p(-28). Factor -6*g + 5/2*g**2 + v.
(g - 2)*(5*g - 2)/2
Let x(p) be the second derivative of p**7/357 + 2*p**6/255 + p**5/170 - 6*p. Factor x(l).
2*l**3*(l + 1)**2/17
Let l(u) be the second derivative of -u**6/300 - u**5/75 - u**4/60 + 3*u**2/2 - 2*u. Let m(j) be the first derivative of l(j). Find s, given that m(s) = 0.
-1, 0
Let i = -18 + 18. Let k(c) be the third derivative of -1/180*c**6 + 1/315*c**7 + i*c**3 + 0 + 0*c + 1/270*c**5 + 0*c**4 - 1/1512*c**8 - c**2. Factor k(w).
-2*w**2*(w - 1)**3/9
Suppose 4*v + 20 = 8*v. Suppose -3*x = -x + v*u + 11, 1 = -4*x - 3*u. Solve 1/4*s**5 + 1/4*s + 1/4 + 1/4*s**4 - 1/2*s**3 - 1/2*s**x = 0 for s.
-1, 1
Suppose 3*b = -95 - 175. Let w = b + 632/7. Solve -10/7*o**5 + 0 - w*o**3 + 0*o + 16/7*o**4 - 4/7*o**2 = 0.
-2/5, 0, 1
Factor -3/5 - 2/5*a + 1/5*a**2.
(a - 3)*(a + 1)/5
Let k = -18 - -27. Suppose 15 = 5*i + z, -5*i + k*z = 4*z + 15. Factor o**2 + 4*o**2 - 4*o**i + o.
o*(o + 1)
Let v(p) = p**3 + 3*p**2 - 6*p - 6. Let k be v(-4). Determine m so that -m**3 + 0*m**2 + m**2 + m - m**k = 0.
-1, 0, 1
Let w = -2899437 - -3392342221/1170. Let h = w - -1/234. What is m in 0*m**2 - 2/5*m + 0*m**4 - 2/5*m**5 + 0 + h*m**3 = 0?
-1, 0, 1
Let o = -3569/4 + 161401/180. Let z = -21/5 + o. What is l in -2/3*l - 4/9 - z*l**2 = 0?
-2, -1
Let f(n) be the third derivative of 0*n - 1/40*n**5 + 0 + 0*n**6 + 1/280*n**7 + 0*n**4 + 3*n**2 + 1/8*n**3. Factor f(l).
3*(l - 1)**2*(l + 1)**2/4
Factor -o**3 - 23*o**2 + 0*o**3 - 26*o**2 - 7*o - 3 + 44*o**2.
-(o + 1)**2*(o + 3)
Let q(w) be the second derivative of 0 - w + 1/6*w**3 - w**2 + 1/12*w**4. Find y, given that q(y) = 0.
-2, 1
Let u(v) be the first derivative of v**8/672 - v**7/420 - v**6/120 - 3*v**2/2 - 4. Let g(p) be the second derivative of u(p). Suppose g(q) = 0. What is q?
-1, 0, 2
Suppose 3*j - 9 = -5*i + 18, 0 = -i + 5*j + 11. Let k be ((-5)/(-15))/(7/i). Factor -2/7*f**2 + k + 0*f.
-2*(f - 1)*(f + 1)/7
Suppose 2*x + x + 3 = 0. Let y be (2 - 2)*x/2. Suppose 2*l - 3*l + y*l + l**2 = 0. Calculate l.
0, 1
Let c(t) be the first derivative of 2*t**3/39 - t**2/13 + 14. Factor c(u).
2*u*(u - 1)/13
Let o be 14/6 - (-20)/30. Let 0 + 0 - 12*u**2 - 12*u - 2*u**o - u**3 = 0. What is u?
-2, 0
Let s be (-17)/(-15) - 5/75*-3. Factor -2/3*w + s*w**2 - 2/3*w**3 + 0.
-2*w*(w - 1)**2/3
Let t(w) = -w + 16. Let r be t(12). Factor -7*x**3 + 16*x + 8*x**4 - 7*x**3 + r*x**5 - 16*x**2 + 2*x**3.
4*x*(x - 1)**2*(x + 2)**2
Let c be (0 + 4 - 2)/2. Let m be -2 + ((-24)/(-9))/c. Factor 8/3*z**3 - 4*z**2 + 8/3*z - m*z**4 - 2/3.
-2*(z - 1)**4/3
Factor -2/9*o**4 + 0 + 0*o + 0*o**2 + 4/9*o**3.
-2*o**3*(o - 2)/9
Let x = 33 - 28. Let c(b) be the third derivative of 0*b + 0 + 0*b**4 + 1/60*b**x - b**2 - 1/120*b**6 + 0*b**3. Suppose c(v) = 0. Calculate v.
0, 1
Factor -1/9*z**3 + 0*z - 4/9*z**2 + 0.
-z**2*(z + 4)/9
Let z = 4/3 + -1. Find w, given that z*w**2 - 1/3*w - 2/3 = 0.
-1, 2
Let v = -71 + 73. What is k in 0*k + 2/5*k**v + 0 = 0?
0
Let y = -621 + 3113/5. Factor 4/5*f**4 + 2/5*f + 0 + 2*f**3 + y*f**2.
2*f*(f + 1)**2*(2*f + 1)/5
Let x(b) be the first derivative of 0*b + 0*b**3 + 2 - 1/5*b**4 + 0*b**2. Determine f so that x(f) = 0.
0
Let o(p) be the first derivative of -p**4/4 + 2*p**3 - 6*p**2 - 5*p + 4. Let y(i) be the first derivative of o(i). Factor y(b).
-3*(b - 2)**2
Factor 3/5*g**4 + 27/5*g**2 + 0 - 12/5*g - 18/5*g**3.
3*g*(g - 4)*(g - 1)**2/5
Let b(u) = -2*u**4 - 3*u**3 + 4*u. Let o(p) = -p**4 - p**2 + p. Let w(m) = b(m) - o(m). Solve w(j) = 0.
-3, -1, 0, 1
Let i(g) be the first derivative of -3*g**5/5 + 3*g**4/4 + 6*g**3 + 36. Solve i(h) = 0 for h.
-2, 0, 3
Determine i, g