he second derivative of g**5/40 - g**3/4 - g**2 + g. Let d(k) be the first derivative of o(k). Factor d(q).
3*(q - 1)*(q + 1)/2
Let m(g) be the first derivative of -1 + 1/9*g**3 - 1/6*g**2 - 2/3*g. Solve m(s) = 0.
-1, 2
Factor 3*c + 9/2*c**2 + 3/4*c**4 + 3/4 + 3*c**3.
3*(c + 1)**4/4
Let w(z) be the third derivative of -1/90*z**5 + 5*z**2 - 1/36*z**4 + 0 + 0*z**3 + 0*z. Let w(d) = 0. What is d?
-1, 0
Determine q so that -4*q - q**2 + 2*q - 4 - 2*q = 0.
-2
Let a be 1/(2/(-3) - (-133)/42). Suppose -o - 2 = -2*o. Determine f so that 0 - 2/5*f**o + a*f = 0.
0, 1
Let c(f) = 3*f - 12. Let m be c(5). Let -m*w**3 - 3*w + w**2 + 5*w**2 + w - w = 0. What is w?
0, 1
Let f be (37/(-11))/(2/(-34)). Let t = -57 + f. Factor -2/11 + 0*k + 4/11*k**2 - t*k**4 + 0*k**3.
-2*(k - 1)**2*(k + 1)**2/11
Let g = 1/3 + 7/15. Suppose 0*s + 0*s**2 - 4/5*s**4 + 0 + g*s**3 = 0. What is s?
0, 1
Let d = 4 + -2. Factor 5*m + 2*m**2 - m**d - 3*m - m.
m*(m + 1)
Let y(x) be the third derivative of x**5/210 - x**4/42 - x**3/7 - 2*x**2 - 28*x. Let y(q) = 0. What is q?
-1, 3
Let k(p) be the third derivative of -p**6/48 + p**5/8 + 5*p**4/48 - 5*p**3/4 - 9*p**2. Factor k(m).
-5*(m - 3)*(m - 1)*(m + 1)/2
Factor -4*h**2 - 32*h**3 + 48*h + 2 + 20*h**2 - 34*h.
-2*(h - 1)*(4*h + 1)**2
Let v = 55/3 + -53/3. Let s be (1/(-4)*2)/((-3)/20). Find k such that -2/3*k**4 - s*k**3 + 16/3*k + v*k**5 + 8/3 + 2/3*k**2 = 0.
-1, 2
Suppose 0 = 6*t - t - 15. Factor 4*l**4 + 0*l + t*l**3 + l + 5*l**2 - 2*l**2 - 3*l**4.
l*(l + 1)**3
Let m(t) = 2*t**2 + 4*t + 3. Let o be m(-2). Factor 1/3*w**o + 1/3*w - 2/3*w**2 + 0.
w*(w - 1)**2/3
Factor -v + 1/2*v**3 - 1/4*v**4 - 1 + 3/4*v**2.
-(v - 2)**2*(v + 1)**2/4
Let y(b) be the second derivative of -b**7/42 - 2*b**6/15 - 3*b**5/10 - b**4/3 - b**3/6 + 7*b. Factor y(p).
-p*(p + 1)**4
Let y(m) be the third derivative of 4*m**7/1365 - m**6/39 + 29*m**5/390 - 4*m**4/39 + m**3/13 + 16*m**2. Find u, given that y(u) = 0.
1/2, 1, 3
Suppose 2*o - 9 = 3. Suppose 2*f = -f - o, -4*f - 11 = -q. Suppose -1/4*g**2 + 1/4*g**4 + 0 - 1/4*g + 1/4*g**q = 0. What is g?
-1, 0, 1
Let h(n) be the first derivative of -2*n**3/21 - 4*n**2/7 - 8*n/7 + 13. Factor h(j).
-2*(j + 2)**2/7
Determine y, given that 0 - y**3 - 7/4*y**2 - 3/4*y = 0.
-1, -3/4, 0
Let v(i) be the first derivative of -3*i**4/4 + 2*i**3 + 9*i**2/2 - 3. Solve v(n) = 0 for n.
-1, 0, 3
Let m = -122 - -1221/10. Let x(q) be the second derivative of m*q**5 - 1/15*q**6 + 0 + 3*q + 1/6*q**4 + 0*q**2 - 1/3*q**3. Factor x(c).
-2*c*(c - 1)**2*(c + 1)
What is j in -j - 5 + 1069*j**2 + 3 - 1068*j**2 = 0?
-1, 2
Let f = 73/154 + 1/14. Factor f*d + 4/11 + 2/11*d**2.
2*(d + 1)*(d + 2)/11
Let w be 3 - -8*1299/(-15). Let z = -687 - w. Factor -z*j**3 + 24/5*j**2 - 6/5*j - 4/5.
-2*(j - 1)**2*(7*j + 2)/5
Let k be 4/14 + 33/7. Suppose 3*u**3 - k*u**3 + 2*u**2 - 2*u**5 + 4*u**3 - 2*u**4 = 0. Calculate u.
-1, 0, 1
Let c be 3/(3 - 0)*2. Factor 0 + 2/5*x**c - 2/5*x.
2*x*(x - 1)/5
Let w(l) be the third derivative of l**8/10080 + l**7/840 + l**6/180 + l**5/20 + 4*l**2. Let n(m) be the third derivative of w(m). What is d in n(d) = 0?
-2, -1
Suppose 4/7 + 0*q - 4/7*q**2 = 0. What is q?
-1, 1
Let m(b) = -b + 24*b**2 + 28*b**4 + 0*b + 13*b + 20*b**3. Let r(a) = -a**4 + a**3 - a**2 - a. Let g(v) = -m(v) - 10*r(v). Factor g(u).
-2*u*(u + 1)*(3*u + 1)**2
Suppose -4*o + 30 = 10. Let g(y) be the third derivative of 0*y**3 + 0*y + 3*y**2 + 0 + 1/150*y**o + 1/30*y**4. Factor g(d).
2*d*(d + 2)/5
Let s(u) = -u + 0*u**2 + 1 + u**2 - u. Let o be s(-2). Determine b so that 5 + b**2 + 6*b**2 - 3 - o*b = 0.
2/7, 1
Suppose -3*p + 5 + 1 = 0, -25 = -3*u - 5*p. Let n(d) be the third derivative of 0 + 1/90*d**u + 0*d**3 + 2*d**2 - 1/360*d**6 + 0*d - 1/72*d**4. Factor n(a).
-a*(a - 1)**2/3
Let v(c) = -c**3. Let k(u) = -2*u**4 - 3*u**3 + 2*u**2 - 6*u. Let y(r) = -2*k(r) + 18*v(r). Factor y(q).
4*q*(q - 3)*(q - 1)*(q + 1)
Suppose -z + 0*z = -2. What is j in j**3 - z - 5*j + 2*j + 0*j**3 = 0?
-1, 2
Let n(h) = -h**4 + 1. Let c(p) = 3*p**4 - 2*p**3 - 7*p**2 + 20*p - 14. Let j(m) = -c(m) - 2*n(m). Factor j(r).
-(r - 2)**2*(r - 1)*(r + 3)
Let h(i) be the third derivative of -i**6/40 + i**5/20 + 5*i**4/8 + 3*i**3/2 + 8*i**2. Factor h(k).
-3*(k - 3)*(k + 1)**2
Let x(d) = -d**2 + d - 1. Let l(o) = -12*o**2 + 24*o - 24. Let w(a) = -l(a) + 8*x(a). Suppose w(g) = 0. Calculate g.
2
Let c(b) be the second derivative of -9*b**5/100 + b**4/5 + b**3/10 - 3*b**2/5 - 5*b. Solve c(l) = 0 for l.
-2/3, 1
Let w(k) be the third derivative of 0 - 1/336*k**8 + 0*k**3 + 0*k**5 + 0*k**4 + 0*k + 3*k**2 - 1/30*k**6 + 2/105*k**7. Factor w(y).
-y**3*(y - 2)**2
Suppose -2*v - 10 = -s - 3*s, 5*v = -s - 3. Let g(x) be the first derivative of 1 + 0*x**s + 3/4*x**4 + 2/3*x**3 + 0*x + 1/5*x**5. Factor g(k).
k**2*(k + 1)*(k + 2)
Solve 6*n**4 - 3*n**4 + 22*n - 28*n + 15*n**3 - 3*n**2 - 9*n**5 = 0.
-1, -2/3, 0, 1
Suppose -3 + 1 = -i. Suppose 12 = i*o + 2*o. Suppose 2*b**o + 3*b**2 + 4*b**3 - 5*b**2 = 0. What is b?
0, 1/3
Suppose 4*g + v = 3*v - 66, 5*g + 3*v = -55. Let a = -9 - g. Factor 2*x**a + 0*x**4 + 3*x**3 - x**3 + 4*x**4.
2*x**3*(x + 1)**2
Suppose -3*n - 12 = 0, a - 5 = 3*n + 9. Let z(j) be the third derivative of 0*j**3 + 0 + 0*j + 1/48*j**4 - 1/120*j**5 - j**a. Factor z(c).
-c*(c - 1)/2
Let n = -10537/18 + 585. Let y = n - -95/36. Factor 2 + y*l**3 + 7*l + 15/2*l**2.
(l + 2)*(3*l + 2)**2/4
Let q(a) be the third derivative of a**8/756 - a**7/945 - a**6/90 - a**5/270 + a**4/54 + 7*a**2. Determine d so that q(d) = 0.
-1, 0, 1/2, 2
Suppose 12*t = 21*t - 36. Let c(j) be the second derivative of 0 + 13/30*j**t - 4/5*j**2 + 1/10*j**5 + j + 4/15*j**3. Factor c(g).
2*(g + 1)*(g + 2)*(5*g - 2)/5
Let y = 159/668 - -2/167. Factor -y*l**4 + 0*l**3 + 1/4*l**5 + 0 + 0*l**2 + 0*l.
l**4*(l - 1)/4
Let t(p) be the first derivative of p**6/36 - p**5/15 + p**3/9 - p**2/12 + 14. Factor t(l).
l*(l - 1)**3*(l + 1)/6
Let x(g) = g. Let f(p) = 2*p**3 + 6*p**2 - p. Let o(d) = -2*f(d) - 10*x(d). Factor o(z).
-4*z*(z + 1)*(z + 2)
Let z(s) = -s**3 - 13*s**2 + 15*s + 17. Let x be z(-14). Suppose -k + 0*k + 3 = 0. Factor 3*q**2 + 9*q**4 - k*q**2 - 12*q**2 - x*q**5.
-3*q**2*(q - 2)**2*(q + 1)
Let l(m) be the second derivative of -m**4/42 + m**3/21 - 15*m. Suppose l(q) = 0. Calculate q.
0, 1
Let y(x) be the second derivative of 0*x**3 + 0*x**2 - 3/5*x**5 - 1/3*x**4 + x + 0. Solve y(b) = 0.
-1/3, 0
Let i(m) be the second derivative of -m**7/105 - m**6/60 - m**2 + 3*m. Let d(p) be the first derivative of i(p). What is w in d(w) = 0?
-1, 0
Factor -h**3 - h**2 - h - 7*h - 3*h**2 + 4*h.
-h*(h + 2)**2
Let a(i) be the first derivative of -i**6/600 - i**5/300 + i**4/60 + 5*i**2/2 - 8. Let l(z) be the second derivative of a(z). Factor l(y).
-y*(y - 1)*(y + 2)/5
Let j(u) = u**2 - 3*u - 2*u**2 + 8*u - 1. Let o be j(4). What is p in 5*p**2 - 5*p**4 - 3*p**2 + 2*p - 10*p**o + 11*p**4 = 0?
-1/3, 0, 1
Suppose 5*g + 5*r = -5, 0*g + 4*g + 3 = -3*r. Suppose -4*h - 4*z + 11 + 5 = g, -z - 8 = -5*h. Factor -5*f**h + 2*f - 1 + 3*f**2 + f**2.
-(f - 1)**2
Let k(a) be the third derivative of -a**7/315 + a**6/90 - a**5/90 - 5*a**2. Solve k(i) = 0 for i.
0, 1
Let p be (-46)/(-40) + 2/(-5). Let z = -166 + 667/4. Factor -p*i - z*i**2 - 1/4 - 1/4*i**3.
-(i + 1)**3/4
Suppose -8*c + 3*c = -25. Suppose c*w - 2 = 3. Find l such that l + 2*l**3 - 3*l**3 - 1 - w + 2*l**2 = 0.
-1, 1, 2
Suppose -5*n + 25 = 6*w - 9*w, 2*n = -4*w - 16. Find p such that 0 - 1/4*p**3 - 1/2*p + 3/4*p**n = 0.
0, 1, 2
Let n be (-117)/(-42) - 0 - 4/14. Suppose -3/4*t**4 + 3/2*t - 3*t**2 - 1/4 + n*t**3 = 0. Calculate t.
1/3, 1
Let u(g) be the second derivative of -g**5/40 - g**4/24 - 3*g. Factor u(m).
-m**2*(m + 1)/2
Let v(d) = -d + 13. Let j be v(10). Factor -49*h**2 - j*h**3 + 50*h**2 + 2*h**3.
-h**2*(h - 1)
Let o(h) = h + 10. Let u be o(-10). Let b(a) = -a**3 + a**2. Let c be b(u). Factor -2/9*f**3 - 2/9*f + 4/9*f**2 + c.
-2*f*(f - 1)**2/9
Let s(v) be the second derivative of v**10/105840 - v**9/8820 + v**8/1960 - 2*v**7/2205 + v**4/6 - v. Let r(o) be the third derivative of s(o). Factor r(w).
2*w**2*(w - 2)**3/7
Let n(c) be the first derivative of -c**5/10 - c**4/4 + c**3/2 + c**2 - 2*c + 41. Factor n(v).
-(v - 1)**2*(v + 2)**2/2
Let k(a) = a**3 + 7*a**2 + 5*a - 1. Let t be k(-1). Factor 16/5*b**2 + 