, 2
Let p(f) = 4*f. Let w be p(1). Determine z, given that 4*z**5 + 6*z**3 - 6*z**4 - 5*z**4 - z**2 + z**4 + z**w = 0.
0, 1/4, 1
Let f(p) be the second derivative of 3/40*p**5 + 1/28*p**7 + 0*p**4 + 0*p**2 - p + 1/10*p**6 + 0 + 0*p**3. Determine j, given that f(j) = 0.
-1, 0
Let v = -1 - -5. Let u(w) be the second derivative of 0*w**2 - 4/165*w**6 - 1/231*w**7 + 0 - 2*w + 0*w**3 - 1/33*w**v - 1/22*w**5. Factor u(y).
-2*y**2*(y + 1)**2*(y + 2)/11
Let k be (-39)/(-52)*(-8)/(-3). Factor 4*m**k - 3*m + 2/3 - 5/3*m**3.
-(m - 1)**2*(5*m - 2)/3
Let p = 45 + -45. Let y(j) be the first derivative of -1/36*j**6 + p*j**5 - 2 - 1/3*j + 1/9*j**3 + 1/6*j**4 - 1/4*j**2. Factor y(v).
-(v - 2)*(v - 1)*(v + 1)**3/6
Suppose -5*a + 3*h = -14, 2*a - 5*h - 2 = -a. Let v be (0 - a) + (-5 - -11). Find t, given that 8/9*t - 10/9*t**3 + 4/3*t**v + 2/9*t**4 - 16/9 = 0.
-1, 2
Let r be 12 + -15 + (-16)/(-2). Let o(y) be the first derivative of 1/12*y**3 + 3 + 0*y**2 - 1/24*y**6 - 1/20*y**r + 1/16*y**4 + 0*y. Let o(m) = 0. Calculate m.
-1, 0, 1
Let q be 22/15 + ((-234)/(-27))/(-13). Factor -o**4 - q*o**2 + 0*o + 0 - 1/5*o**5 - 8/5*o**3.
-o**2*(o + 1)*(o + 2)**2/5
Suppose 20 = -2*t + 7*t. Determine l so that -6*l**3 + 17 - 17 + 2*l**2 + 4*l**t = 0.
0, 1/2, 1
Let p(h) = -h**4 - 2*h**3 + 9*h**2 + 8*h + 2. Let r(c) = -15*c**4 - 33*c**3 + 144*c**2 + 129*c + 33. Let f(s) = 33*p(s) - 2*r(s). Factor f(u).
-3*u*(u - 2)*(u + 1)**2
Let d(y) be the second derivative of y**7/28 + 3*y**6/20 + 3*y**5/40 - 3*y**4/8 - y**3/2 - y. Let d(p) = 0. What is p?
-2, -1, 0, 1
Let p be 30*(-3)/(-30)*4. Suppose -5*s + p + 3 = 0. Determine r, given that 0*r**s - 4*r + r**3 + 0*r**3 + 3*r = 0.
-1, 0, 1
Let y = 336 + -1006/3. Factor 1/3 + 1/3*l**2 - y*l.
(l - 1)**2/3
Let a(d) be the first derivative of -d**5/15 + d**4/3 + 2*d**2 + 10. Let l(m) be the second derivative of a(m). What is i in l(i) = 0?
0, 2
Let l be (-110)/33*9/(-5). Let c(g) be the second derivative of 1/90*g**l + 0 - 1/30*g**5 + g + 0*g**3 + 0*g**2 + 1/36*g**4. Let c(t) = 0. Calculate t.
0, 1
Let p = 3 - -2. Suppose 0 = 3*u - 8*u + q + 16, -p*q - 8 = -u. Factor -2*g**3 - 2*g**2 + 3*g**2 + 2*g**3 - 1 - g**u + g.
-(g - 1)**2*(g + 1)
Let k(h) be the first derivative of -h**6/60 - h**5/30 + h**4/6 + h**2/2 + 1. Let j(p) be the second derivative of k(p). Determine f, given that j(f) = 0.
-2, 0, 1
Let m = -18 + 20. Suppose 0*i = -2*r - m*i - 4, -3*r + 14 = -i. Factor 2/9*g**2 - 2/9*g**4 + 4/9*g + 0 - 4/9*g**r.
-2*g*(g - 1)*(g + 1)*(g + 2)/9
Let q(u) = u**3 - 2*u**2 + u. Let n be q(1). Solve -a**3 - 2*a + 4*a - 4*a + 3*a**2 + n*a**2 = 0 for a.
0, 1, 2
Let l be 1 - (3/3 - 3). Suppose 8 = l*y + y. Find f, given that 2*f - f**2 + 2*f**y - f + 0*f**2 = 0.
-1, 0
Suppose -4*g + 2*m + 3 = 13, 0 = 5*g - 5*m + 25. Determine j so that g - 2/11*j**3 - 4/11*j + 6/11*j**2 = 0.
0, 1, 2
Suppose 69 = 3*z - 111. Let a be (16/z)/((-4)/(-10)). Factor 0 + 0*t**3 + 0*t + a*t**4 + 0*t**2.
2*t**4/3
Let i be ((-24)/14)/(-3) - (-24)/(-140). Factor 1/5*j**2 - i*j + 1/5.
(j - 1)**2/5
Factor 4*g**2 - 7*g + 3*g**2 - 4*g**2 - 5*g.
3*g*(g - 4)
Let w(j) be the third derivative of 4*j**2 + 0 + 0*j**3 + 1/15*j**5 + 0*j - 1/24*j**4. What is v in w(v) = 0?
0, 1/4
Let x(h) = h**3 - 12*h**2 - 2. Let r be x(12). Let i be 1 + 0 + -3 - r. Suppose i*f**2 - 1 + 1 + 2*f**2 - 2 = 0. Calculate f.
-1, 1
Let i(d) be the first derivative of 35*d**4 - 22*d - 14*d**5 + 14*d + 5 + 16*d - 4*d**2 + 2*d**4 - 26*d**3. Suppose i(k) = 0. What is k?
-2/7, 2/5, 1
Factor -2/3*w + 1/6*w**3 + 0*w**2 + 0.
w*(w - 2)*(w + 2)/6
Let p(v) be the third derivative of 1/20*v**6 + 9*v**2 + 1/2*v**3 - 1/70*v**7 + 0*v + 0 - 1/4*v**4 + 0*v**5. Solve p(d) = 0.
-1, 1
Find y, given that 2/3 + 3/2*y + 1/6*y**3 + y**2 = 0.
-4, -1
Let a(g) = -4*g**3 + 5*g**2 + 4*g - 2. Let j = -7 - -12. Let z(d) = 7*d**3 - 9*d**2 - 7*d + 4. Let n(m) = j*a(m) + 3*z(m). Factor n(r).
(r - 2)*(r - 1)*(r + 1)
Let c(z) be the third derivative of -5*z**6/24 - z**5/3 + 35*z**4/24 + 5*z**3 - 16*z**2. Factor c(p).
-5*(p + 1)**2*(5*p - 6)
Let s(i) be the second derivative of i**8/1512 + i**7/945 - i**2/2 + i. Let q(k) be the first derivative of s(k). Suppose q(w) = 0. Calculate w.
-1, 0
Let d be 2/(-6) + (-35)/(-42). Suppose -21*m = -19*m - 8. Let -d*g**m + 0*g + 0*g**3 + g**2 - 1/2 = 0. What is g?
-1, 1
Let b(a) be the second derivative of a**4/36 + 4*a**3/9 - 3*a**2/2 + 23*a. Solve b(s) = 0.
-9, 1
Suppose 0 = -3*y + 3 + 3. Let b be (-4)/3*-3 + -2. Factor -b*r**2 + 2*r**y + 3*r**4 - 6*r**2 + 3.
3*(r - 1)**2*(r + 1)**2
Let h be (-45)/81*8/(-20). Factor -h*w**2 - 2/9*w**3 + 4/9*w + 0.
-2*w*(w - 1)*(w + 2)/9
Let d = 1 - -4. Suppose -d*i = -4*i - 2. Solve 3 + 2*v**3 - 3 - i*v**2 = 0 for v.
0, 1
Factor 10*n**4 + 176*n + 5*n**2 - 5*n**3 - 10*n**3 - 176*n.
5*n**2*(n - 1)*(2*n - 1)
What is v in 38/11*v**2 + 0*v + 30/11*v**3 - 8/11 = 0?
-1, -2/3, 2/5
Suppose -u + 10 = 2*g + u, 0 = -2*g - 5*u + 13. Suppose -p + 2*q = 3 + 1, -p + q = 0. Let 3*w**3 - 2*w**3 + p*w**2 - w**2 - w - w**g - 2*w**2 = 0. What is w?
-1, 0, 1
Let h(k) = -k**2 - 2*k + 2. Let o be h(-4). Let l(g) = 11*g**3 - 6*g**2 + 6*g + 6. Let j(b) = -2*b**3 + b**2 - b - 1. Let x(z) = o*l(z) - 34*j(z). Factor x(i).
2*(i - 1)*(i + 1)**2
Let z(u) be the third derivative of -u**7/1260 + u**6/120 - u**5/30 + u**4/3 - 4*u**2. Let d(i) be the second derivative of z(i). Solve d(b) = 0 for b.
1, 2
Let o be (-10)/(-90) - (-6)/27. Factor 2/3*a - 1/3 - o*a**2.
-(a - 1)**2/3
Let n(v) be the first derivative of -v**6/2 + 3*v**5 - 15*v**4/2 + 10*v**3 - 15*v**2/2 + 3*v - 8. Find r such that n(r) = 0.
1
Factor -4/3*i**4 + 8/3*i**2 + 2/3*i**5 + 8/3*i - 2*i**3 + 0.
2*i*(i - 2)**2*(i + 1)**2/3
Let c(n) be the third derivative of n**6/120 - n**5/60 - 2*n**2. Factor c(p).
p**2*(p - 1)
Let i(s) be the first derivative of -81*s**4 + 120*s**3 - 56*s**2 + 32*s/3 - 7. Let i(x) = 0. Calculate x.
2/9, 2/3
Let f(h) be the first derivative of h**5/5 - h**4/2 - h**3/3 + h**2 - 26. Suppose f(m) = 0. Calculate m.
-1, 0, 1, 2
Let x = 5 + -3. Suppose -4*m - m = 2*c - 9, -x*m - 3*c = -8. Factor u**3 - m - u**2 + u**3 - 3*u**5 - 5*u**4 + 7*u**2 + u.
-(u - 1)*(u + 1)**3*(3*u - 1)
Let z(t) be the second derivative of 2/21*t**3 + 0 + 0*t**2 + 1/14*t**4 + 4*t. Factor z(g).
2*g*(3*g + 2)/7
Let a(z) = -z**2 + 9*z - 4. Let k be a(9). Let o be (3 + k)/(0 - 4). Suppose u + 2*u**5 - u**4 + o - 5/2*u**3 + 1/4*u**2 = 0. What is u?
-1/2, 1
Factor 0 + 4/3*w + 0*w**2 - 1/3*w**3.
-w*(w - 2)*(w + 2)/3
Let a = 14 - 70. Let l = a + 225/4. Let 0 + 1/2*h**3 - 1/4*h**2 - l*h**4 + 0*h = 0. What is h?
0, 1
Suppose 1/4 + 1/4*h - 1/2*h**2 = 0. What is h?
-1/2, 1
Let t(b) be the third derivative of 0 - 1/630*b**7 - 1/18*b**3 + 0*b**4 + 1/90*b**5 + 2*b**2 + 0*b**6 + 0*b. Determine z so that t(z) = 0.
-1, 1
Let f(k) = -k**3 + 8*k**2 + 8. Let n be f(8). Let m be (7/70)/(1/n). Factor -m - 2/5*l + 2/5*l**2.
2*(l - 2)*(l + 1)/5
Let p be (-156)/(-1482) - 49/(-76). Factor -1/4*x**2 - 1/2 + p*x.
-(x - 2)*(x - 1)/4
Let a(d) be the second derivative of -d**7/1120 + d**6/240 - d**5/160 + 2*d**3/3 + 2*d. Let q(c) be the second derivative of a(c). Factor q(j).
-3*j*(j - 1)**2/4
Let s(m) = -2*m**3 - 3*m**2 + m + 2. Let q be s(-2). Find f, given that 17*f**2 - 9*f**5 + 6*f + 3*f**3 - 2*f**2 - 36*f**4 + 21*f**q = 0.
-1, -2/3, 0, 1
Let j be 4/(-20) + (-505)/(-25). Let h be 93/105 - 12/j. Factor -4/7 - 8/7*z**2 + 10/7*z + h*z**3.
2*(z - 2)*(z - 1)**2/7
Let c(g) be the third derivative of g**7/15 - g**6/12 - g**5/15 + 3*g**2. Suppose c(q) = 0. Calculate q.
-2/7, 0, 1
Let q = -1093/3 + 365. Suppose q*c**2 - 4/3*c + 2/3 = 0. Calculate c.
1
Let m(b) = -b**2 - 1. Let k(a) be the first derivative of -a**3/3 - 2*a - 2. Let v(j) = 3*k(j) - 6*m(j). Solve v(f) = 0 for f.
0
Let c(b) be the third derivative of 0*b**4 + 1/180*b**6 + 0 + 0*b**3 + 0*b**5 + b**2 + 0*b. Find a such that c(a) = 0.
0
Suppose 1 = -2*f - 3. Let h be (8/(-12))/(f/6). Factor -3*c**4 - c**3 - 2*c**3 - c**h + 8*c**5 - 9*c**5.
-c**2*(c + 1)**3
Suppose 4*t - 3*s - 12 - 2 = 0, 4*s + 2 = -3*t. Suppose -12 = -c - t*c. Factor 1/3*h**2 + 0 + 0*h + 0*h**3 - 1/3*h**c.
-h**2*(h - 1)*(h + 1)/3
Let z be ((-8)/(-140)*-1)/((-4)/40). Let 0 + 10/7*r**3 + z*r - 2*r**2 = 0. Calculate r.
0, 2/5, 1
Determine u, given that -13 - 3*u - 9*u + 4