
Let d(i) be the first derivative of i**6/50 + 3*i**5/100 - i**4/20 - i**3/10 - 5*i + 8. Let v(q) be the first derivative of d(q). Factor v(f).
3*f*(f - 1)*(f + 1)**2/5
Let w(m) be the third derivative of -m**8/20160 + m**7/840 - m**6/80 + m**5/30 - 4*m**2. Let q(p) be the third derivative of w(p). Let q(y) = 0. Calculate y.
3
Let s be ((-3)/5)/(6/(-5)). Suppose -1/2*d**2 + s*d + 1 = 0. What is d?
-1, 2
What is v in -77*v**2 + 79*v**2 - v - 2*v**4 - v**5 + 2*v = 0?
-1, 0, 1
Suppose 0 = -3*f + 6*f - 48. Suppose 0 = l - 5*l + f. Factor -5*h**5 + 2*h**3 - 5*h**l + 2*h**5 + 4*h**4.
-h**3*(h + 1)*(3*h - 2)
Let b = -2/405 + 836/5265. Factor 2/13 + 0*s - b*s**2.
-2*(s - 1)*(s + 1)/13
Let d = 132 + -2639/20. Let m(c) be the third derivative of d*c**4 + 1/350*c**7 + 0 - 1/100*c**6 + 0*c - 2*c**2 + 0*c**5 - 1/10*c**3. Solve m(w) = 0 for w.
-1, 1
Let m(a) = a**2 + 8*a - 15. Let h be m(-9). Let b be 8/(-126) + h/(-21). Determine c, given that -2/9 - 2/9*c + 2/9*c**2 + b*c**3 = 0.
-1, 1
Suppose -v - a + 8 = -2*a, 5*v = -4*a + 4. What is c in -2/11*c**v + 2/11*c**2 + 0 - 2/11*c**3 + 0*c + 2/11*c**5 = 0?
-1, 0, 1
Solve 1/4*b**2 + 0 + 5/4*b = 0 for b.
-5, 0
Let l(r) be the third derivative of r**8/13440 - r**7/1680 + r**6/720 + r**4/8 + 8*r**2. Let j(z) be the second derivative of l(z). Factor j(o).
o*(o - 2)*(o - 1)/2
Let u(s) = 34*s**3 - 2*s**2 + 2*s - 1. Let j be u(1). Factor 4*x**2 + j*x**3 - 17*x + 90*x**4 + 3*x - 40*x**2 + 2*x - 75*x**5.
-3*x*(x - 1)**2*(5*x + 2)**2
Suppose -76*w - 20 = -80*w. Let 4/9*z**3 + 14/9*z**w + 0*z**2 + 0 + 0*z + 2*z**4 = 0. Calculate z.
-1, -2/7, 0
Let w(r) be the third derivative of 0*r - 1/12*r**4 - 5*r**2 + 0*r**3 + 0*r**5 + 0 + 0*r**7 + 1/30*r**6 - 1/168*r**8. Solve w(u) = 0 for u.
-1, 0, 1
Let f(l) = 31*l - 246. Let g be f(8). Let b be (0 + 0)*(-1)/2. Determine h so that 0*h + 1/4*h**3 + 1/4*h**g + b = 0.
-1, 0
Let r(b) be the second derivative of -5*b**4/12 + 5*b**3/2 + 10*b**2 + 9*b. Suppose r(x) = 0. Calculate x.
-1, 4
Factor -4/9*u**3 + 0*u + 2/3*u**2 + 0 - 2/9*u**4.
-2*u**2*(u - 1)*(u + 3)/9
Let q be 3 - 2*(-2 + 1). Let p = 5 - q. What is m in 2/7*m**4 + 0*m + 2/7*m**3 + 0 + p*m**2 = 0?
-1, 0
Let n = 59/204 - 2/51. Factor 1/4*m**2 + 0 + n*m.
m*(m + 1)/4
Let u(s) be the first derivative of s**4/22 + 4*s**3/33 + s**2/11 - 9. Determine j, given that u(j) = 0.
-1, 0
Let h(t) be the second derivative of t**6/165 + t**5/110 - t**4/22 - 5*t**3/33 - 2*t**2/11 + t. Determine p so that h(p) = 0.
-1, 2
Let y(m) be the first derivative of m**6/18 - m**4/2 + 8*m**3/9 - m**2/2 + 15. Factor y(b).
b*(b - 1)**3*(b + 3)/3
Let y = 8 + -15/2. Let h(u) be the second derivative of 3/2*u**2 + 0 + y*u**3 - 1/4*u**4 + u - 3/20*u**5. Find q such that h(q) = 0.
-1, 1
Let n(f) = f**3 + 6*f**2 + 5*f - 9. Let u(g) = 4*g**3 + 19*g**2 + 16*g - 27. Let w(i) = 7*n(i) - 2*u(i). Let y be w(4). Factor -3/5*o**2 + 0 + 3/5*o**y + 0*o.
3*o**2*(o - 1)/5
Let i = 54535/42 - 1301. Let p = 17/6 + i. Factor -2/7*s**5 + 2/7*s**4 - p*s**2 + 0*s + 2/7*s**3 + 0.
-2*s**2*(s - 1)**2*(s + 1)/7
Let n(t) be the first derivative of 3*t**4/20 - t**3/5 - 3*t**2/10 + 3*t/5 + 1. Solve n(c) = 0 for c.
-1, 1
Let l(c) be the third derivative of 9*c**6/40 - 13*c**5/5 + 69*c**4/8 + 9*c**3 - 24*c**2. Suppose l(w) = 0. Calculate w.
-2/9, 3
Let n = -15 - -9. Let w be (4/(-18))/(2/n). Factor -4/3 - w*c + 2/3*c**2.
2*(c - 2)*(c + 1)/3
Suppose -11*y + 9*y = 0. Let j(b) be the second derivative of y*b**2 + 2*b - 1/21*b**3 - 1/42*b**4 + 0. Factor j(t).
-2*t*(t + 1)/7
Let r(g) = -g**3 + 11*g**2 - 5*g - 4. Let b be r(8). Let i be (b/36 - 4)*6. Determine a, given that 2/3 - 4/3*a**2 - 4/3*a**3 + 2/3*a + 2/3*a**5 + i*a**4 = 0.
-1, 1
Suppose 7*d = 56 - 21. Suppose 0*c + 0 + 2*c**4 + 1/2*c**d + 5/2*c**3 + c**2 = 0. What is c?
-2, -1, 0
Factor -55*k - 7*k**3 - k**3 + 40*k**2 + 3*k**3 - 50*k + 90.
-5*(k - 3)**2*(k - 2)
Let o(f) be the first derivative of 6/5*f**2 + 18/5*f + 2/15*f**3 - 1. Factor o(k).
2*(k + 3)**2/5
Let a(m) = -m**2 + m - 1. Let s(i) = -4*i**2 + 6*i - 3. Let t(q) = 3*a(q) - s(q). Factor t(p).
p*(p - 3)
Factor -3*t**2 - t + t + t + 5*t.
-3*t*(t - 2)
Let z(w) be the third derivative of 0*w - 9/20*w**5 - 1/3*w**3 + 0 + w**2 + 13/24*w**4 - 1/30*w**7 + 23/120*w**6. Suppose z(b) = 0. Calculate b.
2/7, 1
Let k be (-1)/((-23)/(-8) - 3). Factor -9*x**2 - 16*x - k + 8 - 12 - 8*x.
-3*(x + 2)*(3*x + 2)
Let h = 787 - 3145/4. Factor h*x**2 - 3/2*x + 3/4.
3*(x - 1)**2/4
Let w be ((-8)/(-1) + -5)/(-3) - -1. Solve w + 3/7*f**2 - 3/7*f**3 + 0*f = 0 for f.
0, 1
Let j = -962 - -962. Let 1/2*n + 1/6*n**2 + j = 0. What is n?
-3, 0
Let b be -5*(0 + 18/15). Let a be 3/b - 7/(-2). Factor 2*y**2 + y**a + 0*y - 2 - y + 0.
(y - 1)*(y + 1)*(y + 2)
Factor -4/9*v**5 + 0 - 8/3*v**3 + 16/9*v**2 + 16/9*v**4 - 4/9*v.
-4*v*(v - 1)**4/9
What is z in -645/8*z**3 + 27/4 - 495/8*z + 1203/8*z**2 + 99/8*z**4 = 0?
2/11, 1/3, 3
Suppose 3*x = -3*x + 18. Let f(r) be the second derivative of -5/24*r**x + 7/48*r**4 + 3*r + 0 - 1/4*r**2. Determine o so that f(o) = 0.
-2/7, 1
Factor u**4 - 8*u**4 + 6*u**4.
-u**4
Let c(s) = 2*s**3 + 30*s**2 + 3*s + 48. Let n be c(-15). Factor -2/11*g**5 + 4/11*g**n - 2/11*g - 2/11 + 4/11*g**2 - 2/11*g**4.
-2*(g - 1)**2*(g + 1)**3/11
Let l(q) = -q**4 + q**3 + q**2 + 13*q + 7. Let f(i) = -4*i - 2. Let r(j) = 14*f(j) + 4*l(j). Find m such that r(m) = 0.
-1, 0, 1
Let t(m) be the first derivative of 1/5*m**5 + 1/3*m**3 + 0*m**2 - 1/2*m**4 + 0*m - 2. Factor t(g).
g**2*(g - 1)**2
Suppose 2*j - 4 = p + 4, 0 = -p - 2*j + 12. Let q = 1 + p. Factor 0*i + 0*i**2 + 0*i**q + 0 + 1/3*i**4.
i**4/3
Let x(t) be the third derivative of -t**6/30 - 2*t**5/15 + t**4/6 + 4*t**3/3 + 21*t**2. Solve x(i) = 0 for i.
-2, -1, 1
Let d = -391 + 2743/7. Factor -4/7*m + d*m**2 - 2/7.
2*(m - 1)*(3*m + 1)/7
Let i(n) be the first derivative of -n**6/360 - n**5/60 - n**3/3 + 1. Let a(d) be the third derivative of i(d). Find j such that a(j) = 0.
-2, 0
Let h(b) = -b**2 + 12*b - 13. Let t be h(10). Let s = t + -4. Find q such that -4*q + 13*q + 54*q**s + 6*q + 21*q**4 + 60*q**2 + 9*q + 3*q**5 = 0.
-2, -1, 0
Let q(x) be the first derivative of x**8/168 + x**7/105 - x**6/60 - x**5/30 + 4*x**2 - 6. Let t(v) be the second derivative of q(v). Factor t(y).
2*y**2*(y - 1)*(y + 1)**2
Suppose 0 = 4*v + 8 - 36. Let z = v + -4. Factor 2*n**2 - z*n + 5*n + 2*n.
2*n*(n + 2)
What is g in -2/3*g**2 - 6 + 20/3*g = 0?
1, 9
Let b(k) be the first derivative of 2/3*k**2 + 0*k - 9 + 1/6*k**4 + 2/3*k**3. Solve b(n) = 0.
-2, -1, 0
Let z = 5 + -8. Let p(c) = c**2 - 7*c + 4. Let k(g) = 4*g**2 - 20*g + 11. Let w(i) = z*k(i) + 8*p(i). Factor w(b).
-(2*b - 1)**2
Determine r so that 0 + 0*r**3 - 1/5*r**5 + 2/5*r**4 - 2/5*r**2 + 1/5*r = 0.
-1, 0, 1
Let r(d) be the first derivative of 4*d**2 - 5 + 0*d - 32/3*d**3 + 5/2*d**4 + 10*d**5. Let r(q) = 0. Calculate q.
-1, 0, 2/5
Let s = -143 + 143. Let a(y) be the third derivative of -81/20*y**5 - 2/3*y**3 + s + 9/4*y**4 + 243/80*y**6 + 0*y + y**2. Factor a(u).
(9*u - 2)**3/2
Let i be ((-5)/((-5)/2))/6. Suppose 10*f = 6*f + 8. Let 4/3 + i*s**f - 4/3*s = 0. What is s?
2
Let h(j) = -j**2 + 4. Let f be h(0). Solve f*k + 2*k**2 - 4*k**2 - 6*k = 0.
-1, 0
Suppose 2*f - 23 = -5*m, -5*f = 4*m - 12 - 20. Suppose -2/9*k**m + 0 - 4/9*k**2 + 0*k = 0. Calculate k.
-2, 0
Let j(p) be the first derivative of 5 + 0*p**2 - 1/9*p**3 + 0*p. Determine s so that j(s) = 0.
0
Let p(h) = 8*h**4 - 8*h**3 + 4*h. Let l(u) = -17*u**4 + 17*u**3 - u**2 - 8*u. Let k(w) = 4*l(w) + 9*p(w). Find n such that k(n) = 0.
-1, 0, 1
Let p be -3 - 33*6/(-54). Factor 2/3*m + p*m**2 + 0.
2*m*(m + 1)/3
Let r(v) = 2*v**2 - 12*v. Let a be r(6). Solve 1/2*c**4 - 1/2*c**3 + 0*c**2 + a + 0*c = 0 for c.
0, 1
Let r = -173 + 89. Let t be (-2)/7 - 80/r. Factor 0 + 2/3*x**4 + t*x**3 + 0*x + 0*x**2 - 4/3*x**5.
-2*x**3*(x - 1)*(2*x + 1)/3
Let m(r) be the third derivative of 1/480*r**6 + 1/96*r**4 + 0 + 0*r - 1/120*r**5 - r**2 + 0*r**3. Factor m(p).
p*(p - 1)**2/4
Let 27/5 + 51/5*l**4 - 6/5*l**5 + 42*l**2 - 156/5*l**3 - 126/5*l = 0. What is l?
1/2, 1, 3
Let x(f) = -4*f**3 - 2. Let c(n) = n**5 - n**4 + n**3 + n**2 + 1. Let w(v) = 4*c(v) + 2*x(v). Let w(o) = 0. What is o?
-1, 0, 1
Let z be (-72)/(-16)*(-4)/6. Let n be z/(-30) + (-4)/(-10). Determine p so that -3/2*p + 3/2*p**4