-8)/(-32) + (-23)/(-4). Suppose 3*y - s = -0. Factor -1/2 + 1/4*r + 1/4*r**y.
(r - 1)*(r + 2)/4
Let m be 58/4 - 6/(-12). Suppose 9*y - m = 4*y. What is c in 0*c - 3*c**y + c + c**3 + 3*c**3 + 2*c**2 = 0?
-1, 0
Let l be -3*-2*1/3. Suppose l*n - 4*n = 2*z - 8, z - n = 0. Let t + 4*t**z - 3*t**3 - 2*t - t + t**3 = 0. Calculate t.
0, 1
Let g(a) be the second derivative of -a**6/105 + 3*a**5/70 + a**4/42 - a**3/7 + 12*a. Factor g(v).
-2*v*(v - 3)*(v - 1)*(v + 1)/7
Let b(g) be the second derivative of 0 - 1/6*g**3 + 1/12*g**4 - 4*g - g**2. Factor b(q).
(q - 2)*(q + 1)
Factor 5*i**3 - 4*i**4 + 3*i**4 - 6*i**3.
-i**3*(i + 1)
Let p = -101519/120 + 846. Let d(u) be the third derivative of 0*u + 0*u**3 + 1/210*u**7 + 0 + 0*u**4 + p*u**6 + 0*u**5 - 2*u**2. Let d(f) = 0. What is f?
-1, 0
Let g(i) = -3*i - 2. Let u be g(-2). Solve -14*w**3 - 6*w**2 - w + w + 4*w**u + 2*w**2 + 14*w**5 = 0.
-1, -2/7, 0, 1
Let r(n) be the first derivative of -n**5/20 + n**4/4 - n**3/2 - 9*n**2/2 + 4. Let y(h) be the second derivative of r(h). Determine b, given that y(b) = 0.
1
Let o(j) be the third derivative of -j**6/160 - 3*j**5/16 - 3*j**4/2 + 8*j**3 + 3*j**2 - 3*j. Factor o(r).
-3*(r - 1)*(r + 8)**2/4
Suppose -6*a = -3*a. Determine x, given that -2*x**2 + a - 2 - 4*x + 0 = 0.
-1
Let t = 17 - 12. Suppose -2*x + 4*d = x - 18, t*d + 21 = 3*x. Determine g so that 4*g - g**2 - g**x + 0*g**2 = 0.
0, 2
Suppose 0*s = -2*s + 4. Suppose -s*d = -2 - 2. Factor -t**3 - 1 + d + 0 + t - t**2.
-(t - 1)*(t + 1)**2
What is v in -4/3 + 50/3*v**2 + 10/3*v = 0?
-2/5, 1/5
Let a = -2413/9 + 269. Suppose 0*t + 2/3*t**2 - a + 2/9*t**3 = 0. What is t?
-2, 1
Let d(y) be the second derivative of 0*y**5 + 0*y**2 - 4*y - 1/90*y**6 + 1/36*y**4 + 0*y**3 + 0. Find m, given that d(m) = 0.
-1, 0, 1
Suppose 0*s + 5*s = -5, p + s = 8. Determine f so that 0*f - 7*f**3 + 7*f**2 + 4*f**2 - 11*f**4 - 2*f + p*f**5 = 0.
-1, 0, 2/9, 1
Let 8/7*h**3 - 12/7 - 4/7*h**4 - 8/7*h + 16/7*h**2 = 0. What is h?
-1, 1, 3
Suppose -5*j = 2*s + 54, -3*j + 7 - 55 = -4*s. Let n be ((-2)/j)/((-3)/(-12)). Find t, given that n*t**3 + 0 + 0*t + 1/3*t**4 + 1/3*t**2 = 0.
-1, 0
Factor 1/5 + 1/5*y**4 + 1/5*y**5 + 1/5*y - 2/5*y**2 - 2/5*y**3.
(y - 1)**2*(y + 1)**3/5
Let d be ((12/(-6))/2)/(1/(-3)). Factor 0*n**2 - 1/5*n + 1/5*n**d + 0.
n*(n - 1)*(n + 1)/5
Let g(u) be the second derivative of u**5/30 + u**4/6 - u**3/9 - u**2 - 20*u. Factor g(q).
2*(q - 1)*(q + 1)*(q + 3)/3
Let h(g) be the second derivative of 0 - 1/12*g**4 + 1/20*g**5 + 5*g + 0*g**2 - 1/3*g**3. Factor h(k).
k*(k - 2)*(k + 1)
Let q(i) be the first derivative of -i**5/3 - 5*i**4/4 - 10*i**3/9 - 6. Suppose q(c) = 0. What is c?
-2, -1, 0
Let g(f) be the third derivative of 2/25*f**5 + 2/15*f**3 + 3/20*f**4 + 0 + 1/60*f**6 + 0*f + 3*f**2. Find r such that g(r) = 0.
-1, -2/5
Suppose -6*l + 12 = -3*l. Suppose w = -4*x - 6, -l*w + 3*x - 2 + 16 = 0. Solve 2/9*p**w + 0 + 2/9*p = 0 for p.
-1, 0
Let k = 8 + -2. Let n(q) = -5*q**4 + 10*q**3 + 6*q**2 + 4*q - 5. Let g(u) = u**4 - u**3 + 1. Let d(c) = k*g(c) + n(c). Factor d(t).
(t + 1)**4
Let r be (-1 + (-20)/(-12))*6. Let a be (1/3)/(r/6). Let -a + 0*z + 1/2*z**2 = 0. What is z?
-1, 1
Factor 56*b - 6*b**2 - 53*b + 3*b**4 + 3*b**2 - 3*b**3.
3*b*(b - 1)**2*(b + 1)
Let z be (-5)/(-25)*(-3)/(18/(-20)). Factor 0 + 11/3*i**4 + 3*i**2 + z*i + 5*i**3 + i**5.
i*(i + 1)**3*(3*i + 2)/3
Let w be 2*(-3)/(-3 - 0). Let c = -1 - -5. Suppose 9/4*j**5 + 15/4*j**w - 5/4*j**3 - 1 - 15/4*j**c + 0*j = 0. What is j?
-2/3, 1
Suppose 4*r = p + 9, -1 = -r + 4*p - 10. Let k(j) be the first derivative of 9*j**2 - 4*j - 14/3*j**r - 5. Determine g so that k(g) = 0.
2/7, 1
Let d(o) be the first derivative of o**4/6 - 4*o**3/3 + 4*o**2 - 8*o + 5. Let j(g) be the first derivative of d(g). Factor j(v).
2*(v - 2)**2
Suppose -2 = a - 4. Let j be a/(-4) - 3/(-6). Factor j*l + 0*l**2 + 0 + 1/4*l**4 + 1/2*l**3.
l**3*(l + 2)/4
Let t(m) be the first derivative of -2*m**5/35 + m**4/14 + 2*m**3/21 - m**2/7 - 10. Factor t(j).
-2*j*(j - 1)**2*(j + 1)/7
Factor 2*n**5 + n**5 + 3*n**4 - 6*n**2 + 5 - 6*n**3 + 0 + 3*n - 2.
3*(n - 1)**2*(n + 1)**3
Let o be 21/6 - 6/(-9). Let y = o + -7/2. Determine m so that -y*m - 20/3*m**2 - 22*m**3 + 0 - 80/3*m**4 - 32/3*m**5 = 0.
-1, -1/4, 0
Let l(t) = t**2 + 11*t + 13. Let o be l(-10). What is g in o*g**2 - 4*g**2 + 15*g**3 + 2*g - 24*g**3 + 13*g**4 - 5*g**5 = 0?
-2/5, 0, 1
Let g(f) be the second derivative of -f**5/70 - f**4/14 - 2*f**3/21 - 2*f. Suppose g(n) = 0. Calculate n.
-2, -1, 0
Suppose -4*n = -8, 5*g - 3*g + 5*n - 10 = 0. Let f be 0 + -4 - (-361)/76. Find s, given that -9/4*s**2 - f*s**3 + g - 3/2*s = 0.
-2, -1, 0
Let l(j) = -j + 4. Let c be l(6). Let i be ((-2)/3*6)/c. Let -4 + 0*h + 4*h - 4*h**3 + 2*h**4 + i = 0. What is h?
-1, 1
Let t(u) be the third derivative of -u**8/1344 + u**6/120 - u**5/120 - u**4/32 + u**3/12 + 4*u**2. Factor t(a).
-(a - 1)**3*(a + 1)*(a + 2)/4
Let v be 1*(2 - 1) + 2. Let b be 8/60*10*1/3. Solve -2/9*o - 2/9*o**v + 0 - b*o**2 = 0.
-1, 0
Let n(v) = -v**2 + v - 1. Let h(x) = 2*x**2 + 8*x - 3. Let k(s) = -h(s) + 3*n(s). Solve k(p) = 0.
-1, 0
Let d(s) = s**3 - 13*s**2 + 25*s - 30. Let z be d(11). Let x(b) be the second derivative of 0 - 121/54*b**4 + b - 4/9*b**2 - 44/27*b**z. Factor x(p).
-2*(11*p + 2)**2/9
Let o(j) be the third derivative of -j**5/60 - j**4/3 - 8*j**3/3 + 8*j**2. Determine l, given that o(l) = 0.
-4
Let x = -5963/42 - -142. Let o(p) be the second derivative of 0 + x*p**4 + 4/7*p**2 - p + 4/21*p**3. Let o(h) = 0. Calculate h.
-2
Let t(k) be the third derivative of -1/180*k**5 - 1/1008*k**8 - 1/210*k**7 + k**2 + 0*k**4 + 0*k + 0*k**3 - 1/120*k**6 + 0. Factor t(f).
-f**2*(f + 1)**3/3
Let b(n) be the first derivative of 3/10*n**2 - 2 - 3/20*n**4 + 0*n + 0*n**3. Factor b(j).
-3*j*(j - 1)*(j + 1)/5
Let c = -3 - -3. Let t(r) be the first derivative of 2/3*r**2 - 2/9*r**3 + c*r - 1. Factor t(q).
-2*q*(q - 2)/3
Let s be 6*(-3)/(-9)*1. Let u = 12 + -7. Factor -u*h**s + 3*h + 1 + 3*h**3 + 8*h**2 - 2*h**3.
(h + 1)**3
Let n(a) be the third derivative of 0*a**3 - 2*a**2 + 1/330*a**5 - 1/1155*a**7 - 1/660*a**6 + 0 + 1/132*a**4 + 0*a. Solve n(t) = 0 for t.
-1, 0, 1
Let t(w) be the third derivative of -2/105*w**7 + 2/15*w**6 + 4/3*w**4 + 0*w - 8/15*w**5 + 1/840*w**8 - 32/15*w**3 + 3*w**2 + 0. Determine l so that t(l) = 0.
2
Let q(r) be the third derivative of r**7/2520 + r**6/360 + r**4/24 - 2*r**2. Let v(b) be the second derivative of q(b). Factor v(h).
h*(h + 2)
Suppose -o - 3*b = -14, 0*o + 5*b = -3*o + 50. Let j be (3/2)/(35/o). Let j*u - 2/7 - 6/7*u**2 + 2/7*u**3 = 0. What is u?
1
Let h(m) be the first derivative of m**3/3 + m**2 + 27. Let h(c) = 0. Calculate c.
-2, 0
Factor 2/21*w**4 - 4/21 + 10/21*w - 2/7*w**2 - 2/21*w**3.
2*(w - 1)**3*(w + 2)/21
Let m(l) be the third derivative of l**8/1344 - l**7/840 - l**6/240 + l**5/120 + l**4/96 - l**3/24 + 3*l**2. Suppose m(r) = 0. What is r?
-1, 1
Let q(f) be the second derivative of f**7/70 + 2*f**6/25 + 3*f**5/100 - f**4/2 - 2*f**3/5 + 12*f**2/5 - 6*f. Factor q(y).
3*(y - 1)**2*(y + 2)**3/5
Let x = 553/6 + -92. Let j(k) be the first derivative of 0*k + 1/3*k**3 + k**2 + 3 - 3/4*k**4 + x*k**6 - 1/5*k**5. Factor j(r).
r*(r - 2)*(r - 1)*(r + 1)**2
Let n(q) be the second derivative of 0*q**3 - q**2 + 1/60*q**5 + 0 + 1/24*q**4 - 2*q. Let t(z) be the first derivative of n(z). Factor t(b).
b*(b + 1)
Let g(v) be the third derivative of v**6/180 - v**4/12 - 2*v**3/9 + 5*v**2. Determine c so that g(c) = 0.
-1, 2
Suppose -1 = l, l = -g - 0*g - 6. Let f be (18 + 0)*g/(-15). Determine o so that f + o - 2 - 7*o + 2*o**2 = 0.
1, 2
Suppose -4*l + 2 + 18 = 0. Let j(v) be the second derivative of -2*v - 1/42*v**4 + 0 + 0*v**2 - 1/70*v**l + 0*v**3. Factor j(y).
-2*y**2*(y + 1)/7
Suppose a + 0*a - 2 = 0. Factor 4*w**2 - 4*w**2 + 2*w - 2*w**a.
-2*w*(w - 1)
Let c be (10/6)/(1/3). Find u such that -2*u**5 - 8 + 72*u**3 - 32*u + c*u**4 - 110*u**3 - 50*u**2 - 19*u**4 = 0.
-2, -1
Let d(n) be the third derivative of 1/120*n**5 + 0*n - 1/24*n**4 + 0*n**3 - 2*n**2 + 0 + 1/240*n**6. Determine r, given that d(r) = 0.
-2, 0, 1
Let v(d) be the first derivative of -d**3 + 0*d - 3 + 3/5*d**5 + 3/4*d**4 - 3/2*d**2. Solve v(o) = 0.
-1, 0, 1
Suppose 0 = t + 4*t - 3*l - 30, 2*t = -5*l - 19. Let w(n) 