0
Let r(m) be the first derivative of -3*m**3/4 - 3*m**2/8 + 3*m/2 + 3. Determine q, given that r(q) = 0.
-1, 2/3
Let m(p) be the third derivative of -p**6/20 - p**5/15 - p**4/12 + 2*p**2. Let h(t) = -t**3. Let y(o) = 4*h(o) - m(o). Solve y(u) = 0.
-1, 0
Suppose 7 = 2*b - 1. Suppose -b*r - r = 0. Suppose 0*f + r - 1/3*f**3 - 2/3*f**2 = 0. What is f?
-2, 0
Let x(j) be the second derivative of -j**7/98 + 4*j**6/35 - 15*j**5/28 + 19*j**4/14 - 2*j**3 + 12*j**2/7 - j + 47. Factor x(n).
-3*(n - 2)**3*(n - 1)**2/7
Suppose 0 = -5*q + 3*q + 12. Suppose -w + q*w = 0. Factor -2/5*d + 2/5*d**2 + w.
2*d*(d - 1)/5
Let 2/5 - 6/5*h**2 + 1/5*h = 0. What is h?
-1/2, 2/3
Let x(g) be the third derivative of -g**7/7560 - g**6/2160 + g**4/8 - g**2. Let o(s) be the second derivative of x(s). Factor o(d).
-d*(d + 1)/3
Let u(v) be the second derivative of -v**5/15 - v**4/18 + v**3/9 - 39*v. Determine j, given that u(j) = 0.
-1, 0, 1/2
Let z(f) be the third derivative of f**7/105 - f**5/15 + f**3/3 + 8*f**2. Find x such that z(x) = 0.
-1, 1
What is w in 1/3*w**3 + 0*w - 2/3*w**4 - 1/3*w**5 + 2/3*w**2 + 0 = 0?
-2, -1, 0, 1
Let c(h) = h**3 - 3*h**2 + 2*h - 4. Let s be c(3). Let l be (-788)/(-56) - 13 - (-4)/(-7). Find p such that 0*p**4 + p**3 - l*p**s - 1/4*p**5 + 1/2 - 3/4*p = 0.
-2, -1, 1
Let x(z) be the third derivative of z**8/16800 + z**7/2100 + z**6/600 + z**5/300 + z**4/12 + 2*z**2. Let j(s) be the second derivative of x(s). Factor j(l).
2*(l + 1)**3/5
Find q, given that -2/3*q**3 + 1/3*q + 4/3*q**2 - 2/3*q**4 - 2/3 + 1/3*q**5 = 0.
-1, 1, 2
Let p(b) = -b**2 - 6*b - 4. Let w be p(-2). Let -9*t**3 + 2*t**3 - 8*t**3 + 12*t - w*t**2 - 4*t**4 + 3*t**3 + 8 = 0. Calculate t.
-2, -1, 1
Let k(x) be the first derivative of -x**4 + 0*x - 7 + 0*x**2 + 2/3*x**6 + 0*x**5 + 0*x**3. Solve k(g) = 0.
-1, 0, 1
Let s(v) be the first derivative of 1/12*v**6 + 0*v + 1/2*v**2 - 1/6*v**3 - 8 + 1/10*v**5 - 3/8*v**4. Factor s(m).
m*(m - 1)**2*(m + 1)*(m + 2)/2
Solve -2/7*u**4 - 2/7*u**2 + 0*u + 0 + 4/7*u**3 = 0 for u.
0, 1
Let k be 1/((-129)/63 - -2). Let c be (-4)/(-14) + (-36)/k. Factor -t**2 + t**4 + 0*t**2 + 2*t**3 + 2*t**c.
t**2*(t + 1)**2
Suppose 2*t = -t - h + 14, 2*t + 5*h = 18. Factor 30*f**3 - 42*f**4 + 12*f**5 + 6 - 3*f**5 - 15*f + 12*f**t.
3*(f - 1)**4*(3*f + 2)
Let x(r) be the first derivative of -5*r**3/6 - 5*r**2/4 - 8. Factor x(p).
-5*p*(p + 1)/2
What is c in 1/4*c**4 + 0 + 1/2*c**3 + 0*c + 1/4*c**2 = 0?
-1, 0
Let q(x) be the first derivative of -x**3/18 + x**2/12 - 58. Factor q(a).
-a*(a - 1)/6
Let u(c) be the first derivative of -4/7*c - 16/7*c**3 + 3 - 9/14*c**4 - 13/7*c**2. Factor u(j).
-2*(j + 2)*(3*j + 1)**2/7
Let a(p) = 14*p**3 - 17*p**2 - 11*p. Let k(c) = 5*c**3 - 6*c**2 - 4*c. Let f(b) = 4*a(b) - 11*k(b). Suppose f(h) = 0. Calculate h.
0, 2
Let l(n) be the second derivative of -2/7*n**2 - 1/3*n**3 - 3/14*n**4 + 0 + 6*n - 1/105*n**6 - 1/14*n**5. Factor l(j).
-2*(j + 1)**3*(j + 2)/7
Suppose 4*a = -0 + 16. What is t in -3*t**3 - 2*t + 8*t**3 - 3*t**3 + 4*t**3 + a*t**2 = 0?
-1, 0, 1/3
Let t(u) = 4*u - 8*u + 0*u**2 - 5*u**2. Let n(d) = 11*d**2 + 9*d. Let h(y) = 8*y**3 - 2*y**2 + 2*y + 3. Let o be h(-1). Let w(p) = o*t(p) - 4*n(p). Factor w(s).
s**2
Let p(v) be the first derivative of -2*v**7/245 + v**6/210 + 2*v**5/105 + v**2/2 + 5. Let l(t) be the second derivative of p(t). Factor l(y).
-4*y**2*(y - 1)*(3*y + 2)/7
Let n(r) be the second derivative of -r**6/270 + r**5/180 + r**4/36 - r**3/54 - r**2/9 - 18*r. Factor n(c).
-(c - 2)*(c - 1)*(c + 1)**2/9
Let c(r) be the second derivative of 0*r**3 + 0 + 0*r**2 + 1/78*r**4 + 5*r. Factor c(k).
2*k**2/13
Let y be (3 - (-3)/(-2))*1. Factor 1/2*k**2 + 0 - y*k.
k*(k - 3)/2
Suppose 2*w = 5*j - 4*j + 1, -2*w + 7 = j. Let 6*d + 0*d + 2 + j*d**2 - 2*d - d**2 = 0. Calculate d.
-1
Let z(l) be the third derivative of l**7/70 + 3*l**6/40 + 3*l**5/20 + l**4/8 - 7*l**2. Factor z(a).
3*a*(a + 1)**3
Suppose 4*o + 4 - 8 = 0. Suppose 0 = 4*x + 20, 2*h - 2*x = -o + 11. Factor -3*b + h*b - b + 2*b**2 - 4*b**2.
-2*b*(b + 2)
Let n(r) be the first derivative of -r**7/105 - r**6/15 - r**5/6 - r**4/6 + r**2 + 2. Let b(q) be the second derivative of n(q). Let b(i) = 0. Calculate i.
-2, -1, 0
Let p(k) = k**3 + 6*k**2 + 4*k - 5. Let g be p(-5). Solve -4*w**2 + 4*w - 8*w + g*w = 0 for w.
-1, 0
Determine y, given that -3*y**3 + 7*y**3 - 9*y - 9 - 22*y**2 + 33*y + 4*y**3 - y**4 = 0.
1, 3
Let o = 20 + -18. Solve -10*c**4 + c**4 - 3*c - 3*c**o + 4*c**3 + 11*c**3 = 0.
-1/3, 0, 1
Let h(f) be the third derivative of -f**8/392 + 3*f**6/140 + f**5/35 - 8*f**2. Factor h(c).
-6*c**2*(c - 2)*(c + 1)**2/7
Let u(h) be the first derivative of h**6/70 + 9*h**5/140 + h**4/14 + 4*h + 8. Let q(g) be the first derivative of u(g). What is a in q(a) = 0?
-2, -1, 0
Let c(r) = r**2 - 2*r. Let y be c(4). Let x = y - 8. Suppose x*s + 0 + 2/7*s**4 + 0*s**2 + 2/7*s**3 = 0. Calculate s.
-1, 0
Determine o, given that 1/2*o - 1/8*o**3 + 0*o**2 + 0 = 0.
-2, 0, 2
Let 111*n**2 - 58*n**2 - 50*n**2 + n**3 + 1 + 3*n = 0. Calculate n.
-1
Let c = -10 - -13. Let x(a) be the first derivative of 0*a - 2/27*a**c - 1/9*a**2 + 3. Factor x(b).
-2*b*(b + 1)/9
Let l be -10 - 23/((-46)/24). Find q, given that 1/2*q + 1/2*q**l + 0 = 0.
-1, 0
Let 10/11*b**2 + 8/11 - 2/11*b**3 - 16/11*b = 0. What is b?
1, 2
Let l be -3 - (-2 - -1) - 2. Let p = -2 - l. Solve 21*z - 21*z**3 + 0*z**2 - 6 + 5*z**p + z**2 = 0 for z.
-1, 2/7, 1
Let s(p) be the third derivative of -p**6/360 - p**5/45 + p**4/24 + p**3 + 20*p**2. Find b, given that s(b) = 0.
-3, 2
Let j(g) be the third derivative of g**8/3696 + g**7/330 + 3*g**6/220 + g**5/33 + g**4/33 + 5*g**2. Factor j(l).
l*(l + 1)*(l + 2)**3/11
Let g(i) be the third derivative of i**8/10080 + i**7/5040 - i**6/2160 - i**5/720 + i**3/6 - 3*i**2. Let x(n) be the first derivative of g(n). Solve x(z) = 0.
-1, 0, 1
Let t(j) be the third derivative of 5/42*j**4 - 11/70*j**5 + 0*j - 2*j**2 + 2/21*j**6 - 1/21*j**3 - 16/735*j**7 + 0. Let t(k) = 0. What is k?
1/4, 1
Suppose -10 + 30 = 5*a. Factor 3*v**5 + v**3 - 4*v**3 - 6*v**5 - 6*v**a.
-3*v**3*(v + 1)**2
Suppose 2/7*i**2 + 6/7*i - 6/7*i**3 - 4/7 + 2/7*i**4 = 0. What is i?
-1, 1, 2
Let j be ((-11)/(-66))/((-2)/(-4)). Let l(r) be the first derivative of -2/9*r**3 + j*r**2 - 2 + 0*r. Find u such that l(u) = 0.
0, 1
Let k(d) = -d**2 - 7*d + 1. Let a be k(-5). Let v = a + -7. Factor 5/2*u + 5*u**3 + 5*u**2 + 1/2*u**5 + 5/2*u**v + 1/2.
(u + 1)**5/2
Suppose 2*f = 5*f - 4*s + 134, -5*s = -2*f - 101. Let m = f + 43. Factor 4/5*i + 1/5*i**m - 6/5*i**4 - 12/5*i**2 + 13/5*i**3 + 0.
i*(i - 2)**2*(i - 1)**2/5
Solve 16/5*g + 1/5*g**2 + 64/5 = 0.
-8
Let b = 113/112 - 7/16. Factor -2/7*l**2 + b*l + 0 - 2/7*l**3.
-2*l*(l - 1)*(l + 2)/7
What is a in -2/11*a**3 + 4/11*a**2 + 0 - 2/11*a**4 + 0*a = 0?
-2, 0, 1
Let m be (-16)/(-56) - 24/(-14). Factor -8*u**2 + 14/3*u**3 + m*u + 4/3.
2*(u - 1)**2*(7*u + 2)/3
Let o(f) be the second derivative of -f**6/75 - 3*f**5/50 - f**4/15 + 3*f. Factor o(c).
-2*c**2*(c + 1)*(c + 2)/5
Let v(q) = q**3 + 7*q**2 + 5*q - 1. Let j(o) = o**2 + o. Let g(w) = 30*j(w) - 5*v(w). Suppose g(a) = 0. What is a?
-1, 1
Let n be -5 - -9 - 1/1. Solve -4/3*d**2 + 0*d - 3*d**5 - 7*d**4 + 0 - 16/3*d**n = 0.
-1, -2/3, 0
Let s(u) be the third derivative of u**6/40 - 21*u**5/10 + 147*u**4/2 - 1372*u**3 + 10*u**2 + 2. Factor s(v).
3*(v - 14)**3
Let i(x) = -2*x**2 + 11*x - 5. Let z be i(5). Factor z*g**2 + 0 + 9/4*g**3 - 3/2*g**4 - 3/4*g.
-3*g*(g - 1)**2*(2*g + 1)/4
Let w(h) = h**2 - 19*h - 16. Let u be w(20). Let m(r) be the second derivative of 0 - 1/6*r**u - r - r**2 - 2/3*r**3. Factor m(g).
-2*(g + 1)**2
Let h(v) be the third derivative of -v**6/320 + 3*v**5/80 - 9*v**4/64 + v**3/4 + 7*v**2. Factor h(k).
-3*(k - 4)*(k - 1)**2/8
Let i(j) be the second derivative of -3*j**5/20 - j**4/4 + j**3/2 + 3*j**2/2 + 15*j. Solve i(t) = 0.
-1, 1
Let v(z) be the third derivative of z**8/144 - 23*z**7/630 + 13*z**6/360 + 19*z**5/180 - 5*z**4/18 + 2*z**3/9 - 4*z**2. Suppose v(g) = 0. What is g?
-1, 2/7, 1, 2
Find g such that 4*g**2 - 8*g**3 + 11*g - 4*g**3 - 4 + g = 0.
-1, 1/3, 1
Suppose 0 = 5*l - 2*l - 12. Let i(o) = -7*o**3 + 10*o**2 - o - 2. Let k(s) = s**3 - s**2 + s - 1. Let w(z) = l*k(z) + i(z). Factor w(c).
-3*(c - 2)*(c - 1)*(c + 1)
Let c(k) = -9*