 1
Let m = 10 - 5. Factor 3*k**3 + 5*k**2 + 6*k**2 - m*k**2.
3*k**2*(k + 2)
Let u(r) be the second derivative of 0 + 0*r**2 - 5*r - 1/42*r**4 + 1/7*r**3. Solve u(g) = 0.
0, 3
Let q(z) be the third derivative of z**7/840 + z**6/180 + z**5/120 - 5*z**3/6 + 5*z**2. Let y(w) be the first derivative of q(w). What is o in y(o) = 0?
-1, 0
Let p(z) be the second derivative of -2*z - 1/6*z**3 + 0*z**2 + 0 + 1/20*z**5 + 0*z**4. Determine k so that p(k) = 0.
-1, 0, 1
Let d(z) be the first derivative of z**3/12 - z**2/4 - 3*z/4 + 9. Determine c, given that d(c) = 0.
-1, 3
Let a = 97 + -64. Let s be (a/(-12) - -1) + 2. Solve -s*c**2 - 3/4*c - 1/2 = 0.
-2, -1
Suppose -27*l**4 - 34*l + 48*l**3 + 59*l**2 - l - 12 - 13*l - 20*l**2 = 0. Calculate l.
-1, -2/9, 1, 2
Let i be ((-10)/120)/(2/(-6)). Let -i*r**4 + 0 - 1/4*r + 1/4*r**2 + 1/4*r**3 = 0. What is r?
-1, 0, 1
Let t(o) be the second derivative of o**7/210 - o**6/90 - o**5/30 + o**4/6 + o**3/3 + o. Let q(i) be the second derivative of t(i). Factor q(y).
4*(y - 1)**2*(y + 1)
Let u = 31 - 19. Factor 37*x - 56*x**3 + 7*x + 2*x**2 + 2*x - u.
-2*(x + 1)*(4*x - 3)*(7*x - 2)
Factor 26/9*c - 16/9*c**2 + 2/9*c**3 - 4/3.
2*(c - 6)*(c - 1)**2/9
Let a(y) be the first derivative of 7*y**4/6 - 2*y**3/3 + 5*y - 3. Let h(w) be the first derivative of a(w). Factor h(f).
2*f*(7*f - 2)
Let g(r) = -r**3 + 4*r**2 + 6*r - 3. Let a be 3 - (0 + 2 + -4). Let j be g(a). Factor 0 + 4/7*o + 2/7*o**j.
2*o*(o + 2)/7
Let j(o) be the third derivative of -5*o**6/24 + o**5/6 + 25*o**4/24 - 5*o**3/3 + 12*o**2. Factor j(s).
-5*(s - 1)*(s + 1)*(5*s - 2)
Let x(w) = 3*w**2 - 2*w + 1. Let l be x(1). Let k be 7/42 - (-1)/(-6). What is n in -n**2 - l - 2 - 4*n + k = 0?
-2
Let m(k) be the third derivative of k**7/105 - k**6/30 + k**5/30 - 4*k**2. What is h in m(h) = 0?
0, 1
Let u(d) = 484*d**2 - 180*d + 12. Let o(l) = -l - 1. Let y(g) = -4*o(g) + u(g). Determine a, given that y(a) = 0.
2/11
Let k(q) = 12*q + 26. Let o be k(-2). Find r, given that 1/3*r**o + 0 + 1/3*r = 0.
-1, 0
Suppose -5*z + 33 = 3*x - 9, -z = -x - 10. Let n(r) = 2*r**2 + 2*r + 8. Let v(j) = 5*j**2 + 4*j + 17. Let h(a) = z*n(a) - 4*v(a). Factor h(d).
-2*(d - 2)*(d + 1)
Let u be (-1)/(-2)*(0 + 0). Suppose u = 2*b + b - 6. Suppose 0*h**2 + 2*h**2 - b*h**3 + 2*h**4 - 2*h**3 = 0. What is h?
0, 1
Suppose -25*d + 0*d = 6*d. Factor -1/2*l + d + 1/2*l**2.
l*(l - 1)/2
Suppose 3 = -h + j + 8, -j + 1 = h. Factor -2*t**2 - 8/3*t**h - 2/3*t**4 + 0 + 0*t.
-2*t**2*(t + 1)*(t + 3)/3
Let x(b) be the third derivative of 5*b**6/12 + 11*b**5 - 23*b**4 + 56*b**3/3 + 39*b**2. Factor x(l).
2*(l + 14)*(5*l - 2)**2
Solve -7*g**2 + 4 - g**2 + 16*g**3 - 2*g**4 - 8*g**5 + 3*g**4 - 8*g + 3*g**4 = 0.
-1, 1/2, 1
Let n(d) = d**3 + d**2 + d. Let x(m) = 35*m**2 - 55*m + 40. Let q(v) = 5*n(v) - x(v). Find i such that q(i) = 0.
2
Let i(j) = 7*j**3 - 6*j**2 + j - 4. Let g(y) = -y**3 + y**2 + 1. Let s(r) = 6*g(r) + i(r). Let c be s(-1). Solve c*p - 1/3*p**2 - p**4 + 0 - 4/3*p**3 = 0 for p.
-1, -1/3, 0
Suppose 2*k + 7*x = 2*x + 1, -5*k + 17 = -2*x. Let m(y) be the first derivative of 0*y**2 + 2/21*y**k - 2/7*y + 2. Factor m(f).
2*(f - 1)*(f + 1)/7
Let m(b) = -b**3 + 4*b**2 + 2*b - 5. Let h be m(4). Solve 0 + 0*j**h - 3/7*j**4 + 3/7*j**2 + 0*j = 0.
-1, 0, 1
Factor 6*l**2 - 430*l + 428*l - 4*l**3 - l**2 + l**4.
l*(l - 2)*(l - 1)**2
Let h(y) be the second derivative of 0 - 9*y + 3*y**2 - 5/12*y**4 + 13/6*y**3. Factor h(t).
-(t - 3)*(5*t + 2)
Let w(v) be the second derivative of 3/2*v**2 + 0 + 0*v**4 + 0*v**3 + 1/270*v**5 + v. Let j(x) be the first derivative of w(x). Factor j(q).
2*q**2/9
Suppose 57*p**2 + 0 - 55*p**2 - 6 - 4*p = 0. Calculate p.
-1, 3
Let c(x) be the third derivative of x**6/1260 - x**4/252 + x**2. Factor c(h).
2*h*(h - 1)*(h + 1)/21
Let s(v) = -16*v**4 - 40*v**3 - 32*v**2 - 2*v - 6. Let l(j) = -47*j**4 - 119*j**3 - 96*j**2 - 7*j - 17. Let n(c) = -6*l(c) + 17*s(c). Factor n(o).
2*o*(o + 1)*(o + 2)*(5*o + 2)
Let b(h) be the third derivative of h**7/280 + h**6/80 + h**5/80 + 13*h**2. Factor b(q).
3*q**2*(q + 1)**2/4
Let 5/2*q**5 + 25/2*q**3 + 0*q + 0 + 10*q**4 + 5*q**2 = 0. Calculate q.
-2, -1, 0
Let r = 5 + -2. Let s be 4/12*30/4. Determine k, given that -1/2 + 2*k + k**r - s*k**2 = 0.
1/2, 1
Let m(j) = -j**3 - 9*j**2 - 18*j. Let z be m(-6). Let p(b) be the first derivative of 1 - 1/3*b**3 + 1/2*b**2 + z*b. Factor p(k).
-k*(k - 1)
Let d = -37/24 + 15/8. Let s(b) be the third derivative of -1/15*b**5 - b**2 + 1/105*b**7 + 1/168*b**8 + 1/12*b**4 - 1/30*b**6 + d*b**3 + 0*b + 0. Factor s(z).
2*(z - 1)**2*(z + 1)**3
Let q(f) be the first derivative of -2 + 1/4*f**2 - 1/2*f**3 + 0*f - 1/8*f**4 + 3/10*f**5. Factor q(u).
u*(u - 1)*(u + 1)*(3*u - 1)/2
Factor -4/3*w**2 - 12 + 8*w.
-4*(w - 3)**2/3
Let h(k) be the second derivative of -k**5/5 + 8*k**4/3 - 34*k**3/3 + 20*k**2 + 41*k. Factor h(m).
-4*(m - 5)*(m - 2)*(m - 1)
Let g be ((-4)/6)/((-4)/(-6)). Let f = g + 4. Determine j, given that 3*j**5 - 3*j**2 - 9*j**4 + j - j + 6*j**3 + f*j**3 = 0.
0, 1
Let a(r) = -9*r**2 - 75*r + 171. Let w(q) = -43 - 3*q**2 + 2*q**2 + 3*q**2 + 19*q. Let k(i) = -5*a(i) - 21*w(i). Factor k(y).
3*(y - 4)**2
Solve 3/8*c + 3/8*c**3 - 3/4*c**2 + 0 = 0 for c.
0, 1
Let c(l) be the first derivative of l**3/3 + 4*l**2 - 6*l - 4. Let d be c(-9). Let -4/5*j**2 + 2/5*j**4 + 0*j**d + 0*j + 2/5 = 0. Calculate j.
-1, 1
Let o(m) be the third derivative of -1/210*m**5 + 0*m - 7*m**2 + 0*m**3 + 0*m**4 + 0 - 1/420*m**6. Let o(i) = 0. What is i?
-1, 0
Let f(l) be the first derivative of -6*l**5/35 + 9*l**4/28 + 2*l**3/7 + 6. Find x, given that f(x) = 0.
-1/2, 0, 2
Let x(w) be the first derivative of 1/24*w**4 - 3 - 1/60*w**6 + 0*w**2 - w - 1/6*w**3 + 1/20*w**5. Let v(f) be the first derivative of x(f). Solve v(k) = 0.
-1, 0, 1, 2
Let g be (-283)/(-1698) - (-1)/(84/22). Suppose -3/7*n - g*n**2 + 0 = 0. Calculate n.
-1, 0
Suppose 0 = -2*v - 2 - 2. Let s = v - -2. Find w such that 0*w**3 - 4/7*w**2 + s*w + 2/7*w**4 + 2/7 = 0.
-1, 1
Suppose -11*v**2 - 8*v**3 + 10*v**3 + 5*v**3 + 41*v**2 + 8*v = 0. What is v?
-4, -2/7, 0
Let n(m) be the second derivative of -2/3*m**3 - 9/10*m**5 - 3*m + 0 + 7/6*m**4 + 1/3*m**6 + 0*m**2 - 1/21*m**7. Factor n(z).
-2*z*(z - 2)*(z - 1)**3
Let o(a) be the second derivative of a**7/420 - a**6/60 + a**5/20 - a**4/12 + a**3/2 + 2*a. Let s(t) be the second derivative of o(t). Factor s(r).
2*(r - 1)**3
Let v(c) = c**5 + 5*c**4 - c**3 - 5*c + 5. Let u(o) = 4*o**5 + 24*o**4 - 4*o**3 - 24*o + 24. Let x(s) = -5*u(s) + 24*v(s). Factor x(f).
4*f**3*(f - 1)*(f + 1)
Let j be 1/(-4) - 36/(-16). Factor 3*d**2 + d**j - 2*d**2 + 2*d.
2*d*(d + 1)
Suppose -4*q = q - 25. Find g such that -3/5*g**q - 3*g + 3/5 - 6*g**3 + 3*g**4 + 6*g**2 = 0.
1
Let h(b) be the second derivative of 4*b + 1/3*b**2 + 0 + 0*b**4 - 1/6*b**3 + 1/60*b**5. Factor h(w).
(w - 1)**2*(w + 2)/3
Let s(b) be the first derivative of b**4/24 - 2*b**3/3 + 4*b**2 - 32*b/3 - 8. Factor s(o).
(o - 4)**3/6
Suppose 0 = -4*z + 3*z - 11. Let m = 15 + z. What is c in 2*c**2 - 4*c**2 + 6*c**3 + c - c - m*c = 0?
-2/3, 0, 1
Let v(p) be the second derivative of -p**5/300 - p**4/60 - p**3/30 - 2*p**2 - p. Let w(z) be the first derivative of v(z). Let w(j) = 0. Calculate j.
-1
Suppose n = 2 + 1. Let t be n*(0 + 1/12). Factor 0 - t*u + 1/4*u**3 + 0*u**2.
u*(u - 1)*(u + 1)/4
Let b(q) = q**2 - q. Let z be (-4)/18 + (-7)/9. Let i(h) be the first derivative of -h**3 + 2*h**2 + 6. Let f(u) = z*i(u) - 4*b(u). Solve f(w) = 0 for w.
0
Let h(w) be the second derivative of 0*w**5 - 2*w + 1/3*w**3 - 1/21*w**7 + 0 + 2/15*w**6 - 1/3*w**4 + 0*w**2. Solve h(b) = 0.
-1, 0, 1
Let s = -4 + -2. Let b be ((-9)/(-6))/((-3)/s). Solve u**2 - b*u**2 + u + u**2 = 0 for u.
0, 1
Let r = -822 + 822. Factor r*s + 0 - 1/6*s**2.
-s**2/6
Let t(b) be the first derivative of -b**6/720 + b**4/48 - b**3 - 1. Let w(k) be the third derivative of t(k). Factor w(n).
-(n - 1)*(n + 1)/2
Let q(x) be the second derivative of -x**8/26880 - x**7/1120 - 3*x**6/320 - 9*x**5/160 - 2*x**4/3 + x. Let r(z) be the third derivative of q(z). Factor r(y).
-(y + 3)**3/4
Let f(y) be the third derivative of 0 + 0*y + 1/30*y**3 - 1/60*y**4 + 0*y**5 + 1/300*y**6 + y**2 - 1/1050*y**7. Determine m so that f(m) = 0.
-1, 1
Let v(g) be the third derivative of 0 + 0*