 be the first derivative of -2*t**6/3 - 36*t**5/35 + 5*t**4/7 + 12*t**3/7 + 4*t**2/7 + 45. Suppose x(k) = 0. What is k?
-1, -2/7, 0, 1
Let g(t) = t**4. Let i(a) = -8*a**3 + 4*a**2 + 8*a. Let x(h) = -4*g(h) + i(h). Determine q so that x(q) = 0.
-2, -1, 0, 1
Let r be 21/2*4/75. Let q(c) be the first derivative of 8/15*c**3 - 8/5*c**4 + 1 + r*c**5 + 0*c**2 + 0*c. Find l, given that q(l) = 0.
0, 2/7, 2
Suppose -4 + 0 = -q. Find o, given that -5/3*o**q + 7/3*o**3 + 2/3 + o**2 - 7/3*o = 0.
-1, 2/5, 1
Let f = -1 + -4. Let s = f - -5. Factor 2*n**3 - 3/4*n**4 + 0 - 9/4*n**5 + s*n + n**2.
-n**2*(n - 1)*(3*n + 2)**2/4
Let u be 2/6*(11 + -1). Let k = -12/67 + 572/201. Factor k*v**2 - u*v - 2/3*v**3 + 4/3.
-2*(v - 2)*(v - 1)**2/3
Suppose 2*r - 7 = -3. Suppose -r*s - s = 0. What is p in -2/5*p**3 + 2/5*p + s + 2/5*p**2 - 2/5*p**4 = 0?
-1, 0, 1
Let f(g) be the first derivative of g**6/14 - 3*g**5/7 + 3*g**4/4 - 3*g**3/7 + 1. Solve f(v) = 0.
0, 1, 3
Let c(i) = -3*i**2 + 2. Let g(k) = -k**2 + 1. Let h(f) = c(f) - 4*g(f). Let r be h(2). Factor 8*j - 3*j**3 - 3*j - r*j.
-3*j*(j - 1)*(j + 1)
Let n(u) be the third derivative of u**8/112 - 3*u**7/70 + u**6/20 + u**5/10 - 3*u**4/8 + u**3/2 - 11*u**2. Factor n(x).
3*(x - 1)**4*(x + 1)
Let x(c) be the first derivative of -2*c**3/15 + 6*c**2/5 - 18*c/5 + 25. Determine l so that x(l) = 0.
3
What is h in 0*h**2 + 0*h**3 + 5*h**2 + 6*h**3 - 2*h**2 = 0?
-1/2, 0
Factor -9/4*b**2 - 15/4*b + 3/4*b**4 - 3/2 + 3/4*b**3.
3*(b - 2)*(b + 1)**3/4
Let v(c) = c**3 - 34*c**2 + 32*c + 33. Let x be v(33). Determine g, given that 0*g**2 + 2/3*g**3 + x*g + 0 = 0.
0
Let r(m) = -2*m**2 + m + 9. Let g(t) = -10*t**2 + 4*t + 46. Let v(d) = -d**2 - 9*d + 8. Let q be v(-8). Let l(f) = q*r(f) - 3*g(f). Let l(k) = 0. What is k?
-1, 3
Factor -104*a**2 + 3*a + 100*a**2 + 3*a - 2*a**3.
-2*a*(a - 1)*(a + 3)
Let t(k) be the first derivative of -k**7/126 - k**6/90 + k**5/60 + k**4/36 + 4*k + 1. Let s(l) be the first derivative of t(l). Factor s(a).
-a**2*(a - 1)*(a + 1)**2/3
Let a be 3 + -1*(-3 + 6). Suppose 0 + 5 = 5*l - t, l - 25 = 5*t. Suppose -q**2 + q**3 + l*q - q + 1 + a*q**3 = 0. Calculate q.
-1, 1
Let m = -7 + 11. Suppose m*a - 2*a - 4 = 0. Factor -2*l + 1 + 3*l - 3*l + a*l**3 - l**4.
-(l - 1)**3*(l + 1)
Let p(n) be the third derivative of -n**5/30 + n**4/6 - 10*n**2. Factor p(w).
-2*w*(w - 2)
Let p(x) be the first derivative of -x**7/280 + x**6/60 - x**5/40 - 2*x**3/3 + 10. Let d(t) be the third derivative of p(t). Let d(z) = 0. What is z?
0, 1
Suppose 4*m = 2*a + 4, 5*a + 12 = -m + 2. Factor 2/5*d**2 - 4/5*d + m.
2*d*(d - 2)/5
Suppose 0 = 4*x + 8*x. Let l(h) be the second derivative of x*h**3 - 1/6*h**4 + 0 + h**2 - h. Factor l(z).
-2*(z - 1)*(z + 1)
Let n be 18*(10/3)/5. Let b be (-3)/n - (-36)/16. Factor 0 + 2/5*c + 2/5*c**b.
2*c*(c + 1)/5
Let l(b) = -b**3 - 2*b**2 - b. Let z(s) = -2*s**3 - s**2 - 2*s. Let j = -8 + 11. Let i(c) = j*z(c) - 4*l(c). Determine g, given that i(g) = 0.
0, 1/2, 2
Solve 3*g - 5/2*g**2 + 0 + 1/2*g**3 = 0 for g.
0, 2, 3
Suppose -3/5 + 2/5*a + 1/5*a**2 = 0. What is a?
-3, 1
Suppose 3*s + 4 = -8. Let q be (-10)/(-4) - 2/s. Factor 0 - 2/7*i**2 + 2/7*i**q + 0*i.
2*i**2*(i - 1)/7
Let h(p) be the first derivative of 3*p**4/4 - 5*p**3 + 12*p**2 - 12*p + 19. Factor h(g).
3*(g - 2)**2*(g - 1)
Let x(s) = -2*s**4 - 5*s**3 - 4*s**2 + 1. Let t(r) = r**4 + r**3 - r**2 + 1. Let c(o) = -t(o) + x(o). Solve c(y) = 0.
-1, 0
Let n(g) be the second derivative of g**6/10 + 9*g**5/20 + 3*g**4/4 + g**3/2 - g - 7. Find x such that n(x) = 0.
-1, 0
What is z in 1/3 - 1/3*z**2 + 2/3*z - 2/3*z**3 = 0?
-1, -1/2, 1
Let h(g) be the first derivative of 7*g**4 - 40*g**3 + 72*g**2 - 32*g - 5. Let h(n) = 0. Calculate n.
2/7, 2
Let u(t) be the second derivative of -t**7/168 + t**6/20 - 11*t**5/80 + t**4/8 + 5*t - 1. Suppose u(l) = 0. Calculate l.
0, 1, 2, 3
Let d(t) be the second derivative of -5*t**4/12 - 10*t**3/3 - 15*t**2/2 - t. Find q such that d(q) = 0.
-3, -1
Let u be (16/14)/1 + 0. Suppose 5*p + 5*z = 4*p + 25, -4*p = -5*z. Factor 0*v + 4/7*v**2 + 0 + 2/7*v**3 - 6/7*v**p - u*v**4.
-2*v**2*(v + 1)**2*(3*v - 2)/7
Suppose 0 = 7*t - 5*t - 6. Suppose -t = v + b, 0*v + 3*v + 3 = -b. Factor 2/3*f**3 - 2/9*f**4 + 2/9*f + v - 2/3*f**2.
-2*f*(f - 1)**3/9
Let q(u) = 2*u**4 - 5*u**3 - u**2 + 3. Let r(s) = -2*s**4 + 6*s**3 - 4. Let p(b) = -4*q(b) - 3*r(b). Solve p(m) = 0 for m.
-1, 0, 2
Let m = -5 + 10. Let h be 2/(-4)*(-7 + -3). Determine n, given that -5*n**4 + n**h - 2*n**m + 0*n**3 - 8*n**3 - 7*n**2 + 3*n**2 = 0.
-2, -1, 0
Let r(z) be the third derivative of z**7/210 + z**6/24 + 2*z**5/15 + z**4/6 - z**2. Determine i so that r(i) = 0.
-2, -1, 0
Factor -4/3*o + 0 + 2/3*o**2 + 4/3*o**3 - 2/3*o**4.
-2*o*(o - 2)*(o - 1)*(o + 1)/3
Let p(v) be the second derivative of -v**7/3780 + v**6/540 - v**5/180 + v**4/108 + v**3 + 9*v. Let o(k) be the second derivative of p(k). Factor o(r).
-2*(r - 1)**3/9
Suppose -2*m - 6 = -2. Let d(c) = 2*c**2 - 9*c + 25. Let k(j) = -j + 1. Let q(s) = m*d(s) - 14*k(s). Factor q(i).
-4*(i - 4)**2
Let i = -5 + 5. Let u(d) be the second derivative of -1/24*d**3 + i*d**4 + 1/80*d**5 + 0*d**2 + 0 + 2*d. Suppose u(o) = 0. Calculate o.
-1, 0, 1
Let m(h) be the second derivative of h**6/105 + 2*h**5/35 + h**4/14 - 4*h**3/21 - 4*h**2/7 + 65*h. Find a such that m(a) = 0.
-2, -1, 1
Suppose 5*l + 5 = 5*h + 10, 2*h - 10 = -l. Let w(i) be the first derivative of -4/9*i**3 - 1/6*i**l + 0*i + 2 - 1/3*i**2. Factor w(y).
-2*y*(y + 1)**2/3
Let p(f) be the first derivative of -f**6/60 - f**5/20 - f**4/24 + 3*f - 1. Let h(a) be the first derivative of p(a). Determine t, given that h(t) = 0.
-1, 0
Let u be 2/10 - (-4)/(-20). Let s be (-44)/(-12) + u + -3. Factor -s*h**2 + 0 + 0*h + 1/3*h**3.
h**2*(h - 2)/3
Let t = 775/133 - 89/19. Factor -24/7*p - 18/7 - 2/7*p**4 + 4/7*p**2 + t*p**3.
-2*(p - 3)**2*(p + 1)**2/7
Let i(x) be the first derivative of -5*x**6/39 + 24*x**5/65 + 11*x**4/26 - 4*x**3/13 - 46. Let i(j) = 0. Calculate j.
-1, 0, 2/5, 3
Solve 3*s**4 - 6*s + 3*s**2 - 3*s**2 - 3*s**5 + 9*s**3 - s**2 - 2*s**2 = 0 for s.
-1, 0, 1, 2
Factor -4/3*x + 2/3*x**2 + 0 + 2/3*x**3.
2*x*(x - 1)*(x + 2)/3
Let n = -337/3160 + 5/158. Let i = 17/40 - n. Factor 1 - 3/2*a + i*a**2.
(a - 2)*(a - 1)/2
Let f(r) be the third derivative of -r**5/30 + r**4/12 + 2*r**3/3 + 4*r**2. Find u such that f(u) = 0.
-1, 2
Let t(z) be the second derivative of -1/54*z**4 + 1/90*z**5 + 0*z**2 - 5*z + 1/135*z**6 - 1/27*z**3 + 0. Solve t(h) = 0.
-1, 0, 1
Let t(w) be the third derivative of w**8/112 + w**7/420 - w**6/12 + 3*w**5/40 + w**4/6 - w**3/3 - 23*w**2. Suppose t(d) = 0. Calculate d.
-2, -2/3, 1/2, 1
Let b(d) be the second derivative of -d**4/3 + 2*d**2 + d. Suppose b(t) = 0. Calculate t.
-1, 1
Let v(h) be the third derivative of -h**6/180 - 2*h**5/15 - 4*h**4/3 + h**3/6 - h**2. Let q(m) be the first derivative of v(m). What is p in q(p) = 0?
-4
Let s(u) = u - 1. Let c be (-1)/(-1) - 0/2. Let n(x) = -2*x - 5 + 3 + x**2 + 4. Let w(l) = c*n(l) - 2*s(l). Factor w(j).
(j - 2)**2
Suppose -28 + 8*d + 70*d**2 - 68*d**2 + 36 = 0. Calculate d.
-2
Let m be -2 + 0 + (-10)/35*-7. Let d(x) be the second derivative of 0 + x - 1/3*x**3 + m*x**2 + 1/12*x**4. Suppose d(w) = 0. Calculate w.
0, 2
Suppose -2*y + 5*i = 5, 3*y - 3 = 5*i - i. Let u = 5 - y. Determine n so that u + 4/9*n**2 - 2/9*n - 2/9*n**3 = 0.
0, 1
Factor -6/13*a + 6/13*a**2 + 2/13 - 2/13*a**3.
-2*(a - 1)**3/13
Factor 64*l + 76*l**4 + 43*l**2 + 93*l**2 - 76 + 144*l**3 + 16*l**5 + 88.
4*(l + 1)**4*(4*l + 3)
Let a = -42 - -44. Let j(h) be the first derivative of -1/10*h**5 - 1 + 1/2*h**4 - 1/3*h**6 + 0*h**a + 1/6*h**3 + 0*h. Suppose j(z) = 0. Calculate z.
-1, -1/4, 0, 1
Let l(w) be the second derivative of w**9/15120 + w**8/6720 - w**4/4 + 2*w. Let g(v) be the third derivative of l(v). Factor g(h).
h**3*(h + 1)
Let p(b) = -2*b**2 + 2*b. Let v(d) = -d**2 + d. Let u(s) = -6*p(s) + 15*v(s). Factor u(q).
-3*q*(q - 1)
Let v(o) be the first derivative of -1/21*o**3 + 2 + 1/14*o**2 + 0*o. Factor v(x).
-x*(x - 1)/7
Suppose 16*f = 21*f - 50. Let h = -8 + f. Solve 1/4*j**4 + 0*j**3 + 1/4 + 0*j - 1/2*j**h = 0 for j.
-1, 1
Find y, given that 12/7 + 108/7*y + 351/7*y**2 + 480/7*y**3 + 225/7*y**4 = 0.
-1, -2/5, -1/3
Let g(w) be the first derivative of