0.
0, 2/3, 1
Let g be ((-4)/3)/(18/(-12)). Let a be (-1 - -3) + (-16)/9. Suppose -2/9*d + 0 - g*d**2 + a*d**3 + 8/9*d**4 = 0. Calculate d.
-1, -1/4, 0, 1
Let q(g) be the second derivative of -g**5/110 + g**3/33 + g. Determine s so that q(s) = 0.
-1, 0, 1
Let x(o) be the third derivative of o**6/90 - o**5/15 + o**4/9 + 10*o**2. What is p in x(p) = 0?
0, 1, 2
Let n(f) be the third derivative of 1/50*f**5 + 1/525*f**7 + 0*f + 0 + f**2 - 1/100*f**6 + 0*f**3 - 1/60*f**4. What is h in n(h) = 0?
0, 1
Suppose 16*w = 12*w. Factor w*d**2 + 1/3*d + 0 - 1/3*d**3.
-d*(d - 1)*(d + 1)/3
Factor 35*w**2 + 6*w + 6*w**3 + 29*w**2 - 79*w**2.
3*w*(w - 2)*(2*w - 1)
Let w(j) be the first derivative of 2/9*j**4 - 1 + 4/9*j**2 + 4/9*j**3 + 2/9*j + 2/45*j**5. Solve w(d) = 0 for d.
-1
Let k = -1 - -2. Let b be ((-3)/4)/(k/(-4)). Factor -b*w + w - 4*w**2 + 0*w.
-2*w*(2*w + 1)
Let y(k) be the third derivative of k**8/4032 + k**7/756 + k**6/432 + k**4/8 - 5*k**2. Let s(q) be the second derivative of y(q). Factor s(j).
5*j*(j + 1)**2/3
Suppose -r - 3 = -2*a, 3*r - 1 = 2*r. Factor z**a - 1/4*z**3 + 0 - z**4 + 1/4*z.
-z*(z - 1)*(z + 1)*(4*z + 1)/4
Suppose 0 = 5*a - 10 - 15. Let t(x) be the third derivative of 0*x + 0 + 0*x**4 - 1/120*x**6 + 0*x**3 - x**2 + 0*x**a + 1/210*x**7. Factor t(i).
i**3*(i - 1)
Suppose j = -3*u + u - 3, 3 = -j + 3*u. Let a be 1*j/6 - -1. Solve 0*c + 1/2 + a*c**4 + 0*c**3 - c**2 = 0.
-1, 1
Let y(a) be the second derivative of a**4/4 + a. Let c be y(1). Factor -4/3*n**5 - 2/3*n**4 + 0*n + 2/3*n**c + 0 + 0*n**2.
-2*n**3*(n + 1)*(2*n - 1)/3
Let t be ((-12)/10)/((-2)/(-40)). Let w be (-2)/5 - t/10. Suppose -z**2 + 6*z**2 - 2*z**w - 2*z - z**2 = 0. Calculate z.
0, 1
Factor 0*m**4 + m**4 + 4*m**2 - 5*m**4.
-4*m**2*(m - 1)*(m + 1)
Let p(f) be the first derivative of 7*f**5/20 - 33*f**4/16 + 3*f**3/2 + f**2 - 18. Find r, given that p(r) = 0.
-2/7, 0, 1, 4
Suppose 7*z - 20 = 2*z. Let u(k) be the first derivative of 1/14*k**z + 5/7*k**2 + 1 - 8/21*k**3 - 4/7*k. Let u(j) = 0. Calculate j.
1, 2
Let k(v) be the first derivative of -2*v**5/25 - v**4/10 + 2*v**3/5 + v**2/5 - 4*v/5 + 15. Find z, given that k(z) = 0.
-2, -1, 1
Let m(s) be the first derivative of -3*s**4/8 - 2*s**3 - 15*s**2/4 - 3*s - 3. Factor m(w).
-3*(w + 1)**2*(w + 2)/2
Let a = 150 - 148. Let o(r) be the third derivative of 0 - 1/210*r**7 + 0*r**5 + 0*r + 0*r**4 + 0*r**3 - 1/120*r**6 + 4*r**a. Factor o(c).
-c**3*(c + 1)
Let l be (4/5)/((-4)/(-10)). Suppose 2 - f + f - 2*f**l + 0*f = 0. What is f?
-1, 1
Let j(i) be the second derivative of -i**6/1260 - i**5/105 - i**4/28 + i**3 + i. Let m(s) be the second derivative of j(s). Determine u so that m(u) = 0.
-3, -1
Suppose 2 = v, -2*v + 8 = 3*d - 5. Factor -2/7 - 16/7*o**2 + 8/7*o**d + 10/7*o.
2*(o - 1)*(2*o - 1)**2/7
Let p = -15 - -18. Let i(x) be the first derivative of -2 + 1/9*x**p + 1/3*x - 1/3*x**2. Factor i(a).
(a - 1)**2/3
Let b = 109 - 109. Let w be 8/10 - 2 - -2. Let 2/5*t**5 + 0 - w*t**3 + 2/5*t + b*t**4 + 0*t**2 = 0. What is t?
-1, 0, 1
Factor 7*x**2 + 7*x**2 - 2*x**3 + 10 - 22*x + 0 + 0*x**2.
-2*(x - 5)*(x - 1)**2
Factor -2/17*u**3 - 2/17*u**2 + 0 + 0*u.
-2*u**2*(u + 1)/17
Factor 2/9*d - 2/9*d**2 + 0.
-2*d*(d - 1)/9
Factor 4/3*y**5 + 4/3*y**3 + 32/3 + 16/3*y**4 - 16/3*y - 40/3*y**2.
4*(y - 1)**2*(y + 2)**3/3
Let l be (-16)/14 - 10/((-30)/6). Factor -2/7*h**3 + l*h**2 - 8/7 + 0*h.
-2*(h - 2)**2*(h + 1)/7
Let r be (21/(-9))/7*(-4 - -4). Let b(x) be the first derivative of r*x - 2/3*x**3 + 2 + 0*x**2. Let b(g) = 0. Calculate g.
0
Let k(n) = -5*n**4 + 7*n**3 + 3*n**2 - 7*n + 9. Let p(l) = l**4 - l**3 - l**2 + l - 1. Let v(j) = -2*k(j) - 14*p(j). Find h such that v(h) = 0.
-1, 1
Let l = 9/74 + 14/37. Suppose l*f**2 - 1/2*f - 1 = 0. Calculate f.
-1, 2
Let t(u) = 4*u**2 + 14*u - 9. Let b(a) = -1. Let n(l) = -2*b(l) + 2*t(l). Determine f so that n(f) = 0.
-4, 1/2
Let v(t) be the third derivative of -t**6/40 + 17*t**5/90 - 7*t**4/18 - 4*t**3/9 - 3*t**2. Let v(i) = 0. Calculate i.
-2/9, 2
Suppose -d**4 - 2/5*d**5 + 0 + 1/5*d - 3/5*d**3 + 1/5*d**2 = 0. What is d?
-1, 0, 1/2
Suppose -8 = -3*o + 4. Let 1 - 3 - 5*u**4 - u**5 + 0*u**4 - 14*u**3 - 16*u**2 - u**o - 9*u = 0. What is u?
-2, -1
Suppose -50 = -4*f - 2*r, -4*f + 0*r = -r - 53. Let x = -9 + f. Factor -o - 8*o**3 - o + x - 14*o**2 + 20*o**3.
2*(o - 1)*(2*o + 1)*(3*o - 2)
Let k(y) be the third derivative of -y**5/20 - 3*y**4/8 - y**3 - 9*y**2. Factor k(l).
-3*(l + 1)*(l + 2)
Suppose 4*b + 5*q - 15 = -46, -b = 2*q + 7. Let j be 2/3 - (-6)/b. Factor 4*c**2 + j*c - 2*c - 18*c**3 - 16*c**2.
-2*c*(3*c + 1)**2
Let o be (-6)/(1*2) + (-493)/(-145). Factor -2/5*a**4 + 0 + 2/5*a**2 - 2/5*a + o*a**3.
-2*a*(a - 1)**2*(a + 1)/5
Let l(a) = 24*a**4 - 26*a**2 + 14*a + 14. Let h(p) = -5*p**4 + 5*p**2 - 3*p - 3. Let s(y) = 28*h(y) + 6*l(y). Find x, given that s(x) = 0.
-2, 0, 2
Let h(p) = 320*p**2 - 440*p - 220. Let o(q) = -29*q**2 + 40*q + 20. Let j(t) = 4*h(t) + 45*o(t). Factor j(z).
-5*(z - 2)*(5*z + 2)
Let m(w) be the second derivative of w**4/12 + 7*w**3/6 - 2*w**2 - 3*w. Let o(b) = -b + 1. Let t be (-10)/(-2) + (1 - 1). Let d(a) = t*o(a) + m(a). Factor d(v).
(v + 1)**2
Let w(a) be the second derivative of -a**4/6 - a**3/3 + 2*a**2 - 2*a. Factor w(s).
-2*(s - 1)*(s + 2)
Let j be 0 + 5/(50/4). Let n(p) be the first derivative of -1/6*p**6 + 0*p**4 + 1/2*p**2 - j*p**5 + 2 + 0*p + 2/3*p**3. Factor n(a).
-a*(a - 1)*(a + 1)**3
Let y(t) = 3*t**2 - t - 4. Let c = 7 + -14. Let w(f) = -2*f**2 + 2. Let l(n) = c*w(n) - 4*y(n). Let l(d) = 0. Calculate d.
-1
Let y(v) be the third derivative of 0*v - 1/1155*v**7 - 1/660*v**6 + 0*v**4 + 1/330*v**5 + 0*v**3 - 2*v**2 + 0 + 1/1848*v**8. Factor y(j).
2*j**2*(j - 1)**2*(j + 1)/11
Suppose f = 3*q - 0 + 17, 2*q + 4 = -3*f. Find m such that 1/3*m**f + 0*m - 1/3 = 0.
-1, 1
Suppose 2*g + 2*l = 6, 0*g = -g - 4*l + 3. Suppose -2/5*b - 2/5*b**g + 0 - 4/5*b**2 = 0. Calculate b.
-1, 0
Suppose 3*a - f - 15 = 0, f - 21 - 4 = -5*a. Suppose -7 = -x + a*v + 12, -x - 8 = 4*v. Determine d so that -8/9*d - 16/9*d**2 + 0 + 2*d**x + 2/3*d**3 = 0.
-2/3, 0, 1
Let g(k) be the second derivative of -3*k**5/40 + 3*k**4/4 - 3*k**3 + 6*k**2 + 8*k. Suppose g(h) = 0. Calculate h.
2
Let m(k) be the first derivative of 1/6*k**2 + 2/3*k + 1/6*k**6 - 2 - 2/3*k**3 - 1/3*k**4 + 4/15*k**5. Solve m(g) = 0 for g.
-1, 2/3, 1
Let r(t) be the third derivative of -t**5/300 - t**4/15 - 8*t**3/15 - 2*t**2. Suppose r(p) = 0. What is p?
-4
Let h be 111/(-105) + 0 + 1. Let v = 76/105 + h. Suppose 2/3*j + v*j**2 + 0 = 0. Calculate j.
-1, 0
Let n(c) be the first derivative of c**5/270 + c**4/27 + 4*c**3/27 - c**2 - 6. Let w(j) be the second derivative of n(j). Factor w(t).
2*(t + 2)**2/9
Let v(l) = -3*l**2 - 3*l. Let h(y) = -2*y**2 - 2*y. Let x = 3 + 1. Let g(k) = x*h(k) - 3*v(k). Determine u so that g(u) = 0.
-1, 0
Let u(p) = -13*p - 61. Let o be u(-5). Factor 3/7*g**o - 12/7*g**3 + 15/7*g**2 - 6/7*g + 0.
3*g*(g - 2)*(g - 1)**2/7
Let t = 4 + 1. Let f(x) be the first derivative of 2 + 5/16*x**4 + 1/2*x - 5/8*x**2 + 7/20*x**t - 3/4*x**3. Factor f(r).
(r - 1)*(r + 1)**2*(7*r - 2)/4
Let m = 19/28 - 3/28. Find i such that -2/7*i**2 - m + 6/7*i = 0.
1, 2
Let y(a) be the third derivative of a**7/945 - a**6/540 - 2*a**5/135 + a**4/27 + 10*a**2. Factor y(z).
2*z*(z - 2)*(z - 1)*(z + 2)/9
Let k be 2*30/(-144)*-8. Solve 32/3*g + 8/3 + 34/3*g**2 + k*g**3 = 0 for g.
-2, -1, -2/5
Let a(u) = -5*u**3 - 3*u. Suppose 19*k - 15*k = 32. Let w(j) = 2*j**3 + j. Let f(y) = k*w(y) + 3*a(y). Solve f(i) = 0.
-1, 0, 1
Let v(l) = -l**2 + 39*l - 290. Let r be v(10). Suppose -8/5*m**2 + 2/5*m**3 + r + 8/5*m = 0. Calculate m.
0, 2
Let v(i) be the second derivative of i**9/3780 + i**8/280 + i**7/70 - i**4/2 + 8*i. Let u(m) be the third derivative of v(m). Solve u(b) = 0 for b.
-3, 0
Let d(x) be the second derivative of -25*x**4/42 + 20*x**3/21 - 4*x**2/7 + 7*x. Factor d(s).
-2*(5*s - 2)**2/7
Let f(m) be the first derivative of m**4/28 - 4*m**3/21 + 5*m**2/14 - 2*m/7 + 4. Factor f(y).
(y - 2)*(y - 1)**2/7
Let s(x) be the first derivative of -2/25*x**5 - 1/5*x**2 - 1 - 2/5*x**3 - 3/10*x**4 + 0*x. What is l in s(l) = 0?
-1, 0
Factor 3*u**5 - 4*u**3 + 9*u**4 - 8*u**4 - 2*u**5 - 4*u**2.
u**2*(u - 2)*(u + 1)*(u + 2)
Let 6*g - 9*g - 5*g**2 - 7*g = 0. What is g?
-