Suppose r(g) = 0. What is g?
0, 2
Let k = 235 + -35249/150. Let u(i) be the third derivative of 1/15*i**3 + 0 - 1/525*i**7 - 1/30*i**4 + 0*i + 0*i**5 + k*i**6 - 2*i**2. Factor u(s).
-2*(s - 1)**3*(s + 1)/5
Let c be (-2)/14 + (-156)/(-14). Let g(k) = 4*k**2 - 5*k + 16. Let r(b) = -2*b**2 + 2*b - 8. Let o(i) = c*r(i) + 6*g(i). Factor o(n).
2*(n - 2)**2
Suppose -5*m + 2*k = -4, -m + 2*k = 3*m - 2. Suppose -2*c = -3*c + m. Suppose -c*b + 4*b + 12*b**2 - 5*b = 0. Calculate b.
0, 1/4
Let 10*s**4 + s**4 - 27*s**3 + 6*s**2 + s**4 = 0. Calculate s.
0, 1/4, 2
Find p, given that 4*p**2 + 3*p**2 - 5*p**2 + 8*p + 8 = 0.
-2
Let t(j) be the second derivative of -19/48*j**4 + 1/2*j**2 - 1/6*j**3 + 0 + 1/8*j**5 + j. Solve t(v) = 0 for v.
-1/2, 2/5, 2
Suppose 20*k**5 - 4/7*k + 39/7*k**3 + 16/7*k**2 - 191/7*k**4 + 0 = 0. What is k?
-2/7, 0, 1/4, 2/5, 1
Let m(g) be the second derivative of 1/45*g**6 - 1/189*g**7 + 0 + 1/54*g**4 + 0*g**3 + 0*g**2 + 4*g - 1/30*g**5. Factor m(y).
-2*y**2*(y - 1)**3/9
Let s be 4/(-28)*5 - -1. Factor 2/7 + s*q**2 - 4/7*q.
2*(q - 1)**2/7
Suppose -2*t + 3 = -t. Let m(k) be the second derivative of 1/60*k**6 - 2*k + 1/168*k**7 + 0 + 0*k**2 - 1/24*k**4 - 1/24*k**t + 0*k**5. Factor m(g).
g*(g - 1)*(g + 1)**3/4
Let a be 1/(-3) - 7/(-3). Solve 0*t + 1 + 3*t + 0*t**a - 5*t + t**2 = 0.
1
Let l(a) be the second derivative of a**8/112 - a**6/20 + a**4/8 - a**2/2 + 2*a. Let h(w) be the first derivative of l(w). Factor h(q).
3*q*(q - 1)**2*(q + 1)**2
Suppose -12 = 2*l - 0*l - 2*w, 0 = -5*l + 3*w - 30. Let g be (-12)/(-5) - l/(-15). Determine h, given that -h**g - 4*h + 4*h = 0.
0
Let g(i) = -i**3 + 8*i**2 - 7*i. Let r be g(7). Solve 2/7*m**3 + r - 6/7*m**2 + 4/7*m = 0.
0, 1, 2
Let f(r) = -6*r**3 + 26*r**2 - 82*r + 58. Let b(v) = -2*v**3 + 9*v**2 - 27*v + 19. Let o(i) = 10*b(i) - 3*f(i). Factor o(k).
-2*(k - 2)**3
Let c(h) be the first derivative of -h - 1/70*h**5 - 2 + 1/42*h**4 + 0*h**3 + 0*h**2. Let w(b) be the first derivative of c(b). Factor w(k).
-2*k**2*(k - 1)/7
Suppose 1 = h + 2. Let x be (-7)/49*h/1. Factor -1/7*i**2 + 0*i + x.
-(i - 1)*(i + 1)/7
Let y(n) be the first derivative of n**5 + 15*n**4/4 - 26. Factor y(g).
5*g**3*(g + 3)
Let i(m) be the second derivative of m**10/45360 - m**8/5040 + m**6/1080 - m**4/12 - 3*m. Let g(k) be the third derivative of i(k). Factor g(n).
2*n*(n - 1)**2*(n + 1)**2/3
Let x(p) be the second derivative of -32*p**6/15 + 72*p**5/5 - 97*p**4/3 + 24*p**3 - 8*p**2 - 3*p. Factor x(o).
-4*(o - 2)**2*(4*o - 1)**2
Let q(k) be the second derivative of k**6/540 - k**5/180 - k**4/18 + 7*k**3/6 - 8*k. Let h(d) be the second derivative of q(d). Factor h(r).
2*(r - 2)*(r + 1)/3
Let f(s) be the third derivative of s**8/2016 + s**7/630 - s**5/180 - s**4/144 - 2*s**2. What is b in f(b) = 0?
-1, 0, 1
Suppose 0 + 0*x - 1/4*x**2 + 1/4*x**3 = 0. What is x?
0, 1
Suppose -3*g - 35 = -4*y, y = -3*y + 4*g + 36. What is c in c**3 - y*c**3 + 6*c**3 = 0?
0
Let a(p) be the second derivative of p**6/50 - 3*p**5/100 - 3*p**4/20 + p**3/2 - 3*p**2/5 - 2*p. Suppose a(y) = 0. Calculate y.
-2, 1
Let f(c) be the first derivative of -3*c**4/20 - 26*c**3/5 - 507*c**2/10 + 24. Factor f(s).
-3*s*(s + 13)**2/5
Let i = -7 - -7. Suppose 0 = -i*y - y + 2. Factor 10/3*g**4 + 2/3*g**3 + 0*g + 0 + 0*g**y.
2*g**3*(5*g + 1)/3
Let w be ((-6)/(-9))/(2/3). Suppose 0 - w + 3 + 1 - 3*g**2 = 0. Calculate g.
-1, 1
Let i(d) be the third derivative of d**7/56 - 11*d**6/60 + 7*d**5/10 - d**4 + d**3 - 2*d**2. Let c(p) be the first derivative of i(p). What is n in c(n) = 0?
2/5, 2
Let l(w) = w**3 - 2*w**2 + w + 1. Let v be l(2). Let s = -12 + 14. What is r in 3*r**4 - r**4 + 9*r**s - 8*r**2 + 3*r**v = 0?
-1, -1/2, 0
Let w(l) = -l**2 - 4*l. Let s be w(-3). Let m be (-3)/((-4 + s)/1). Factor -2*i**2 + i**5 + 0*i + 4*i**2 - 3*i + 0*i + 2*i**m + 1 - 3*i**4.
(i - 1)**4*(i + 1)
Let v(k) be the third derivative of k**6/20 + k**5/10 - k**4/36 - k**3/9 + 6*k**2. Find s, given that v(s) = 0.
-1, -1/3, 1/3
Suppose 0 = -z + 4, -z + 0*z = -k + 12. Suppose 1 - k = -5*o. Determine a, given that 0*a**5 - 4*a**2 - 7*a**3 - 6*a**4 + 2*a**2 + a**o - 2*a**5 = 0.
-1, 0
Let q be ((-3814)/21)/(2/3). Let f = q + 273. Factor 6/7*v + 0*v**2 + f - 2/7*v**3.
-2*(v - 2)*(v + 1)**2/7
Let n(j) = -j + 17. Let q be n(12). Suppose -2 = -q*t + 4*t. Solve -t - 12*h - 35/2*h**2 = 0.
-2/5, -2/7
Let o = -1 - -5. Suppose -o*x - 4 = f - 5*f, 4*x - 16 = 0. Factor n**3 - n**4 + 3*n**3 - 3*n**3 - n**f + n**2.
-n**2*(n - 1)*(n + 1)**2
Let v(w) be the second derivative of -w**7/420 + w**6/120 - w**5/120 + 3*w**2/2 + 5*w. Let r(a) be the first derivative of v(a). Find n, given that r(n) = 0.
0, 1
Let h = -401201/143028 - 2/3973. Let k = 32/9 + h. Factor 3/4 - 3/4*u**2 - k*u + 3/4*u**3.
3*(u - 1)**2*(u + 1)/4
Let s(i) = -2*i**2 + 11*i + 6. Let j(l) = -l**2 + 5*l + 3. Let o(v) = 7*j(v) - 3*s(v). Factor o(x).
-(x - 3)*(x + 1)
Let f = 718/7 + -2767/28. Let 0 + 15/4*g**3 + 3/4*g - 15/4*g**4 + f*g**2 - 9/2*g**5 = 0. Calculate g.
-1, -1/2, -1/3, 0, 1
Let q(u) be the second derivative of 2*u**6/15 - u**4/3 + 9*u. Solve q(a) = 0 for a.
-1, 0, 1
Let y(k) = k + 1. Let n be y(-2). Let i be (0/n)/(-1)*-1. Factor 1/3*h**4 + i - 1/3*h**3 + 1/3*h - 1/3*h**2.
h*(h - 1)**2*(h + 1)/3
Determine b so that -1/4 - 1/4*b**3 + 1/4*b**2 + 1/4*b = 0.
-1, 1
Suppose 0 + 1/4*d**2 + 1/4*d = 0. What is d?
-1, 0
Let j(u) be the first derivative of -u**2 + 1/135*u**6 + 0*u**4 + 0*u**3 + 1 - 1/270*u**5 + 0*u. Let t(c) be the second derivative of j(c). Factor t(y).
2*y**2*(4*y - 1)/9
Let g be -3*(-2 - 1) - -2. Let b = -9 + g. Factor -3 + 2*n**2 + 1 + 2 + 2*n - 2*n**3 - b*n**4.
-2*n*(n - 1)*(n + 1)**2
Let q(l) be the third derivative of 1/1365*l**7 + 1/65*l**5 + 0 + 1/156*l**6 - 8/39*l**3 - 1/39*l**4 + 0*l + 4*l**2. Factor q(x).
2*(x - 1)*(x + 2)**3/13
Suppose -4*m + m + 13 = -2*s, 2*m - 4*s - 14 = 0. Let b be 4 + ((-30)/6 - -3). Factor 0*h - 2/5*h**b - 2/5*h**m + 0.
-2*h**2*(h + 1)/5
Let s(a) be the second derivative of -3*a**5/100 + a**4/5 - a**3/10 - 9*a**2/5 - a + 11. Suppose s(c) = 0. What is c?
-1, 2, 3
Let v(k) be the third derivative of k**8/1400 - 2*k**7/2625 - k**6/1500 - 15*k**2. Let v(d) = 0. Calculate d.
-1/3, 0, 1
Let z(y) be the third derivative of y**8/336 + y**7/210 - y**6/60 - y**5/30 + y**4/24 + y**3/6 + 3*y**2. Factor z(j).
(j - 1)**2*(j + 1)**3
Let t(r) be the first derivative of -3 - 9/4*r**3 + 21/16*r**4 + 3/4*r**2 + 0*r. Factor t(o).
3*o*(o - 1)*(7*o - 2)/4
Let w(j) = 32*j**4 - 51*j**3 + 21*j**2 + 8*j - 5. Let t(p) = 48*p**4 - 77*p**3 + 31*p**2 + 12*p - 7. Let c(o) = -5*t(o) + 7*w(o). Solve c(q) = 0.
-1/4, 0, 1
Let x(q) be the third derivative of q**7/70 - q**6/24 + 7*q**5/180 - q**4/72 + q**2. Suppose x(y) = 0. Calculate y.
0, 1/3, 1
Suppose 2*s + 2*z = -22, 4*z - 16 = s - 0*z. Let q = -23/2 - s. Factor 0 + q*j - 1/4*j**2 - 1/4*j**3.
-j*(j - 1)*(j + 2)/4
Suppose 54 = 5*v + 9. Let f be (-6)/v*6/(-8). Factor r**2 - f*r**4 - r**3 + 1/2*r**5 + 1/2*r - 1/2.
(r - 1)**3*(r + 1)**2/2
Suppose -8*v + 213 = -4*v + 3*d, -2*d - 238 = -4*v. Let g = -283/5 + v. Let -g*m**2 + 0 + 2/5*m = 0. What is m?
0, 1
Let q(i) = -i**3 - i**2 - i. Let u(d) = -10*d**3 - 16*d**2 - 10*d. Let p(w) = -12*q(w) + u(w). Factor p(m).
2*m*(m - 1)**2
Let n(l) be the third derivative of 0*l**3 + 1/420*l**5 - 3*l**2 + 0*l - 1/168*l**4 + 0. Factor n(s).
s*(s - 1)/7
Let y(x) be the first derivative of 4*x**3/21 + 8*x**2/7 + 16*x/7 + 38. Factor y(h).
4*(h + 2)**2/7
Let m(d) = 4*d - 1. Let w be m(1). Let p(g) = -g**3 - 7*g**2 - 8*g - 7. Let s be p(-6). Factor -3*a**w - s*a**3 - 2 + 4*a**3 + 3*a**3 + 3*a.
-(a - 1)**2*(a + 2)
Let k(n) be the second derivative of n**5/30 - n**3/3 - n**2/2 + 5*n. Let o(a) be the first derivative of k(a). Factor o(q).
2*(q - 1)*(q + 1)
Let s(l) be the third derivative of -l**5/60 + 11*l**4/12 - 121*l**3/6 - 2*l**2 - 2*l. Factor s(j).
-(j - 11)**2
Let c(o) be the second derivative of 0*o**5 + 1/21*o**4 - 1/105*o**6 - 1/7*o**2 + 0 + 6*o + 0*o**3. Find q, given that c(q) = 0.
-1, 1
Suppose 0*g - 4*o - 12 = 3*g, -2*g = -4*o - 12. Let u(w) be the third derivative of 1/30*w**5 + g*w + 0*w**4 + 0*w**3 + 0 + w**2. Suppose u(x) = 0. Calculate x.
0
Determine m so that 6 + 4*m + 11*m - 6*m**3 + 0*m**2 + 3*m**2 = 0.
-1, -1/2, 2
Suppose 0 = 5*n - 90 