uppose m(k) = 0. What is k?
-2, 0
Let m be ((-15)/(-27))/((-300)/(-90)). Factor -1/2*u + m + 1/3*u**2.
(u - 1)*(2*u - 1)/6
Suppose -k + 8 = d, -2*k + 3*d - 6 = -42. Let n be 3/(-8)*k/(-18). Factor -1 - n*z**2 - z.
-(z + 2)**2/4
Let g = -44 - -46. Factor 8/5*d - 8/5 - 2/5*d**g.
-2*(d - 2)**2/5
Let j(f) = -14*f**2 + 14. Let x(z) = 1 - 6 + 6*z**2 - z**2. Suppose 16 = -0*s + 2*s - 2*o, -s - 3*o = -20. Let n(q) = s*x(q) + 4*j(q). Let n(k) = 0. What is k?
-1, 1
Let c = -66 - -69. Let l(p) be the first derivative of -1/12*p**c + 0*p - 1/8*p**2 - 3. Suppose l(y) = 0. Calculate y.
-1, 0
Suppose 0 = -2*p - 4*y + 62, 0*p + 5*y - 43 = -p. Let g = p - 21. Factor -1/5*n**5 + 0 - 2/5*n**4 + 2/5*n**g + 1/5*n + 0*n**3.
-n*(n - 1)*(n + 1)**3/5
Let p = 12/305 + -26/1281. Let t(u) be the third derivative of 0*u**4 - 2*u**2 + 1/60*u**6 + 1/168*u**8 + 0*u**5 + 0*u - p*u**7 + 0*u**3 + 0. Solve t(q) = 0.
0, 1
Let h(j) be the third derivative of 0 + 0*j**6 + 0*j**3 + 0*j**5 - 1/336*j**8 + 0*j**4 - 1/210*j**7 - 4*j**2 + 0*j. Factor h(t).
-t**4*(t + 1)
Let c(b) be the third derivative of -b**6/480 + b**5/60 - b**4/32 + 11*b**2. Find j, given that c(j) = 0.
0, 1, 3
Let j(z) be the second derivative of 0 + 1/2*z**4 + 2*z + 4/3*z**3 + z**2. Find g such that j(g) = 0.
-1, -1/3
Let c(o) be the first derivative of -o**4/4 - o**3 - 3*o**2/2 + 4*o + 5. Let h(r) be the first derivative of c(r). Solve h(p) = 0.
-1
Let w(j) be the first derivative of j**9/10584 + j**8/5880 - j**7/2940 - j**6/1260 + j**3 + 1. Let m(i) be the third derivative of w(i). Factor m(a).
2*a**2*(a - 1)*(a + 1)**2/7
Find j, given that -9*j - 3*j**2 - 6*j - 3*j + 9*j = 0.
-3, 0
Let y = 17/2 - 25/3. Suppose 1/2*v**3 + 0 + 0*v + 1/2*v**4 + y*v**5 + 1/6*v**2 = 0. Calculate v.
-1, 0
Let x be 0*(2 + -1)*1. Let a(w) be the third derivative of 1/30*w**5 + 0 + 1/315*w**7 + w**2 + 0*w**3 + 1/60*w**6 + x*w + 1/36*w**4. Factor a(s).
2*s*(s + 1)**3/3
Let l(g) = g**3 - 12*g**2 + 13*g + 14. Let w be l(11). Let h = w - 34. Solve 10/7*s - 4/7 + 2*s**h = 0.
-1, 2/7
Let o(g) be the second derivative of g**4/4 + 3*g**3/2 + 3*g**2 + 5*g. Determine x so that o(x) = 0.
-2, -1
Solve 21/2*x**2 - 21/2*x**4 - 3/4*x**5 + 0 - 36*x**3 + 147/4*x = 0 for x.
-7, -1, 0, 1
Let i(s) = -s**3 - s**2 + 5*s - 6. Let p(h) = -h**2. Let q(v) = -i(v) + 3*p(v). Solve q(o) = 0 for o.
-2, 1, 3
Suppose n - 30 = -4*n. Let r(g) = 5*g**2 - 9*g + 4. Let i(t) = -4*t**2 + 8*t - 4. Let b(m) = n*i(m) + 4*r(m). Suppose b(y) = 0. What is y?
1, 2
Let b be (10/(-20))/(2/(-16)). Suppose 7*j**3 + 6*j**2 + 5*j**3 + j**4 + 2*j**b - 3*j**3 = 0. What is j?
-2, -1, 0
Suppose -5*r + 7 = -8. Determine k, given that -4 + 4*k**2 + 4*k - k - r*k**3 + k**3 - k = 0.
-1, 1, 2
Let l be (-345)/(-138)*16/10. Let 8/7*a**2 - 2/7*a**3 - 1/7 - a**l - 2/7*a + 4/7*a**5 = 0. Calculate a.
-1, -1/4, 1
Let u be 21/(-18)*(-12)/28. Find n such that u*n**4 - n**2 - 1/2*n**5 - 1/2*n + 1/2 + n**3 = 0.
-1, 1
Let p(u) be the second derivative of u**6/180 - u**5/60 - 5*u**3/3 - u. Let v(y) be the second derivative of p(y). What is m in v(m) = 0?
0, 1
Suppose 2/5*b**2 - 8/5*b + 8/5 = 0. What is b?
2
Let m(o) be the second derivative of -3*o + 0 - 1/2*o**3 - 1/12*o**4 + o**2. Let u(n) = 4*n**2 + 9*n - 6. Let j(c) = 21*m(c) + 6*u(c). Solve j(f) = 0 for f.
1, 2
Let u(i) = i**4 + 2*i**3 + 4*i**2 + 12*i + 9. Let m(n) = -n**4 - 3*n**3 - 5*n**2 - 12*n - 9. Let f(z) = -6*m(z) - 7*u(z). Factor f(a).
-(a - 3)**2*(a + 1)**2
Let c(b) be the first derivative of -b**5/50 + 11*b**4/10 - 121*b**3/5 + 1331*b**2/5 - 14641*b/10 - 23. Factor c(a).
-(a - 11)**4/10
Let m(w) be the first derivative of w**8/336 + w**7/70 + w**6/40 + w**5/60 - 3*w**2/2 + 2. Let s(j) be the second derivative of m(j). Factor s(a).
a**2*(a + 1)**3
Let d(y) = y**2 + 3*y - 2. Let v be d(-5). Solve 2 + 17/2*m**2 - 5/2*m**3 - v*m = 0.
2/5, 1, 2
Let h(v) be the first derivative of 1/5*v**5 - 2*v - 5/2*v**2 + 1/4*v**4 + 4 - v**3. Find l such that h(l) = 0.
-1, 2
Let d(i) be the first derivative of i**4/8 - i**3/18 - i**2/4 + i/6 - 8. Factor d(v).
(v - 1)*(v + 1)*(3*v - 1)/6
Let g(y) be the first derivative of -y**4/10 + 2*y**3/5 + y**2/5 - 6*y/5 + 58. Solve g(i) = 0 for i.
-1, 1, 3
Let y(b) = 3*b**2 - 2*b - 1. Let r be y(-3). Suppose 30*g**2 - r*g**2 + 1 + g**4 + 0*g**4 = 0. Calculate g.
-1, 1
Factor -2*s**2 + 1/4*s - 9/4*s**3 + 0.
-s*(s + 1)*(9*s - 1)/4
Find d, given that -5/2*d - 2*d**3 - 1 + 11/2*d**2 = 0.
-1/4, 1, 2
Let x(m) be the first derivative of 4*m**3/21 + 4*m**2/7 + 10. Factor x(u).
4*u*(u + 2)/7
Let j(w) be the third derivative of -w**8/10080 - w**7/840 - w**6/180 - w**5/20 - w**2. Let y(h) be the third derivative of j(h). Factor y(o).
-2*(o + 1)*(o + 2)
Let h(q) be the first derivative of -q**4/13 - 10*q**3/39 + 3*q**2/13 + 64. Let h(a) = 0. Calculate a.
-3, 0, 1/2
Let d(o) be the third derivative of o**6/480 - o**5/120 - o**4/96 + o**3/12 + 25*o**2. Find g, given that d(g) = 0.
-1, 1, 2
Let d(x) be the second derivative of x**6/80 + 3*x**5/16 + x**4/4 - 5*x**3/8 - 27*x**2/16 - 3*x + 3. Suppose d(p) = 0. What is p?
-9, -1, 1
Suppose 0*r = -r. Suppose r = -x + 5. Factor 0*v - x*v**3 + 3*v**3 + 2*v.
-2*v*(v - 1)*(v + 1)
Determine v so that 2*v**3 - 12*v + 19*v - 9*v = 0.
-1, 0, 1
Let j = 18903 + -623708/33. Let z = 45/11 - j. Find q such that 2/3*q**4 - z*q**3 + 0 + 0*q + 0*q**2 = 0.
0, 2
Let o = 7 + -2. Let y(p) = -p**2 + 6*p - 3. Let l be y(o). Factor -2*h**3 + 3*h**2 + 1/2 - l*h + 1/2*h**4.
(h - 1)**4/2
Let a(u) be the second derivative of u**5/80 + 7*u**4/48 + u**3/3 - 2*u**2 + 38*u. Let a(z) = 0. Calculate z.
-4, 1
Factor -1/2*d - 1/4*d**2 + 3/4.
-(d - 1)*(d + 3)/4
Factor -3*d**2 - 21/2*d + 3/2*d**3 - 6.
3*(d - 4)*(d + 1)**2/2
Let n(i) = -i**3 + 11*i**2 - 49*i + 6. Let l(q) = q**3 - 10*q**2 + 49*q - 8. Let y(r) = 3*l(r) + 4*n(r). Determine f so that y(f) = 0.
0, 7
Let x = 8/17 - -1/34. Factor -x*s**2 + s + 0.
-s*(s - 2)/2
Suppose 0 = -4*v + v + 15. Let f(r) be the third derivative of 1/30*r**v + 1/6*r**4 + 0*r + 0 - 3*r**2 + 1/3*r**3. Find g such that f(g) = 0.
-1
Let m(j) be the second derivative of -j**5/90 + j**4/27 + j**3/27 - 2*j**2/9 + 7*j. Determine k so that m(k) = 0.
-1, 1, 2
Let d(k) be the second derivative of k**4/108 - k**2/18 + 5*k. Factor d(q).
(q - 1)*(q + 1)/9
Let m(z) be the third derivative of -1/280*z**7 + 0*z**4 + 0*z**3 + 0 + 3*z**2 + 1/160*z**6 - 1/240*z**5 + 0*z + 1/1344*z**8. Suppose m(q) = 0. What is q?
0, 1
Let q = 2 - 2. Suppose q = -3*c - 2*s - 1, -4*c + 2*s = -s - 27. Factor -3*w + w**c + w**3 + 2*w - w**5.
-w*(w - 1)**2*(w + 1)**2
Let q(s) = -s**2. Let d(x) = -16*x**2 - 8*x + 4. Let m(n) = -d(n) + 20*q(n). Let m(w) = 0. Calculate w.
1
Let l(z) = z**3 - 10*z**2 - 13*z - 5. Let n be l(11). Let v be n/(-18)*(-4)/(-3). Factor 1/2 + 3/4*y + 1/4*y**v.
(y + 1)*(y + 2)/4
Let m = -1/20 - -4/5. Let h(j) be the first derivative of -1 - 1/4*j**2 - 15/16*j**4 + 0*j - 11/20*j**5 - m*j**3 - 1/8*j**6. What is x in h(x) = 0?
-1, -2/3, 0
Let d(r) be the third derivative of -r**8/8960 + r**6/960 - r**4/24 - 2*r**2. Let s(u) be the second derivative of d(u). Factor s(h).
-3*h*(h - 1)*(h + 1)/4
Factor -2*s**5 - 364*s**2 + 4*s - 6*s**5 + 356*s**2 + 4*s**5 + 8*s**4.
-4*s*(s - 1)**3*(s + 1)
Let j(a) be the second derivative of -a**5/3 + 32*a**4/9 - 74*a**3/9 + 20*a**2/3 + 2*a. What is q in j(q) = 0?
2/5, 1, 5
Factor 2 - i**2 - 10*i + 0 + 3*i + 6*i.
-(i - 1)*(i + 2)
Let c(o) = -o - 3. Let u be c(-4). Let v be -1*u + 9/9. Solve -2/3*r - 1/3*r**2 + v + 1/3*r**3 = 0 for r.
-1, 0, 2
Let r(f) be the first derivative of -4*f**5/25 + 2*f**4/5 + 11*f**3/15 + 3*f**2/10 + 5. Factor r(t).
-t*(t - 3)*(2*t + 1)**2/5
Let w = 135/16 + -35/16. Let h = 7 - w. Factor 1/2 + 1/4*s**2 + h*s.
(s + 1)*(s + 2)/4
Let w(a) = -3*a**3 + a**2 + 2*a. Let m be w(-1). Factor -2/9*c - 4/9*c**m + 0 - 2/9*c**3.
-2*c*(c + 1)**2/9
Let q(g) be the first derivative of -g**6/105 - g**5/70 + g**4/21 - 2*g + 3. Let f(j) be the first derivative of q(j). Find a such that f(a) = 0.
-2, 0, 1
Let o = 13 - 9. Factor -324*g + 162*g**2 - 36*g**3 + o*g**4 + 5*g**4 + 243 - 6*g**4.
3*(g - 3)**4
Let c(r) be the first derivative of 0*r**2 + 1/8*r**4 + 1/36*r**6 + 1/18*r**3 + 0*r - 2 + 1/10*r**5. Factor c(b).
b**2*(b + 1)**3/6
Let z(p) be the first derivative of p**6/6 - p**4/4 -