ive of q(x). Factor a(u).
-2*u*(u - 1)*(u + 1)**2/7
Let f = 542/9 + -60. Factor -f*c**2 + 0 - 2/9*c.
-2*c*(c + 1)/9
Let w(n) = n + 13. Let l be w(-10). Let z(m) be the second derivative of -m + 0*m**2 + 0*m**l + 0*m**4 + 0 - 1/10*m**5. Find y such that z(y) = 0.
0
Let g = -134 - -136. Factor 0 + 3/2*b**g + 3/2*b.
3*b*(b + 1)/2
Let z(p) be the first derivative of -p**4/54 - 3*p + 4. Let u(y) be the first derivative of z(y). Let u(v) = 0. Calculate v.
0
Suppose 3/4*a - 3/4*a**3 - 1 - 1/4*a**4 + 5/4*a**2 = 0. What is a?
-4, -1, 1
Let z(b) be the second derivative of 1/24*b**3 + 1/168*b**7 - 1/120*b**6 + 0 - 1/40*b**5 - 1/8*b**2 + b + 1/24*b**4. Factor z(s).
(s - 1)**3*(s + 1)**2/4
Let i = -3542/3 - -1144. Let m = i - -37. Suppose 2/3*g + 1/3*g**2 + m = 0. Calculate g.
-1
Let v(l) = l**3 + 2*l**2 - 3*l + 4. Let i be v(-3). Let t be (3/(-6))/(i/(-16)). Factor -z**2 - 5*z**3 - 5*z**4 - t*z**2 + 6*z**2 + 7*z - 2*z**3 + 2.
-(z - 1)*(z + 1)**2*(5*z + 2)
Let k(s) be the third derivative of s**8/168 + 2*s**7/35 + s**6/5 + s**5/3 + s**4/4 - 37*s**2. Solve k(b) = 0 for b.
-3, -1, 0
Let w = 12 - 12. Suppose w*l = -l. Suppose 2/5*h + 2/5*h**2 + l = 0. Calculate h.
-1, 0
Let y be 1301/(-8) + 24/(-64). Let z = y - -1143/7. Suppose -2/7*f + z - 4/7*f**2 = 0. Calculate f.
-1, 1/2
Let g be (-18)/30*(-2 - 3). Let m(v) be the first derivative of 2 - 1/2*v - 1/2*v**2 - 1/6*v**g. Suppose m(i) = 0. What is i?
-1
Let h(k) be the second derivative of k**4/3 + 20*k**3/3 + 50*k**2 + 12*k. Factor h(y).
4*(y + 5)**2
Let k be (108/(-42))/9 - (-2)/7. Factor 0*u**4 - 4/5*u**5 + k*u**2 - 4/5*u + 0 + 8/5*u**3.
-4*u*(u - 1)**2*(u + 1)**2/5
Let i(k) be the third derivative of -k**10/15120 + k**8/1680 - k**6/360 - k**4/24 + 2*k**2. Let y(h) be the second derivative of i(h). Factor y(x).
-2*x*(x - 1)**2*(x + 1)**2
Factor -12*y**3 + 8*y**2 - 4*y + 8*y**3 + 0*y**2.
-4*y*(y - 1)**2
Let u be ((-4)/14)/(9*9/(-378)). Let -u + 14/3*b - 10/3*b**2 = 0. What is b?
2/5, 1
Let w(k) be the first derivative of -4/21*k**3 + 0*k - 3 + 1/14*k**4 + 1/7*k**2. Factor w(n).
2*n*(n - 1)**2/7
Let a(o) = 6*o**2 - 4*o - 6. Suppose -c - c + 8 = 0. Let q(s) = 5*s**2 - 3*s - 5. Let h = 32 + -35. Let l(d) = c*q(d) + h*a(d). Determine v so that l(v) = 0.
-1, 1
Let m(w) = 21*w**3 - 2*w**2 + 2*w - 1. Let i be m(1). Suppose -2*p + i = 3*p. Let 0*t**p + t**4 + t**2 + 6*t**3 + 2*t**3 - 6*t**3 = 0. What is t?
-1, 0
Let o be (1454*2/48)/(-3). Let h = -79/4 - o. Factor h*p - 2/9*p**2 - 2/9.
-2*(p - 1)**2/9
Let m be 0 + 2 - (1 - 0). Factor 0 + 0*z**3 - 5 - 3*z**3 + 9*z - m.
-3*(z - 1)**2*(z + 2)
Let j(i) = -5*i**4 - 20*i**3 + 33*i**2 + 25*i - 23. Let b(u) = -u**4 - 5*u**3 + 8*u**2 + 6*u - 6. Let m(k) = 9*b(k) - 2*j(k). Find d, given that m(d) = 0.
-1, 2
Factor -2*h**2 - h**2 + h**2 - h**2 + 12.
-3*(h - 2)*(h + 2)
Find d, given that 1/4*d**3 + 0*d + 5/4*d**2 + 0 = 0.
-5, 0
Suppose -3*f + 2*z + 10 = z, -5*z - 20 = 0. Let j(h) be the third derivative of -1/12*h**4 + 2*h**f + 0*h - 1/30*h**5 + 0*h**3 + 0. Factor j(b).
-2*b*(b + 1)
Suppose -j = -5*t + 2*j + 20, -5*j = 0. Suppose 16 = -3*i + 7*i, 3*y + t*i - 31 = 0. What is p in p**5 - p**3 - p**4 + 6*p**2 - 5*p**2 + 0*p**y = 0?
-1, 0, 1
Let j(p) be the third derivative of -1/420*p**6 + 0*p + 0 + 1/105*p**5 + 0*p**3 - 2*p**2 - 1/84*p**4. Factor j(y).
-2*y*(y - 1)**2/7
Factor -7*d**5 + 13*d**5 + d**2 - 7*d**5 + 2*d**3 - d**3 - d**4.
-d**2*(d - 1)*(d + 1)**2
Suppose 2*l + 6*j = 2*j, 5*l - 2*j = 0. Factor -2/3*x**2 + 0*x**3 + 1/3 + l*x + 1/3*x**4.
(x - 1)**2*(x + 1)**2/3
Let j(a) be the first derivative of 5*a**4/4 - 10*a**3 + 30*a**2 - 40*a - 41. Factor j(f).
5*(f - 2)**3
Let g(z) be the first derivative of 0*z + 0*z**4 + 1/210*z**5 + 0*z**3 - 1/2*z**2 + 2. Let h(j) be the second derivative of g(j). Factor h(f).
2*f**2/7
Let f(q) be the third derivative of 7/24*q**4 - 1/6*q**3 - 2*q**2 + 13/120*q**6 - 2/105*q**7 - 1/4*q**5 + 0 + 0*q. Suppose f(a) = 0. What is a?
1/4, 1
Let z(t) be the second derivative of -t**6/120 - t**5/80 + 5*t**4/48 - t**3/8 + 9*t. Find f such that z(f) = 0.
-3, 0, 1
Let a(d) = -d**2 - 5*d + 6. Let f be a(-6). Let o(n) be the first derivative of 1 + 0*n**2 + 1/6*n**3 + f*n**4 + 0*n - 1/10*n**5. Find w, given that o(w) = 0.
-1, 0, 1
Let q = 94 + -94. Suppose -16/7*r**4 + 0*r + 4/7*r**2 + 10/7*r**5 + 2/7*r**3 + q = 0. Calculate r.
-2/5, 0, 1
Let z(m) be the first derivative of 3*m**4/8 - m**3 - 7. Let z(x) = 0. Calculate x.
0, 2
Let i(g) be the first derivative of -3*g**5/5 + 3*g**4/2 - 3*g**2 + 3*g - 43. Determine y, given that i(y) = 0.
-1, 1
Let g(r) = -4*r**5 - r**3 + 3*r**5 + 0*r**3. Let z(i) = 12*i**5 + 4*i**4 + 12*i**3. Let b be -4 - (-3 + 2) - 7. Let w(k) = b*g(k) - z(k). Solve w(a) = 0 for a.
-1, 0
Let t(l) be the first derivative of -l**4/48 - l**3/12 - l**2/8 - l - 2. Let v(y) be the first derivative of t(y). Factor v(c).
-(c + 1)**2/4
Let z = -4/15 - -23/30. Let l(u) be the first derivative of -2 - z*u**2 + 0*u + 2/3*u**3 - 1/4*u**4. Factor l(v).
-v*(v - 1)**2
Let t = 13 - 11. Let f(a) be the first derivative of 2/7*a - 1 + 0*a**t - 2/21*a**3. Factor f(u).
-2*(u - 1)*(u + 1)/7
Suppose -2/11*i - 12/11 + 2/11*i**2 = 0. Calculate i.
-2, 3
Let t(g) be the second derivative of 1/6*g**4 - 3*g**2 + 2/3*g**3 + 0 - 6*g. Factor t(l).
2*(l - 1)*(l + 3)
Let n(x) be the second derivative of 0 + 2/9*x**3 - 3*x + 1/36*x**4 + 2/3*x**2. Factor n(z).
(z + 2)**2/3
Let o = 4/49 - -38/49. Factor 2/7*a**2 + 4/7 - o*a.
2*(a - 2)*(a - 1)/7
Let l(o) be the first derivative of o**5/30 - o**4/8 + o**3/18 + o**2/4 - o/3 - 2. Suppose l(m) = 0. What is m?
-1, 1, 2
Suppose 2*c = 9 + 5. Let v = 9 - c. Let 2/7*l**5 - 2/7 - 4/7*l**3 + 4/7*l**v - 2/7*l**4 + 2/7*l = 0. Calculate l.
-1, 1
Suppose -4*f + 61 = 45. Determine b so that -1/4*b**f + 0*b + 1/2*b**2 - 1/4 + 0*b**3 = 0.
-1, 1
Let t(q) be the third derivative of -q**9/5040 - q**8/1120 + q**7/210 + q**6/30 - q**4/4 - 8*q**2. Let u(l) be the second derivative of t(l). Factor u(h).
-3*h*(h - 2)*(h + 2)**2
Let q(g) = 8*g**2 - 35*g - 53. Let l(h) = -12*h**2 + 53*h + 79. Let u(n) = -5*l(n) - 7*q(n). Factor u(c).
4*(c - 6)*(c + 1)
Let p(i) be the third derivative of -i**7/2100 + i**6/450 - i**5/300 + i**3 + 4*i**2. Let h(k) be the first derivative of p(k). Factor h(f).
-2*f*(f - 1)**2/5
Let y(s) = -5*s**2 - 2*s. Let n(t) = 14*t**2 + 5*t. Let b(u) = -4*n(u) - 11*y(u). Suppose b(j) = 0. Calculate j.
0, 2
Let l be 18/36*2*3. Factor 2*h**2 + 1 + 2*h**l - 7/2*h.
(h + 2)*(2*h - 1)**2/2
Factor 10/7*s - 2*s**2 + 6/7*s**3 - 2/7.
2*(s - 1)**2*(3*s - 1)/7
Suppose 2*t + 5*i = -4, -3*t + 7*t - 52 = 5*i. Let q = t - 6. Factor -20*b**4 + 0 + 0*b - 16/7*b**q + 50/7*b**5 + 88/7*b**3.
2*b**2*(b - 2)*(5*b - 2)**2/7
Suppose 2*w - 5 + 1 = 0. Find v such that -3*v**2 + 2*v**w - 2*v**4 - 2*v**2 + 5*v**2 = 0.
-1, 0, 1
Let z(i) = 2*i**2 + 4*i - 6. Let q(f) = 1 - 2*f + 4 - f**2 + 0 - 2. Let l(x) = -13*q(x) - 6*z(x). Solve l(k) = 0.
-3, 1
Let a(y) be the third derivative of y**9/3024 - y**8/840 + y**7/840 + y**3/3 - 2*y**2. Let v(t) be the first derivative of a(t). Solve v(s) = 0.
0, 1
Let p be (-5)/20*(-4)/5. Let a = -787/5 + 158. Factor p + 1/5*w**3 + 3/5*w**2 + a*w.
(w + 1)**3/5
Let n(w) be the third derivative of -w**6/540 + w**5/135 - w**4/108 - 6*w**2. Factor n(g).
-2*g*(g - 1)**2/9
Let d(i) be the first derivative of i**2/2 - 5*i + 16. Let s be d(9). Let 3*x**2 + 0 + 12/5*x**5 + 7*x**s + 2/5*x + 36/5*x**3 = 0. Calculate x.
-1, -2/3, -1/4, 0
Suppose 0 = 4*o + 2*c - 14, 3*o - 5*c - 4 = -0. Suppose 0 = -0*d - 3*d + o. Find r such that -4*r**3 - 12*r**2 - d - 4*r + 6*r**2 - r**4 + 0 = 0.
-1
Let b(z) be the third derivative of z**7/3780 - z**6/540 - z**4/12 - 2*z**2. Let y(h) be the second derivative of b(h). Factor y(o).
2*o*(o - 2)/3
Let r(o) = 7*o**3 - 19*o**2 - 7*o + 6. Let l = -5 - -11. Let k(i) = i**3 - 3*i**2 - i + 1. Let d(v) = l*r(v) - 39*k(v). Factor d(w).
3*(w - 1)*(w + 1)**2
Suppose -r = -4, 3*r = -2*a - a + 3. Let q(m) = -5*m**2 - 5*m - 8. Let l(k) = 4 + 9*k**2 + 2 + 8 + 2 + 11*k. Let v(t) = a*l(t) - 5*q(t). Solve v(z) = 0.
-2
Let d(u) be the second derivative of u**4/4 + 2*u**3 - 18*u. Factor d(p).
3*p*(p + 4)
Solve -20*f**2 + 4*f - 50*f**3 + 22*f**3 + 4*f = 0.
-1, 0, 2/7
Let z(o) be the first derivative of -2*o**6/3 - 12*o**5/5 + o**4 + 4*