(j + 1)
Let c(g) be the first derivative of 1/3*g**3 + 12 - 4*g**2 - 1/5*g**5 + 4*g - 1/6*g**6 + 5/4*g**4. Factor c(b).
-(b - 1)**3*(b + 2)**2
Let y(p) be the second derivative of p**5/10 - 13*p**4/6 + 40*p**3/3 - 36*p**2 - 2*p - 2. Factor y(u).
2*(u - 9)*(u - 2)**2
Let s(h) be the first derivative of h**9/6048 - h**8/1680 + h**6/360 - h**5/240 - 8*h**3/3 - 18. Let z(p) be the third derivative of s(p). Factor z(k).
k*(k - 1)**3*(k + 1)/2
Let n(w) be the second derivative of -3/4*w**4 + 1/20*w**5 - 27/2*w**2 + 0 + 9/2*w**3 + 3*w. Let n(h) = 0. Calculate h.
3
Determine r, given that -44/3*r**2 - r**3 - 16/3 + 21*r = 0.
-16, 1/3, 1
Let x(s) be the second derivative of s**5/5 + 6*s**4 + 34*s**3/3 + 19*s. Factor x(u).
4*u*(u + 1)*(u + 17)
Let q be 2380/220 + -11 - 2/(-11). Factor 2/3*p**2 + 0*p + q + 2/3*p**4 - 4/3*p**3.
2*p**2*(p - 1)**2/3
Let f(n) = -3 + 3 + n + 0 - n**2. Let b(o) = -8*o**2 + 11*o. Let g(s) = -4*b(s) + 36*f(s). Find a such that g(a) = 0.
-2, 0
Let w(a) be the first derivative of -2*a**5/55 + 4*a**3/11 - 8*a**2/11 + 6*a/11 + 16. Solve w(k) = 0.
-3, 1
Determine h so that 0 - 105*h**2 - 207/2*h - 3/2*h**3 = 0.
-69, -1, 0
Let f(h) be the first derivative of -h**8/840 - h**7/140 + 5*h**3/3 + 7. Let i(w) be the third derivative of f(w). Determine c, given that i(c) = 0.
-3, 0
Let t be (4014/9)/(8/3). Let l = 168 - t. Suppose 0 + 1/4*f**4 - l*f - 5/4*f**2 - 1/4*f**3 = 0. Calculate f.
-1, 0, 3
Let i = 176/5 - 35. Let m(t) be the first derivative of 0*t + i*t**3 + 2 + 0*t**2. Factor m(h).
3*h**2/5
Let q(r) = -r**3 + r + 1. Let b(f) = -2*f**3 + 11*f**2 + 17*f + 8. Let d(c) = -b(c) + 4*q(c). Factor d(n).
-(n + 1)*(n + 4)*(2*n + 1)
Let g be (14/8)/((-9240)/(-2112)). Let -g*p**4 - 8/5*p**3 - 2*p**2 + 0 - 4/5*p = 0. What is p?
-2, -1, 0
Let y(a) be the first derivative of -a**5 + 15*a**4/4 + 5*a**3/3 - 15*a**2/2 + 137. Solve y(b) = 0 for b.
-1, 0, 1, 3
Let v(t) = t**2 - 2*t + 4. Let n(r) = 2*r**2 - r + 5. Let c be (10/(-12))/(5/(-30)). Let x(m) = c*v(m) - 4*n(m). Factor x(d).
-3*d*(d + 2)
Let f be ((-8)/48)/(-4 - (-35)/9). Factor 4/3*c**3 + c**2 + 0 - c**4 - f*c + 1/6*c**5.
c*(c - 3)**2*(c - 1)*(c + 1)/6
Let f = -2 - -5. Suppose f = -4*r + 7*r. Solve 2*n**2 - 10*n - n**2 - 7 - 3*n**2 - r = 0.
-4, -1
Let i be (-56)/(-11) + 22/(-242). Let -4/5*u**i - 4/5*u + 4/5 + 4/5*u**4 + 8/5*u**3 - 8/5*u**2 = 0. Calculate u.
-1, 1
Let d be (3/(-21))/(2 - 132/63). Let o(z) be the first derivative of -1/3*z**3 - d*z**4 + 6 - 2/3*z**6 + 0*z + 0*z**2 - 9/5*z**5. Suppose o(f) = 0. What is f?
-1, -1/4, 0
Let a be 240/360*(7 - 1)/2. Factor -243/7 - 3/7*u**a + 54/7*u.
-3*(u - 9)**2/7
Let o(d) be the third derivative of -25*d**8/336 + 3*d**7/14 + d**6/24 - 3*d**5/4 + 5*d**4/6 + 6*d**2 - 13. Solve o(p) = 0.
-1, 0, 4/5, 1
Factor 0 - 2/21*q**2 + 0*q + 2/21*q**3.
2*q**2*(q - 1)/21
Let w = -335 - -2011/6. Let c(l) be the second derivative of -l**2 + 0 + 0*l**3 + w*l**4 + l. Factor c(r).
2*(r - 1)*(r + 1)
Let q(t) be the second derivative of -11/2*t**2 - 1/20*t**5 - 9*t + 2*t**3 + 0 + 0*t**4. Let f(u) be the first derivative of q(u). Factor f(b).
-3*(b - 2)*(b + 2)
Factor 40/11*y**2 + 14*y - 44 + 2/11*y**3.
2*(y - 2)*(y + 11)**2/11
Let f(x) be the first derivative of 3*x**5/10 - 3*x**4/4 + 384. Factor f(d).
3*d**3*(d - 2)/2
Factor 800 - 254*l + 8*l**2 + 58*l - 704.
4*(l - 24)*(2*l - 1)
Let o(m) be the second derivative of -m**7/210 + m**6/90 + m**3/3 + 11*m. Let p(n) be the second derivative of o(n). Suppose p(h) = 0. Calculate h.
0, 1
Let r be 0/(2 - (-3 + -2)). Let s(p) be the third derivative of 0*p**4 + r - 8*p**2 + 1/270*p**5 + 0*p + 0*p**3. Suppose s(h) = 0. Calculate h.
0
Let u(f) be the second derivative of f**4/96 - 17*f**3/12 + 289*f**2/4 + 168*f. Determine l, given that u(l) = 0.
34
Let h(u) = u**3 - 4*u**2 - 15*u + 6. Let w(p) = -5*p**2 - 15*p + 5. Let x(k) = -5*h(k) + 4*w(k). What is i in x(i) = 0?
-2, 1
Let l be 13/6 - 12/8. Let f(k) be the first derivative of 1 - l*k**3 - k**4 + 0*k - 2/5*k**5 + 0*k**2. Solve f(u) = 0.
-1, 0
Factor -2/17*u**2 - 8192/17 + 256/17*u.
-2*(u - 64)**2/17
Let n(j) be the second derivative of 147*j**5/5 - 7*j**4 + j**3/2 + j - 18. Suppose n(w) = 0. Calculate w.
0, 1/14
Determine b so that -3/4*b**3 - 15/2 + 9/2*b**2 - 9/4*b = 0.
-1, 2, 5
Let s be 63/2*(-12)/(-18). Let j be (s/(-42))/((-1)/4). Factor -16*z + 56 + 0*z**2 - 24 + j*z**2.
2*(z - 4)**2
Let j(a) = -32*a**2 + 48*a - 40. Let h(c) be the second derivative of 13*c**4/12 - 19*c**3/6 + 8*c**2 + 17*c. Let z(f) = -12*h(f) - 5*j(f). Factor z(s).
4*(s - 2)*(s - 1)
Let f be 2*9/36 + 1*(-6)/24. Find r such that -f - 1/4*r + 1/4*r**3 + 1/4*r**2 = 0.
-1, 1
Let m(s) be the first derivative of -s**3/7 + 291*s**2/14 + 337. Let m(q) = 0. What is q?
0, 97
Let q(w) be the second derivative of -w**4/18 + 2*w**3 - 17*w**2/3 + 125*w - 1. Solve q(n) = 0.
1, 17
Let w = -1/30721 + -20951713/276489. Let r = w - -76. Factor r*s**2 + 0*s + 0 + 2/9*s**3.
2*s**2*(s + 1)/9
Let u(f) be the second derivative of f**7/4410 - f**5/210 + 3*f**4/4 + 10*f. Let j(s) be the third derivative of u(s). Factor j(d).
4*(d - 1)*(d + 1)/7
Let p(i) be the second derivative of 2*i**7/21 + 23*i. Factor p(x).
4*x**5
Factor 3/4*l**3 - 21/4*l - 9/2 + 0*l**2.
3*(l - 3)*(l + 1)*(l + 2)/4
Suppose t + 3*m + 12 = 0, 2*m - 6 = -16. Let j(k) be the first derivative of 2/3*k**3 + t*k**2 + 4*k + 4. Factor j(p).
2*(p + 1)*(p + 2)
Let s be (15/(-2))/((-11)/(-22)). Let g(o) = 6*o**3 - 90*o**2 + 147*o - 78. Let x(u) = u**3 - 13*u**2 + 21*u - 11. Let h(k) = s*x(k) + 2*g(k). Factor h(w).
-3*(w - 3)*(w - 1)**2
Let s = 3188647/24 + -132900. Let i = -118/3 - s. Factor -3/4*g - i*g**2 + 0.
-3*g*(g + 2)/8
Let f(x) be the first derivative of -x**7/210 + x**6/45 + x**5/30 - x**4/3 + 7*x**3 - 7. Let c(k) be the third derivative of f(k). Solve c(i) = 0 for i.
-1, 1, 2
Let z(x) = x**3 - 31*x**2 - 7*x + 32. Let i(k) = k**3 - 15*k**2 - 3*k + 16. Let g be 5/((-40)/4)*(1 - 15). Let u(o) = g*i(o) - 3*z(o). Factor u(j).
4*(j - 2)**2*(j + 1)
Let w be 48/27 + 84/378. Solve 58/3*y**w + 10/3*y**4 - 14*y**3 - 10*y + 4/3 = 0.
1/5, 1, 2
Let p(t) = t**3 - 168*t**2 + 1171*t + 5. Let g(i) = 3*i**3 - 588*i**2 + 4098*i + 18. Let v(a) = 5*g(a) - 18*p(a). What is z in v(z) = 0?
0, 14
Let f(z) be the third derivative of -z**6/30 + 7*z**5/15 - 11*z**4/6 + 10*z**3/3 - z**2 - 33. Determine j, given that f(j) = 0.
1, 5
Let m(j) = 77*j**4 + 12*j**3 - 11*j**2 - 3*j - 3. Let z(y) = -155*y**4 - 24*y**3 + 21*y**2 + 5*y + 5. Let r(x) = 5*m(x) + 3*z(x). Solve r(f) = 0.
-2/5, 0, 1/4
Let f = -365 + 1827/5. Factor -f*l + 2/5*l**3 + 0*l**2 + 1/5*l**4 - 1/5.
(l - 1)*(l + 1)**3/5
Let r(v) be the third derivative of 0 + 1/15*v**5 + 0*v - 2/3*v**3 + 5*v**2 - 1/30*v**6 + 1/6*v**4. Determine i, given that r(i) = 0.
-1, 1
Suppose -30 - 6 = -6*h. Let f(n) be the second derivative of 1/27*n**3 + 4*n + 0*n**h + 0 - 1/45*n**5 + 0*n**4 + 1/189*n**7 + 0*n**2. Let f(d) = 0. What is d?
-1, 0, 1
Let j = 67/30 - 13/6. Let k(g) be the first derivative of -1/3*g**4 - 2/3*g**2 + 4 - 1/3*g - j*g**5 - 2/3*g**3. Find l, given that k(l) = 0.
-1
Let l(s) = -s - 11*s + 12*s**2 - 6 + 3*s**3 - 9*s**2. Let d(t) = 2 - 3 + t**3 - t**2 + 0*t**2 - t. Let m(a) = 6*d(a) - l(a). Solve m(w) = 0.
0, 1, 2
Factor 5*o**3 - 20*o**2 - 11 + 31*o - 27*o + 1 + 0 + 21*o.
5*(o - 2)*(o - 1)**2
Factor -8*q**3 + 22*q**2 - 10*q**2 + 8*q + q**5 + q - 4*q**4 + 6*q**3.
q*(q - 3)**2*(q + 1)**2
Let k(o) be the first derivative of 8/9*o - 11 + 1/18*o**4 + 8/9*o**2 + 10/27*o**3. What is g in k(g) = 0?
-2, -1
Let o(l) = -l. Let n be o(-2). Let b be -10*3/12*(-4)/5. Factor 3*s**3 - s**n + b*s**3 - s**3 + 2*s - 5*s**3.
-s*(s - 1)*(s + 2)
Solve -81*f + 3/4*f**5 - 45/2*f**4 + 66*f**2 + 159/4*f**3 - 84 = 0 for f.
-1, 2, 28
Let h = 11 - 16. Let k(o) = o**2 + 6*o + 9. Let b be k(h). Suppose -18*z + 18*z - 4*z**3 - 2*z**2 - 2*z**b = 0. What is z?
-1, 0
Let y(j) be the third derivative of -j**10/756000 + j**5/10 + 10*j**2. Let r(h) be the third derivative of y(h). Solve r(k) = 0.
0
Let k(w) = 3*w**4 - 20*w**3 + 4*w**2 + 22*w. Let x(q) = -3*q**4 + 19*q**3 - 5*q**2 - 23*q. Let j(y) = -4*k(y) - 5*x(y). Factor j(h).
3*h*(h - 3)**2*(h + 1)
Let b(d) be the first derivative of -20*d**3/3 + 465*d**2/2 - 115*d - 25. Factor b(q).
-5*(q - 23)*(4*q - 1)
What is