*f - f**3 + f**3 - 4*f**3 = 0. What is f?
-1, 19
Let c(a) be the first derivative of -2*a**6/15 - 4*a**5/5 + 11*a**4/3 - 4*a**3 + 2*a + 12. Let n(t) be the first derivative of c(t). Solve n(m) = 0 for m.
-6, 0, 1
Let v(c) be the third derivative of 1/60*c**7 + 0*c**4 + 0 - 20*c**2 + 0*c**3 + 1/160*c**6 + 0*c - 1/120*c**5. Factor v(h).
h**2*(2*h + 1)*(7*h - 2)/4
Let o(j) be the first derivative of 8*j**3 - 46*j**2 - 140*j - 135. Factor o(i).
4*(i - 5)*(6*i + 7)
Let m be (-16)/(-28)*210/60. Let 4/5 - 4/5*y**m + 1/5*y - 1/5*y**3 = 0. What is y?
-4, -1, 1
Let h be (25/((-2250)/108))/((-8)/5). Factor 0 + h*c**2 + 3/2*c.
3*c*(c + 2)/4
Let p(r) be the second derivative of r**4/66 - 4*r**2/11 + 79*r + 2. Factor p(k).
2*(k - 2)*(k + 2)/11
Let y(f) be the third derivative of -f**5/270 - f**4/6 - 5*f**3/3 - 80*f**2. Factor y(m).
-2*(m + 3)*(m + 15)/9
Let m(q) be the first derivative of -q**7/630 + q**5/90 - q**3/18 + 27*q**2/2 - 29. Let g(x) be the second derivative of m(x). Find v, given that g(v) = 0.
-1, 1
Factor -16*n - 12 - 7*n - 21*n - 32*n**2.
-4*(n + 1)*(8*n + 3)
Factor -20*r**4 + 2*r**5 + 402*r**2 + 23*r - 318*r**2 - 95*r + 4*r**3 + 2*r**5.
4*r*(r - 3)**2*(r - 1)*(r + 2)
Let s(c) be the second derivative of -2*c**4/15 - 4*c**3 - 45*c**2 + 20*c. Factor s(f).
-2*(2*f + 15)**2/5
Solve -2 - 11*n - 19/2*n**2 - 9/4*n**3 = 0 for n.
-2, -2/9
Let c(l) be the first derivative of -l**4/54 - l**3/18 - l**2/18 - 10*l + 1. Let d(w) be the first derivative of c(w). What is n in d(n) = 0?
-1, -1/2
Factor 11/8*a + 0 + 5/4*a**2 - 1/8*a**3.
-a*(a - 11)*(a + 1)/8
Suppose -f - 3*f - 100 = 0. Let u = 62 + f. What is r in -9*r**5 - 2*r**3 + r**5 + 0*r**3 + u*r**4 - 47*r**4 = 0?
-1, -1/4, 0
Let h(b) = -b - 1. Let l(m) = -9*m**2 + 183*m - 93. Let r(o) = 15*h(o) + l(o). Determine n, given that r(n) = 0.
2/3, 18
Let b(f) be the second derivative of 0 + 0*f**4 - 11*f + 1/35*f**5 - 2/21*f**3 + 0*f**2. Let b(i) = 0. Calculate i.
-1, 0, 1
Let d = 40 - 37. Let z be 1 + d - (-5)/((-5)/2). Factor 0 + 3/2*r**4 + 1/2*r**z + 0*r + 2*r**3.
r**2*(r + 1)*(3*r + 1)/2
Suppose -4*l + 4*y - 8 = 0, -3*l = 2*l - 4*y + 4. Factor 0 + 0*i + 1/6*i**3 + 0*i**2 - 1/6*i**l.
-i**3*(i - 1)/6
Let g = -221 - -221. Let l(r) be the third derivative of -1/21*r**4 + g*r + 1/70*r**5 + 5*r**2 + 1/21*r**3 + 0. Factor l(z).
2*(z - 1)*(3*z - 1)/7
Let t(j) be the first derivative of -j**6/39 - 8*j**5/13 - 187. Let t(s) = 0. What is s?
-20, 0
Factor -2/7*a**2 + 120/7 - 34/7*a.
-2*(a - 3)*(a + 20)/7
Let f(m) be the third derivative of 1/20*m**5 - 1/2*m**3 + 7*m**2 + 0 + 0*m + 0*m**4. Factor f(z).
3*(z - 1)*(z + 1)
Let k(p) be the third derivative of 0 + 23*p**2 + 13/12*p**5 - 1/6*p**6 + 0*p**3 - 5/8*p**4 + 0*p. Factor k(z).
-5*z*(z - 3)*(4*z - 1)
Let m(d) be the second derivative of -d**6/960 - d**5/320 - 11*d**3/6 - 8*d. Let u(z) be the second derivative of m(z). Let u(h) = 0. Calculate h.
-1, 0
Suppose -13 = 3*l + s, -4*s - 30 = 5*l + 1. Let d be (54/15 - 3)*(-2)/l. Factor -2/5*a**4 + 0 + 2/5*a**3 - 2/5*a + d*a**2.
-2*a*(a - 1)**2*(a + 1)/5
Suppose -14*h + 18*h - 3*i = 0, -5*i = -3*h. Factor -2/7*m**2 - 4/7*m**3 - 2/7*m**4 + h + 0*m.
-2*m**2*(m + 1)**2/7
Solve 2/3*r**2 + 0 + 0*r + 4/3*r**4 + 3*r**3 = 0.
-2, -1/4, 0
Determine u so that -200/11 - 2/11*u**4 - 120/11*u + 12/11*u**3 + 2*u**2 = 0.
-2, 5
What is h in -18/7*h**2 + 1/7*h**3 + 65/7*h + 12 = 0?
-1, 7, 12
Let s(u) be the first derivative of 2*u**5/75 - 29*u**4/30 - 122*u**3/45 - 31*u**2/15 + 504. Let s(k) = 0. What is k?
-1, 0, 31
Let h(a) be the second derivative of a**5/330 - a**4/132 + 3*a**2 + 13*a. Let q(p) be the first derivative of h(p). Suppose q(z) = 0. Calculate z.
0, 1
Let j be 3/9*-28*(-3)/(-2). Let o be -1*4/j - 76/(-28). Factor -7/3*k**2 + 8/3*k + 4/3 - 5/3*k**o.
-(k - 1)*(k + 2)*(5*k + 2)/3
Let a(y) be the first derivative of -y**6/120 - y**5/30 - y**4/24 - y**2/2 + 22. Let k(i) be the second derivative of a(i). Solve k(j) = 0 for j.
-1, 0
Factor -2*p**4 - 5/4*p - 49/4*p**3 - 23/2*p**2 + 0.
-p*(p + 1)*(p + 5)*(8*p + 1)/4
Let y be 27/18*(1 - -1). Let h = 48 + -46. Factor 2 - 17*g**3 - 3*g**h - 7*g - 2*g**2 + 21*g**y.
(g - 2)*(g + 1)*(4*g - 1)
Suppose -83*p = -7*p - 380. Let n(q) be the second derivative of 1/70*q**p - 6*q + 0 + 16/7*q**3 - 64/7*q**2 - 2/7*q**4. Factor n(j).
2*(j - 4)**3/7
Suppose 2*h - 14 = 56. Let n(t) = -2*t**2 + 3*t + 3. Let r(w) = 25*w**2 - 35*w - 35. Let z(f) = h*n(f) + 3*r(f). Factor z(d).
5*d**2
Let k(q) be the third derivative of 0*q**3 + 0 - 1/210*q**5 + 0*q - 1/84*q**4 - 4*q**2. Factor k(h).
-2*h*(h + 1)/7
Let k be 2 - (1 + -1) - (16 - 17). Determine g, given that -8*g**k + 13*g + 2*g**2 - 2*g**5 - 2*g**4 - 29*g + 18*g**3 + 8 = 0.
-2, 1
Let p(a) = a**4 - a**3 - a**2 + 1. Let v(n) be the first derivative of 4*n**5/5 + n**4 + 4*n**3 + 13*n**2/2 + 7*n + 27. Let x(c) = 3*p(c) - v(c). Factor x(m).
-(m + 1)**3*(m + 4)
Let b(m) be the second derivative of 10/3*m**3 + 25*m**2 - 9*m + 1/6*m**4 + 0. Factor b(x).
2*(x + 5)**2
Determine m, given that 3/4*m**2 + m - 7/4 = 0.
-7/3, 1
Let b(x) = x**2 - 4*x + 3. Let z be b(3). Suppose -5*g + 4*h = 20, 4*g + 27*h - 28*h + 5 = 0. Factor z*j**2 + 0*j + g + 1/6*j**3 - 1/6*j**4.
-j**3*(j - 1)/6
Let m(v) be the third derivative of 7*v**6/12 + 59*v**5/30 - 8*v**4/3 - 20*v**3/3 + 76*v**2. Factor m(n).
2*(n + 2)*(5*n + 2)*(7*n - 5)
Let p(v) be the third derivative of -v**6/60 + 3*v**4/4 - 491*v**2. Factor p(q).
-2*q*(q - 3)*(q + 3)
Suppose 83*f - 90*f = -42. Let j(g) be the second derivative of -2*g + 0*g**3 + 0*g**4 + 0*g**2 + 3/10*g**5 + 0 - 1/10*g**f. Factor j(x).
-3*x**3*(x - 2)
Suppose -t = 73 - 77. Determine w, given that 0*w - 4/7*w**3 + 0 + 6/7*w**t + 0*w**2 = 0.
0, 2/3
Let l = 79 - 79. Let g(j) be the third derivative of 121/40*j**5 + l + j**3 + 11/4*j**4 + 0*j + 2*j**2. Factor g(x).
3*(11*x + 2)**2/2
Let n(i) be the first derivative of 0*i + 11/30*i**4 - 14/9*i**3 - 28 + 5/3*i**2 - 2/75*i**5. Factor n(x).
-2*x*(x - 5)**2*(x - 1)/15
Let m = 36 - 56. Let t be (-4)/3*6/m. Determine v, given that 8/5*v - t*v**2 + 2/5 - 8/5*v**3 = 0.
-1, -1/4, 1
Let r(b) be the first derivative of -2*b**3/21 + 4*b**2/7 + 10*b/7 - 2. Factor r(w).
-2*(w - 5)*(w + 1)/7
Let g be (3 + -3 + 3)*1 - 0. Suppose -222*n**2 - n**g - 15*n + 228*n**2 - 18 + 4*n**3 = 0. Calculate n.
-3, -1, 2
Let v = -8421 - -8421. Find i, given that 3/5*i**5 - 6/5 - 12/5*i**3 + 9/5*i + v*i**4 + 6/5*i**2 = 0.
-2, -1, 1
Let b(s) = 2*s - s - s**3 + 2*s**3. Let a(l) = -4*l**4 + 18*l**3 + 2*l + 4. Let m(o) = a(o) - 10*b(o). Factor m(j).
-4*(j - 1)**3*(j + 1)
Let t(g) be the first derivative of -g**7/210 + g**6/90 + g**5/30 - g**4/6 + g**3/3 + 21. Let h(w) be the third derivative of t(w). Factor h(l).
-4*(l - 1)**2*(l + 1)
Let m = 9 - 5. Factor -10*o**2 + 5*o - 3*o**m - 4 + 3 + o**5 - 2*o**4 + 9*o**3 + o**3.
(o - 1)**5
Let m(f) be the third derivative of 0*f - 1/50*f**5 + 1/200*f**6 - 7*f**2 - 2/5*f**3 - 7/40*f**4 + 0. Let m(v) = 0. Calculate v.
-1, 4
Let f be 5/5 + 157/(-835). Let j = -2/167 + f. Suppose -14/5*k**3 + 32/5*k**2 + j - 22/5*k = 0. What is k?
2/7, 1
Let z(c) = c**2 - 40*c + 403. Let k be z(20). Factor 14/3*j**4 + 0 - 6*j**k + 4/3*j**2 + 0*j.
2*j**2*(j - 1)*(7*j - 2)/3
Suppose 5*g = 2*s + 15, 3*s + 3 = 7*s + g. Let b(d) be the second derivative of 3/14*d**4 + 2/21*d**3 + 1/10*d**5 + s*d**2 + 0 - 3*d. Solve b(q) = 0 for q.
-1, -2/7, 0
Let w(u) = u - 2. Let k be w(6). Let v = 2/1003 - -1988/9027. Factor 0*s**2 - 4/9*s + 2/9 - v*s**k + 4/9*s**3.
-2*(s - 1)**3*(s + 1)/9
Let z = -389/81 - -2515/162. Let o = z - 59/6. Let 2/9 + 8/9*p**3 + 4/3*p**2 + 2/9*p**4 + o*p = 0. Calculate p.
-1
Let p(d) = 16*d**2 + 505*d - 89. Let b(h) = -174*h**2 - 5556*h + 978. Let y(a) = -6*b(a) - 68*p(a). Find k such that y(k) = 0.
-23, 2/11
Let b(h) be the third derivative of h**9/10584 + h**8/1470 + h**7/980 - 2*h**3 - 2*h**2. Let t(w) be the first derivative of b(w). Solve t(a) = 0.
-3, -1, 0
Let a = 20520 + -246425/12. Let k = -59/4 - a. Factor k*g**3 + 0*g**2 + 0*g - 2/3*g**4 + 0.
-2*g**3*(g - 1)/3
Factor 293 - 40*r**2 - 569 - 65*r + 246 - 5*r**3.
-5*(r + 1)**2*(r + 6)
Let k(s) be the second derivative of 1/12*s**5 - 13/2*s**2 + 5/6*s**3 - 6*s + 0 - 5/12*s**4. Let v(p) be the first derivative of k(p). Factor v(a).
5*(a - 1)**2
Let h(z) = 18*z**