- 4/5*w**5 + 2/3*w**6 + 0*w + 0*w**2 + 11. Factor r(i).
4*i**3*(i - 2)*(i + 1)
Factor 3/7*t**4 + 144/7*t**2 + 96/7 + 39/7*t**3 + 204/7*t.
3*(t + 1)*(t + 2)**2*(t + 8)/7
Let u(r) be the first derivative of -2*r**5/15 - r**4/6 + 81. Solve u(d) = 0.
-1, 0
Let d = -1195/9 - -133. Let k be (9/(108/(-16)))/(-6). Let k*t - 4/9 + d*t**2 = 0. What is t?
-2, 1
Let r(t) be the first derivative of 7/4*t**2 + 3/2*t**3 - 15 + 1/10*t**5 + 5/8*t**4 + t. Factor r(l).
(l + 1)**3*(l + 2)/2
Let c(q) be the second derivative of 0*q**6 - 2/21*q**7 + 0*q**3 + 1/5*q**5 + 2*q + 0*q**2 + 0*q**4 + 0. Factor c(r).
-4*r**3*(r - 1)*(r + 1)
Let s(g) be the second derivative of -1/42*g**4 + 11*g + 0*g**3 + 0 - 3/70*g**5 + 0*g**2. Suppose s(r) = 0. Calculate r.
-1/3, 0
Let r(g) = 30*g - 2877. Let f be r(96). Suppose 2/3 - 16/3*k - 4*k**f + 26/3*k**2 = 0. What is k?
1/6, 1
Let y(u) be the third derivative of -5*u**8/336 - u**7/42 + u**6/4 - u**5/6 - 25*u**4/24 + 5*u**3/2 + 3*u**2 - 20*u. Determine i, given that y(i) = 0.
-3, -1, 1
Suppose 4*b + 70*q - 54*q - 12 = 0, 2*b - 2*q = 6. Suppose 3/2*a**5 + 0*a**3 + 0 + b*a**2 - 3/2*a - 3*a**4 = 0. Calculate a.
-1, 0, 1
Determine c, given that 12*c**2 - 6*c**2 + 260*c**3 + 4 - 10*c**4 - 14*c - 246*c**3 = 0.
-1, 2/5, 1
Let c(v) = v**2 + 13*v + 30. Let a(t) = 9 + 87 + 50*t + 24 + 5*t**2. Let d(h) = -6*a(h) + 25*c(h). Suppose d(g) = 0. Calculate g.
-1, 6
Suppose -s = -3*s, -i - s = -2. Suppose -3*q + 8 = i. Factor 8/5 + 2/5*p**q - 8/5*p.
2*(p - 2)**2/5
Let a(z) be the first derivative of 2*z**3/39 - 5*z**2 - 268*z/13 - 266. Factor a(h).
2*(h - 67)*(h + 2)/13
Suppose 3*l**4 - 4*l**4 - 3*l**4 + 10*l**3 - 16 + 20*l**2 + 562*l - 2*l**5 - 570*l = 0. Calculate l.
-2, -1, 1, 2
Suppose -5*x + 347 = 327. Let o(c) = -c**3 + 6*c**2 - 5*c - 9. Let q be o(x). Factor 9/2*u**2 + 9*u + 3/4*u**q + 6.
3*(u + 2)**3/4
Let p(k) be the second derivative of k**5/80 + 3*k**4/16 - 7*k**3/8 + 11*k**2/8 - 3*k + 77. Find b, given that p(b) = 0.
-11, 1
Let i(k) be the second derivative of -7*k**6/660 + k**5/66 + k**4/66 - 25*k**2/2 + 24*k. Let w(q) be the first derivative of i(q). Factor w(b).
-2*b*(b - 1)*(7*b + 2)/11
Factor 9/4*b**4 + 0 - 14*b**2 + 33/4*b**3 + 5*b.
b*(b + 5)*(3*b - 2)**2/4
Find h, given that 18*h + 15 + 18*h**3 + 6 - 29 + 52*h**2 - 4*h**4 - 4*h**4 = 0.
-1, 1/4, 4
Determine z, given that -328*z + 457*z**2 + 458*z**2 - 919*z**2 - 324 = 0.
-81, -1
Let w(y) be the second derivative of 1/24*y**4 + 20*y + 0*y**2 + 0 - 1/24*y**7 + 0*y**3 - 11/80*y**5 + 2/15*y**6. Suppose w(m) = 0. What is m?
0, 2/7, 1
Let b(f) be the first derivative of 5*f**4/4 - 5*f**3/3 - 5*f**2/2 + 5*f - 299. Suppose b(h) = 0. Calculate h.
-1, 1
Let m(g) be the first derivative of 4/3*g**3 - 4*g - 3 + 0*g**2. Factor m(s).
4*(s - 1)*(s + 1)
Let f(s) = -4*s - 1. Let k be f(-9). Let j be 8/30 - (-14)/k. Factor -j*y + 14/3*y**4 + 10*y**2 - 38/3*y**3 - 4/3.
2*(y - 1)**3*(7*y + 2)/3
Find y, given that 0 + y**3 + 0*y - 3/10*y**4 - 4/5*y**2 = 0.
0, 4/3, 2
Suppose 4*n**2 + 20*n + 96*n - 33*n + 4356 + 181*n + 0*n**2 = 0. Calculate n.
-33
Let k(w) = -2*w**3 + 11*w**2 - 4*w + 1. Let z be k(5). Factor -9/2 - 3/2*j**2 + z*j.
-3*(j - 3)*(j - 1)/2
Let g(s) = -s**3 + s**2. Let r(c) = -7*c**3 - 13*c + 4*c**3 - 10*c**2 + 13*c**3 + 3*c. Let v(o) = -5*g(o) - r(o). Suppose v(p) = 0. Calculate p.
-1, 0, 2
Let p(x) be the third derivative of 4*x**5/105 - 41*x**4/84 + 5*x**3/21 - 27*x**2 - 5*x. What is k in p(k) = 0?
1/8, 5
Let g(f) be the first derivative of 3*f**4/32 - f**3/8 - 27*f**2/16 + 27*f/8 + 269. What is p in g(p) = 0?
-3, 1, 3
Let s be (-3)/2*4 + 25929/4300. Let a(b) be the third derivative of 1/200*b**6 - 3*b**2 + 1/10*b**3 + 3/40*b**4 + s*b**5 + 0*b + 0. Factor a(l).
3*(l + 1)**3/5
Let h(p) be the second derivative of -p**7/84 - 17*p**6/30 + 619*p. Suppose h(i) = 0. Calculate i.
-34, 0
Suppose 5*g + 2 = -2*f + 4*g, 5*f + 4*g = -11. Suppose -d + f = -2. Factor -2*o**2 - 6*o**4 - 4*o**d + 0*o**4 - 2*o**5 - 2*o**3.
-2*o**2*(o + 1)**3
Let u(a) be the first derivative of a**4/18 - 2*a**3/9 + a**2/3 + 12*a - 6. Let z(y) be the first derivative of u(y). What is x in z(x) = 0?
1
Suppose -321 = 14*i - 391. Determine p, given that -18/5*p**3 + 2*p**4 - 4/5*p + 14/5*p**2 - 2/5*p**i + 0 = 0.
0, 1, 2
Let k(u) be the first derivative of -3*u**4/4 + 7*u**3/12 + 5*u**2/4 - 277. Factor k(o).
-o*(3*o + 2)*(4*o - 5)/4
Let f be (-528)/3432 - (-64)/78. Solve -1/3*i + 1/3*i**2 - f = 0 for i.
-1, 2
Let b = -48 - -50. Factor -5*k**4 + 34*k - k + b*k + 25*k**3 + 65*k**2.
-5*k*(k - 7)*(k + 1)**2
Let g(o) be the first derivative of -o**8/560 + o**7/140 - o**5/20 + o**4/8 - 19*o**3/3 + 13. Let d(b) be the third derivative of g(b). Factor d(n).
-3*(n - 1)**3*(n + 1)
Let p(b) be the second derivative of 0*b**3 + 1/60*b**5 + 5/168*b**7 - b**2 + b + 1/24*b**6 + 0 + 0*b**4. Let j(d) be the first derivative of p(d). Factor j(n).
n**2*(5*n + 2)**2/4
Let q be (-4)/(-22) + 477/99. Suppose 9 = a + q. Determine f, given that 15*f**2 - 15*f**a - 3*f**3 - 4*f**3 + 12*f**5 - 3*f - 2*f**3 = 0.
-1, 0, 1/4, 1
Let a = 4 - 1. Let t = 18 + -16. Determine f so that -f**t + 1/2*f**a + 1/2*f**4 + 0*f + 0 = 0.
-2, 0, 1
Let s be (18/(-15))/((-90)/(-25) - 4). Let a(d) = 4*d**3 + 2*d**2 - 21*d - 8. Let i(u) = -u**3 - u. Let o(x) = s*i(x) - 3*a(x). Factor o(k).
-3*(k - 2)*(k + 2)*(5*k + 2)
Let w(v) be the first derivative of v**6/90 + v**5/15 + 5*v**4/36 + v**3/9 + 15*v + 6. Let f(c) be the first derivative of w(c). Find z, given that f(z) = 0.
-2, -1, 0
Let k = -11 - -12. Let s(w) = w**3 - w**2 + 3*w - 1. Let x be s(k). Factor r**3 + 3*r - 4*r - 2 - r**x + 3.
(r - 1)**2*(r + 1)
Let s(v) be the first derivative of -3/8*v**4 + 0*v - 3/10*v**5 + 5 + 0*v**2 + v**3. Factor s(w).
-3*w**2*(w - 1)*(w + 2)/2
Suppose 4*r + 15 = 59. Suppose 2 - m**5 + 0*m**5 - 4*m**2 - 9*m**3 - m + r*m**3 + 2*m**4 = 0. What is m?
-1, 1, 2
Suppose 18 = 18*h - 15*h. Let a be (0 - h/(-7))/((-24)/(-42)). Suppose 0 + a*o**2 + 0*o - 3/2*o**3 = 0. What is o?
0, 1
Let l(x) be the first derivative of x**7/70 - x**5/20 - 13*x**2/2 + 18. Let z(r) be the second derivative of l(r). Factor z(i).
3*i**2*(i - 1)*(i + 1)
Let q(k) be the second derivative of 3*k + 1/7*k**4 + 1/35*k**6 + 0*k**2 + 0 + 3/20*k**5 - 2/7*k**3. Factor q(u).
3*u*(u + 2)**2*(2*u - 1)/7
Let z(l) be the third derivative of -11/105*l**6 + 0*l**3 - 4/15*l**5 - 4/21*l**4 - 2/147*l**7 + 9*l**2 + 0*l + 0. Factor z(r).
-4*r*(r + 2)**2*(5*r + 2)/7
Let n be (3/(-6))/(3 + (-30)/8 + -1). Factor 6/7*z + 0 - n*z**2.
-2*z*(z - 3)/7
Factor -1/2*z**2 + 559/4*z + 70.
-(z - 280)*(2*z + 1)/4
Suppose 149*f - 145*f = 0. Suppose 3*o**2 + 0*o + f + 3/2*o**3 - 3/2*o**4 = 0. Calculate o.
-1, 0, 2
Suppose -5*b = -k - 9, -6*b - k + 7 = -3*b. What is r in 0 + 3*r**b + 3/2*r**5 - 3/2*r - 3*r**4 + 0*r**3 = 0?
-1, 0, 1
Suppose 19*u - u = 72. Let y(n) be the second derivative of 1/4*n**u + 0*n**2 + 3/20*n**5 - 6*n + 0 + 0*n**3. Factor y(g).
3*g**2*(g + 1)
Let y = 38 - 90. Let v = y - -56. Let -4/7 - 22/7*t**3 + 18/7*t**v - 2*t**2 + 22/7*t = 0. Calculate t.
-1, 2/9, 1
Let o be 1/((-12)/16)*-3. Let c be (-6)/(3 - 0) + o. Factor -2*x**3 + 2*x**c + 1 - 1.
-2*x**2*(x - 1)
Suppose -1 - 75*w - w**2 + 89 + 20*w + 86 = 0. Calculate w.
-58, 3
Let w(c) be the third derivative of c**6/240 + c**5/24 + 332*c**2. Factor w(z).
z**2*(z + 5)/2
Factor -2535/2*c + 7*c**4 - 1/6*c**5 + 2197/3 + 1898/3*c**2 - 313/3*c**3.
-(c - 13)**3*(c - 2)*(c - 1)/6
Let y(p) be the second derivative of 1/4*p**2 - 8*p + 0 + 0*p**3 - 1/24*p**4. Factor y(q).
-(q - 1)*(q + 1)/2
Let b(y) be the third derivative of y**8/20160 - y**7/2520 - 2*y**4/3 - 7*y**2. Let h(w) be the second derivative of b(w). Let h(m) = 0. What is m?
0, 3
Let b(u) = 2*u**2 - 2*u - 6. Let q(s) = -6*s**2 + 5*s + 17. Suppose -8*f = -3*f + 30. Let o(z) = f*q(z) - 17*b(z). Factor o(k).
2*k*(k + 2)
Let h(t) be the first derivative of -t**4/46 + 52*t**3/69 - 25*t**2/23 + 55. Let h(k) = 0. Calculate k.
0, 1, 25
Factor 140*z + 6*z**2 + 96*z + 2*z**2 + 29*z - 3*z**2 + 260.
5*(z + 1)*(z + 52)
Suppose -t - 155 = -5*n - 0*t, 93 = 3*n - 4*t. Suppose -n*j = -27*j - 12. Factor 12/7*o**2 + 8/7 - 18/7*o - 2/7*o**j.
-2*(o - 4)*(o - 1)**2/7
Let n be 10/5 - (9/3 + 1). Let u be (n/(-35))/((-11)/((-616)/12)). Solve -u*o**2 + 2/15*o + 0 + 