8405/3*l**3 + 410*l**2. Solve r(i) = 0 for i.
-2/41
Suppose 0 = n - 4*i + 4376 - 4382, -3 = -3*n - 3*i. Find v such that 34/3*v**3 - 14*v**n - 4/3*v**4 - 50/3 - 130/3*v = 0.
-1, -1/2, 5
Let i = 2/404899 - -809780/3644091. Factor -4/9 + 2/9*v**2 + i*v.
2*(v - 1)*(v + 2)/9
Let i = 50046 + -50044. Factor 1/6*n**i + 0 - 1/6*n.
n*(n - 1)/6
Suppose 8*r - 11 = 21. Factor -r - v**2 - 9*v + 5*v + 1.
-(v + 1)*(v + 3)
Factor -360/11*b - 2/11*b**3 + 864/11 + 48/11*b**2.
-2*(b - 12)*(b - 6)**2/11
Let r(u) be the first derivative of 0*u + 3/16*u**4 - 245 + 5/2*u**3 - 9/16*u**6 + 3/2*u**2 - 63/40*u**5. Determine o, given that r(o) = 0.
-2, -2/3, 0, 1
Let w(b) be the first derivative of -5/4*b**4 - 19 + 33*b + 0*b**2 - 25/4*b**3 - 3/40*b**5. Let y(d) be the first derivative of w(d). Factor y(q).
-3*q*(q + 5)**2/2
Let n(w) be the second derivative of w**4/8 - 35*w**3/2 + 198*w**2 - 1279*w. Suppose n(i) = 0. Calculate i.
4, 66
Let u(j) be the third derivative of j**7/735 + 4*j**6/35 + 41*j**5/210 - 47*j**4/14 + j**2 + 658*j. Factor u(l).
2*l*(l - 2)*(l + 3)*(l + 47)/7
Suppose -p + 318 - 313 = 0. Factor -248*u**4 + 11*u**3 + 196*u**4 + u**p - 167*u**2 + 213*u**3 + 3*u**5 - 153*u**2.
4*u**2*(u - 5)*(u - 4)**2
Let j(t) be the third derivative of 0*t + 73*t**2 + 1/1890*t**7 + 0*t**3 + 0 + 1/216*t**6 + 2/135*t**5 + 1/54*t**4. Factor j(g).
g*(g + 1)*(g + 2)**2/9
What is v in 0 - 1/6*v**4 - 10/3*v + 7/2*v**2 + 0*v**3 = 0?
-5, 0, 1, 4
Let p = 2608 - 2606. Let y(n) = -n**2 + 3*n. Let m be y(0). Factor m*g + 0 - 2/3*g**3 + 2/3*g**p.
-2*g**2*(g - 1)/3
Let s(d) be the second derivative of d**4/42 - 32*d**3/21 - 68*d**2/7 + 1156*d. Factor s(q).
2*(q - 34)*(q + 2)/7
Let p(m) = 9*m**3 - 110*m**2 - 492*m - 516. Let f(w) = 125*w**3 - 1540*w**2 - 6890*w - 7225. Let n(i) = 4*f(i) - 55*p(i). Factor n(d).
5*(d - 26)*(d + 2)**2
Let j(z) be the second derivative of z**6/15 + 13*z**5/10 + 35*z**4/6 - 49*z**3/3 + 2*z + 133. Factor j(u).
2*u*(u - 1)*(u + 7)**2
Let l(q) = q**3 - 30*q**2 + 6*q + 154. Let f(z) = z**3 + 2 + 0 + z - 3. Let s = -2706 - -2707. Let i(p) = s*l(p) - 6*f(p). Suppose i(o) = 0. Calculate o.
-4, 2
Let q(m) be the second derivative of -5*m**4/42 - 8*m**3/21 + 4*m**2/7 + 2207*m. Let q(j) = 0. Calculate j.
-2, 2/5
Suppose -310*q + 33*q + 5495 = -7524. Let w(l) be the second derivative of -1/20*l**5 - 1/120*l**6 + 1/2*l**3 + q*l + 1/24*l**4 - 9/8*l**2 + 0. Factor w(i).
-(i - 1)**2*(i + 3)**2/4
Let g(w) be the second derivative of -w**4/15 - 68*w**3/3 + 688*w**2/5 + 135*w - 12. Determine y so that g(y) = 0.
-172, 2
Suppose -433 + 18748 = 1221*k. Factor -k*z**3 - 85/6*z - 1/6*z**5 + 7/2 + 65/3*z**2 + 25/6*z**4.
-(z - 21)*(z - 1)**4/6
Let z(a) = a**3 - 19*a**2 + 17*a + 20. Let l be z(18). Factor 430*g**l + 335*g**3 - 11*g**4 + 120*g + 52*g**4 - 16*g**4.
5*g*(g + 1)*(g + 12)*(5*g + 2)
Let z(s) = s**3 - 6*s**2 - 8*s + 9. Let o be z(7). Let y = 11/15460 + 154567/46380. Find w such that -2/3*w**o + 0 - y*w = 0.
-5, 0
Suppose -108*z = 103*z - 1266. Let n(a) be the third derivative of 1/840*a**z + 0*a + 0*a**3 + 0*a**4 + 23*a**2 - 1/420*a**5 + 0. Factor n(r).
r**2*(r - 1)/7
Let j(a) be the first derivative of -a**8/112 + a**7/35 + 3*a**6/40 - 19*a**2/2 - 111. Let q(p) be the second derivative of j(p). Factor q(r).
-3*r**3*(r - 3)*(r + 1)
Let u = -44058 - -44058. Let x(v) be the second derivative of -1/20*v**6 + 1/8*v**4 + u*v**2 - 1/10*v**5 - v + 1/6*v**3 - 22 + 1/42*v**7. Solve x(i) = 0 for i.
-1, -1/2, 0, 1, 2
Let h = 5/654 - -1085/654. Let q(j) be the third derivative of -h*j**3 - 1/12*j**5 + 9*j**2 + 0*j + 0 + 5/8*j**4. Find t, given that q(t) = 0.
1, 2
Let q(j) be the third derivative of 0 + 65/24*j**4 + 0*j**3 + 1/24*j**6 + 137*j**2 - 7/6*j**5 + 0*j. Factor q(h).
5*h*(h - 13)*(h - 1)
Let f be 2148/(-40) + 3 - 0. Let q = f - -256/5. Factor 0 + 0*y - q*y**2 - 3/2*y**4 + 3/2*y**3 + 1/2*y**5.
y**2*(y - 1)**3/2
Let r(x) be the second derivative of -1/54*x**4 - 124/27*x**3 + 4*x - 3844/9*x**2 + 0. Suppose r(n) = 0. Calculate n.
-62
Solve -3/4*p**2 + 9/4*p - 1/4*p**3 + 27/4 = 0 for p.
-3, 3
Factor -20*m - 68 - 4*m - 2*m**2 + 32*m - 78*m.
-2*(m + 1)*(m + 34)
Let z(s) be the third derivative of 0 - 3*s**2 - 4*s - 4/13*s**3 - 1/156*s**4 + 1/390*s**5. Factor z(c).
2*(c - 4)*(c + 3)/13
Let c(k) be the second derivative of k**6/15 - 12*k**5/5 + 157*k**4/6 - 82*k**3 + 112*k**2 + 648*k + 2. Let c(z) = 0. Calculate z.
1, 8, 14
Let z(x) be the second derivative of 13/18*x**4 + 3*x + 3/10*x**5 - 50/3*x**2 + 0 + 1/45*x**6 - 5*x**3. What is l in z(l) = 0?
-5, -1, 2
Let n(c) be the first derivative of -c**5/240 + 23*c**4/96 + c**3 - 7*c**2 - 109. Let f(v) be the second derivative of n(v). Let f(y) = 0. What is y?
-1, 24
Let s = 139 - 71. Let t = s + -63. Solve 0 - 3/2*x - 3/2*x**3 + t*x**2 = 0.
0, 1/3, 3
Let a(i) be the second derivative of -i**4/32 - 365*i**3/8 - 2187*i**2/16 + 1446*i. Solve a(v) = 0.
-729, -1
Let s(q) be the first derivative of 3*q**4/16 + 33*q**3/4 + 1053*q**2/8 + 3549*q/4 - 1263. Factor s(p).
3*(p + 7)*(p + 13)**2/4
Let c(x) be the first derivative of x**6/51 - 4*x**5/17 - 25*x**4/17 - 160*x**3/51 - 55*x**2/17 - 28*x/17 - 1204. Factor c(s).
2*(s - 14)*(s + 1)**4/17
Let c(p) = -2*p**2 + 51*p. Let h(k) = 3*k**2 - 3349*k + 578000. Let g(v) = -c(v) + h(v). Factor g(b).
5*(b - 340)**2
Let x(m) = m**3 + 2*m**2 - 38*m + 46. Let k(o) = -4*o**3 - 11*o**2 + 191*o - 229. Suppose -1 + 10 = 3*z, c - z = 8. Let s(g) = c*x(g) + 2*k(g). Factor s(l).
3*(l - 2)**2*(l + 4)
Let d be ((-22)/9)/(390/(-585)). Find y, given that y**2 + d*y - 14/3 = 0.
-14/3, 1
Factor 3*d**2 - 119 + 39*d + 161 - 6.
3*(d + 1)*(d + 12)
Suppose -v = -3*u - 151, v = 2*u + 80 + 66. Factor 16*k**3 - k**5 - 8*k**4 + v*k**2 - 270*k**2 - 3*k**5 + 166*k**2.
-4*k**2*(k - 2)*(k + 2)**2
Let r(n) = -8*n**2 - 23*n + 22. Let g(k) be the third derivative of 23*k**5/60 + 17*k**4/6 - 67*k**3/6 - 189*k**2. Let x(m) = 3*g(m) + 8*r(m). Factor x(u).
5*(u - 1)*(u + 5)
Let u(i) be the first derivative of i**6/30 - 28*i**5/5 + 207*i**4/10 - 412*i**3/15 + 137*i**2/10 - 1523. Find x such that u(x) = 0.
0, 1, 137
Let g(m) be the third derivative of m**7/1680 + m**6/160 + m**5/480 - m**4/8 + m**3/3 - 625*m**2 - 2*m. Factor g(x).
(x - 1)**2*(x + 4)**2/8
Suppose -106*g + 65*g - 166*g + 2332 = 376*g. Find x, given that 6/7 + 27/7*x + 48/7*x**2 + 6*x**3 + 3/7*x**5 + 18/7*x**g = 0.
-2, -1
Let q(r) be the third derivative of 0*r - 7/156*r**4 + 0*r**3 + 1/780*r**6 + 1/65*r**5 + 0 + 6*r**2. Solve q(t) = 0 for t.
-7, 0, 1
Let q(j) = 5*j**2 - 70*j - 1115. Let c(r) = -2*r**2 + 23*r + 373. Let l(g) = 10*c(g) + 3*q(g). What is m in l(m) = 0?
-7, 11
Suppose 0 = i - 3. Suppose i*s = -2*g + 28, 2*g - 12 = -0*s - s. Factor 13*h**2 + 4 + 50*h + 3*h**2 + s*h**2 - 78*h.
4*(h - 1)*(6*h - 1)
Let b(u) be the first derivative of 0*u**4 - 4*u**2 - 1/15*u**5 + 0*u - 24 + 2/3*u**3. Let o(k) be the second derivative of b(k). Factor o(j).
-4*(j - 1)*(j + 1)
Suppose 2 = 3*j - 4. Let i = -509731 - -509733. Find m, given that -3/4*m**3 + i + 1/2*m**j + 3*m - 1/4*m**4 = 0.
-2, -1, 2
Let v(u) be the second derivative of -u**4/16 + 309*u**3/8 - 231*u**2/2 + 989*u - 2. Determine l, given that v(l) = 0.
1, 308
Let b(q) = q**3 + 9*q**2 - 21*q - 22. Let n be b(-12). Let s = n - -204. Factor -2/9*w**3 + 0*w - 2/9*w**s + 0.
-2*w**2*(w + 1)/9
Let d be (428/6)/(3*(-2)/(-9)). Let j = d + -104. Solve -35*w**2 - 32*w**j + 40*w + 51*w**3 - 24*w**3 = 0 for w.
-8, 0, 1
Let 21456*y + 23548*y**2 - 2361 + 2206 + 35*y**3 + 3332*y**2 + 4443 + 65*y**3 = 0. Calculate y.
-268, -2/5
Let c be (-49 + 50)/((-2)/32*1). Let n be (775/(-70) + 11)*c. Let 0 - n*v - 4/7*v**3 + 12/7*v**2 = 0. Calculate v.
0, 1, 2
Let r(j) be the second derivative of 121*j**5/140 - 11*j**4/2 + 21*j**3/2 - 5*j - 78. Factor r(v).
v*(11*v - 21)**2/7
Suppose 3*n + 1758 = 3*m, 6*n + 1174 = 4*n + 4*m. Let s = n - -2341/4. Factor -1/2*r + 0 + 3/4*r**2 - s*r**3.
-r*(r - 2)*(r - 1)/4
Let w(c) be the second derivative of c**5/150 - c**4/15 - c**3/45 + 2*c**2/5 - 19*c + 4. Find k, given that w(k) = 0.
-1, 1, 6
Let u be (0 - (4 - 3))/((-2)/(-4)). Let j be u*(264/80)/(-11). Suppose -2/5 + 1/5*o**2 - 3/5*o + 1/5*o**4 + j*o**3 = 0. What is o?
-2, -1, 1
Let u(c) = -2*c**3 - 20*c**2 + 211*c - 393. Let a be u(4). Factor 0 - 2/5*i + 0*i**2 + 