*m**5 + 7 - 7/24*m**4 - 1/9*m**3 + m**2 + 4/3*m. Solve a(q) = 0.
-2, -1, 2
Let a(r) = -58*r**3 - 354*r**2 - 506*r + 2. Let u(c) = c**4 - 111*c**3 - 708*c**2 - 1013*c + 5. Let k(x) = -5*a(x) + 2*u(x). Solve k(y) = 0 for y.
-28, -3, 0
Let a be (-6)/(-4) - 4/(-8). Factor 4*h**2 - 5*h**a + 10*h - 16*h - 9.
-(h + 3)**2
Let i(l) be the third derivative of l**5/4 - 129*l**4/4 - 52*l**3 - 258*l**2 + 2*l. Solve i(n) = 0 for n.
-2/5, 52
Let k(a) = a**3 - 13*a**2 - 15*a + 16. Let c be k(14). Suppose 0 = -c*z + 4. Suppose 0 - 2/7*g - 2/7*g**z = 0. Calculate g.
-1, 0
Suppose 4*i + 0*i - 32 = 0. Factor -48*u**2 - 31*u + 21*u - 5*u**2 + i*u**2.
-5*u*(9*u + 2)
Let a(c) = -3*c**2 - 5*c. Let p(d) be the first derivative of 10*d**3 + 51*d**2/2 - 2. Let z = -32 + 53. Let j(n) = z*a(n) + 2*p(n). Factor j(h).
-3*h*(h + 1)
Let h(m) be the first derivative of -3*m**4/20 + 42*m**3/5 - 1323*m**2/10 + 127. Factor h(g).
-3*g*(g - 21)**2/5
Let w(i) be the third derivative of i**8/2184 + 2*i**7/273 + 17*i**6/780 + 4*i**5/195 + 2*i**2 - 74. Suppose w(p) = 0. Calculate p.
-8, -1, 0
Let n be (-18)/3 - (0 + (-273)/28). Let v(o) be the first derivative of -10 - 3*o + 5/2*o**3 - 9/10*o**5 - n*o**2 + 15/8*o**4. Let v(y) = 0. What is y?
-1, -1/3, 1, 2
Let w(v) = 83*v**3 - 120*v**2 - 75*v - 4. Let p(x) = -82*x**3 + 120*x**2 + 75*x + 6. Let h(t) = -3*p(t) - 2*w(t). Find o such that h(o) = 0.
-1/4, 2
Let u be 43/84 + 37/(-444). Determine c, given that 0 + u*c**5 + 0*c**2 + 0*c - 3/7*c**3 + 0*c**4 = 0.
-1, 0, 1
Let q be (0 + 1)*(-80)/(-240). Let l(z) be the first derivative of 0*z + 3/2*z**2 - q*z**3 - 7. Factor l(k).
-k*(k - 3)
Let s = 219 + -215. Let l(z) be the first derivative of -1/2*z**4 + 0*z**2 + 0*z - s + 2/3*z**3. Factor l(y).
-2*y**2*(y - 1)
Let p = -14039/21 + 2009/3. Factor -2/7*f**2 + 0 - p*f.
-2*f*(f + 4)/7
Solve -5*q**2 - 10*q - 110411 + 110411 = 0 for q.
-2, 0
Let r = 1517/4 - 377. Let u(m) be the first derivative of -5 - 1/4*m**3 + r*m**2 - 27/4*m. Factor u(p).
-3*(p - 3)**2/4
Let v = -43 + 62. Let u = v + -18. Let r(x) = 5*x**2 + 11*x + 8. Let g(d) = -d**2 + d. Let w(k) = u*r(k) + g(k). Suppose w(o) = 0. What is o?
-2, -1
Let z = 28/13 + -2. Factor z*k**2 - 10/13 - 8/13*k.
2*(k - 5)*(k + 1)/13
Suppose -20/3*s**2 + 1/3*s**3 + 0 + 19/3*s = 0. Calculate s.
0, 1, 19
Let o(g) be the second derivative of -9/140*g**7 + 39/200*g**5 - 2/5*g**3 + 1/5*g**2 - 3/20*g**6 - g + 29/120*g**4 + 0. Find a such that o(a) = 0.
-2, -1, 1/3, 2/3
Suppose -4*v + 296 = 4*t, v - 2*v = -4*t - 49. Let x = -68 + v. Factor -i - 1/4*i**2 - x.
-(i + 2)**2/4
Let s(y) be the second derivative of 3*y**5/40 - 51*y**4/4 + 867*y**3 - 29478*y**2 - 3*y + 3. Find d, given that s(d) = 0.
34
Let u = -1460 + 7304/5. Let b(g) be the first derivative of 2 + 4/15*g**3 + u*g**2 + 4/5*g. Suppose b(l) = 0. Calculate l.
-1
Let c(a) = 5*a**3 - 7*a**3 + a - 2*a + a**2 + a**3. Let o be 112/(-21) + (-2)/(-6). Let l(y) = 22*y**3 - 43*y**2 - 17*y. Let f(p) = o*c(p) + l(p). Factor f(j).
3*j*(j - 2)*(9*j + 2)
Let 26/5*d**2 + 0 + 1/5*d**3 + 169/5*d = 0. Calculate d.
-13, 0
Factor 0*m - 4/13*m**4 - 6/13*m**3 + 0 + 2/13*m**5 + 0*m**2.
2*m**3*(m - 3)*(m + 1)/13
Let m be (15/(-36) + (-32)/96)*-4. Let 0*c - 39/2*c**4 + 36*c**m + 6*c**2 + 0 = 0. What is c?
-2/13, 0, 2
Let l(o) be the first derivative of 1/4*o**4 - 1/2*o**2 + 1/9*o**3 + 1/15*o**5 - 2/3*o - 25. Factor l(c).
(c - 1)*(c + 1)**2*(c + 2)/3
Let q(u) be the first derivative of -u**4/14 + 62*u**3/21 - 139. Determine c so that q(c) = 0.
0, 31
Let c = 98 - 98. Let v(r) be the first derivative of 1/9*r**3 + c*r - 4 + 1/6*r**2. Factor v(m).
m*(m + 1)/3
Let z = 180/13 + -9707/702. Let u(c) be the second derivative of 0*c**2 + z*c**4 + 2/27*c**3 + 2*c + 0. Find k, given that u(k) = 0.
-2, 0
Suppose 0 = -3*p + 2*i, -4 - 1 = 2*p - 3*i. Factor 4*o**p - 8*o**2 - 8*o**3 - 8*o**2 - 3*o**4 - 4*o**3.
-3*o**2*(o + 2)**2
Let l(m) = 135*m**3 - 865*m**2 - 190*m + 865. Let j(n) = 5*n**3 - 32*n**2 - 7*n + 32. Let x(f) = -55*j(f) + 2*l(f). Determine w, given that x(w) = 0.
-1, 1, 6
Let q = 84 - 88. Let m be (q/(-2))/((-196)/(-280)). Solve -m*h**2 + 4/7*h**3 - 12/7 + 4*h = 0.
1, 3
Let o(q) = 2*q**2 + 7*q - 9. Let k be o(-5). Factor t**2 + 2*t**3 + 191*t**4 + k*t - 11*t**2 - 189*t**4.
2*t*(t - 1)**2*(t + 3)
Let s(c) be the second derivative of c**4/48 + c**3/2 + 10*c + 5. Solve s(o) = 0.
-12, 0
Let a(x) be the third derivative of -x**7/105 - x**6/60 + x**5/5 + x**4/3 - 8*x**3/3 + 246*x**2. Factor a(g).
-2*(g - 2)*(g - 1)*(g + 2)**2
Let q(v) be the third derivative of -v**7/525 - v**6/60 + 4*v**5/75 + v**4/5 - v**2 + 58*v. Find f, given that q(f) = 0.
-6, -1, 0, 2
Let x be ((-3)/4)/(-18 - 1377/(-96)). Let u(g) be the first derivative of 0*g + 3/13*g**2 + x*g**3 + 1/26*g**4 - 2. Solve u(i) = 0.
-3, -1, 0
Determine t so that 60*t - 10*t - 52 - 72*t**2 + 74*t**2 = 0.
-26, 1
Suppose -4*v + 17 + 15 = 0. Suppose -2 + v = 3*l. Find w such that -4*w**2 - 2*w + l*w**2 - w**5 - 15*w**4 + 17*w**4 + 3*w = 0.
-1, 0, 1
Factor 6*m + 1/2*m**3 + 3*m**2 + 4.
(m + 2)**3/2
Factor -3/7*c**3 - 46875/7 - 225/7*c**2 - 5625/7*c.
-3*(c + 25)**3/7
Let u(g) = g - 1. Let r be u(4). Find d such that -6*d**4 + 36*d**r + 0*d**4 - 3*d**4 - d**4 + 8 - 34*d**2 = 0.
-2/5, 1, 2
Suppose 1495 = 2*l + 1495. Factor -9/5*b**2 + 0*b**3 + 6/5*b + 3/5*b**4 + l.
3*b*(b - 1)**2*(b + 2)/5
Let p(s) be the first derivative of s**6/160 + 3*s**5/80 + s**4/16 + s**2/2 - 9*s - 50. Let m(h) be the second derivative of p(h). Factor m(y).
3*y*(y + 1)*(y + 2)/4
Let r(l) = -12*l + 78. Let w be r(6). Let p(g) be the third derivative of -1/300*g**w + 4*g**2 + 0*g**3 - 1/150*g**5 + 0 + 0*g + 0*g**4. Factor p(a).
-2*a**2*(a + 1)/5
Let c be (4/(-16))/((-7)/(-28)*-3). Factor c*p**4 + 0*p - 1/3*p**2 + 0*p**3 + 0.
p**2*(p - 1)*(p + 1)/3
Let v(f) be the second derivative of 0 + 1/120*f**5 + 0*f**4 - f - 1/12*f**3 - f**2. Let i(b) be the first derivative of v(b). Factor i(w).
(w - 1)*(w + 1)/2
Let d(s) be the third derivative of 1/90*s**5 + 0*s + 1/54*s**4 - 16*s**2 + 1/540*s**6 + 0*s**3 + 0. Factor d(u).
2*u*(u + 1)*(u + 2)/9
Let t(m) = -11*m**2 + 13*m + 59. Let d be t(-4). Let x = d + 849/5. Factor x*o**4 + 2/5*o**3 + 0 + 0*o + 0*o**2 + 2/5*o**5.
2*o**3*(o + 1)**2/5
Let d(q) be the second derivative of 14*q**6/15 - 278*q**5/5 + 2720*q**4/3 + 1600*q**3/3 + 129*q + 2. Solve d(k) = 0 for k.
-2/7, 0, 20
Let h(k) = -k**3 - 10*k**2 + 4*k - 1. Let z(r) = r**2 - r. Let c(s) = 5*h(s) + 35*z(s). Factor c(t).
-5*(t + 1)**3
Let h(g) be the third derivative of 1/24*g**6 + 5/8*g**4 + 4*g**2 - 1/4*g**5 - 5/6*g**3 + 0 + 0*g. Factor h(i).
5*(i - 1)**3
Factor 4/9*s**4 - 16/9*s - 16/9 + 4/3*s**2 + 16/9*s**3.
4*(s - 1)*(s + 1)*(s + 2)**2/9
Let u(l) = -l - 7. Let i be u(-9). Suppose -5*p + i*p + 12 = 0. Factor -13*s**4 - 5*s**3 - s**2 + s**5 + 8*s + 23*s**4 - 9*s**4 - p.
(s - 1)**3*(s + 2)**2
Let c(j) be the first derivative of 7*j**3 - 51*j**2/2 + 30*j + 83. Let c(u) = 0. Calculate u.
1, 10/7
Let r(j) be the second derivative of 0 - 6*j**2 - 5/4*j**4 - 3/20*j**5 - 6*j - 4*j**3. Factor r(l).
-3*(l + 1)*(l + 2)**2
Let j(b) be the first derivative of -4 + 0*b**2 + 0*b**3 - 2/5*b**5 + 1/3*b**4 + 0*b + 1/9*b**6. Factor j(h).
2*h**3*(h - 2)*(h - 1)/3
Let a = 211/335 + -2/67. Let i(o) be the first derivative of 5 - a*o**5 - 3/4*o**2 + 0*o**4 + o**3 + 1/4*o**6 + 0*o. Factor i(s).
3*s*(s - 1)**3*(s + 1)/2
Suppose 2*o = -2*n + 234, 16*o - 11*o + 2*n = 588. Let d = o + -116. Factor 1/7*h**3 + 2/7*h + 0 - 3/7*h**d.
h*(h - 2)*(h - 1)/7
Let d(u) be the second derivative of -u**5/10 + u**4/6 + 10*u**3/3 + 8*u**2 + 386*u. What is f in d(f) = 0?
-2, -1, 4
Let w(q) be the second derivative of q**7/189 - 2*q**6/135 + q**4/27 - q**3/27 - 2*q - 3. Factor w(m).
2*m*(m - 1)**3*(m + 1)/9
Let y(t) = -5*t**3 - 60*t**2 - 565*t - 685. Let x(q) = -q**3 - 10*q**2 - 94*q - 114. Let w(f) = -35*x(f) + 6*y(f). Suppose w(s) = 0. What is s?
-2, 6
Factor -s**2 - 2*s + 9 - 61 + 9*s + 7*s + 3*s.
-(s - 13)*(s - 4)
Let l(w) be the third derivative of 1/525*w**7 + 0 + 0*w - 1/300*w**6 + 1/420*w**8 + 0*w**3 + 0*w**5 + 0*w**4 - 10*w**2. Factor l(p).
2*p**3*(p + 1)*(2*p - 1)/5
Let c(l) be the second derivative of -l**6/720 + l**5/30 - l**4/3 + 7*l**3/3 - 15*l. Let b(v) be the second derivative of c(v). Solve b(u) = 0.
4
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