 155*u**2 - 26125*u + 2421890. Let s(p) = -85*b(p) + 6*m(p). Determine t, given that s(t) = 0.
186
Let w(i) be the second derivative of -i**7/42 - 44*i**6/15 - 484*i**5/5 - 2*i - 150. Factor w(k).
-k**3*(k + 44)**2
Let b(n) be the third derivative of n**8/84 - n**7/105 - 19*n**6/30 + 79*n**5/30 - 5*n**4/2 - 560*n**2. Solve b(i) = 0.
-5, 0, 1/2, 2, 3
Let v(f) = 2*f**3 + 4*f**2 + 2*f + 4. Let i be v(-2). Solve -3*t**2 + i + 3/8*t + 6*t**3 = 0 for t.
0, 1/4
Factor -5*h**4 + 28*h + 78*h**3 - 2*h**5 - 17*h**4 - 22*h**2 - 69*h**2 + 9*h**2.
-2*h*(h - 1)**3*(h + 14)
Let o = 3296048763470/12483 - 264043000. Let i = 2/1387 - o. Factor -i*k**2 - 8/9*k + 2/9*k**3 + 16/9.
2*(k - 2)**2*(k + 2)/9
Let n be ((-325)/(-24))/(-5) - 8/(-60). Let h = n - -27/8. What is y in 8/5*y**2 + h - 2/5*y**3 - 2*y = 0?
1, 2
Let u be (-24)/28*((-18)/(-3))/(-6). Let r = 4/45 - -152/315. Solve u*t + 2/7*t**2 + r = 0 for t.
-2, -1
Suppose -4*j = -4*p + p + 46, 3*j = -p + 11. Let u be (-7)/p*(-18 - -2). Suppose -2*h**2 + h**5 + 7*h**4 - u*h**4 - h**3 + 3*h**4 = 0. What is h?
-2, -1, 0, 1
Factor 16*p**5 + 3*p**2 - 3*p**2 - 15*p**4 + 48*p**3 - 46*p**3 - 3*p**5.
p**3*(p - 1)*(13*p - 2)
Let v(g) be the second derivative of -g**5/100 - g**4/15 - g**3/30 + 3*g**2/5 + 415*g. Factor v(c).
-(c - 1)*(c + 2)*(c + 3)/5
Let g be (2 - 9/6) + -24 + 1. Let j = g - -24. Factor 3/2*f**2 - 3/2*f**3 - j + 3/2*f.
-3*(f - 1)**2*(f + 1)/2
Let f(g) be the first derivative of 5/2*g**2 + 10/3*g**3 + 5/6*g**6 - 5*g + 23 - 5/2*g**4 - g**5. Factor f(k).
5*(k - 1)**3*(k + 1)**2
Let z(l) be the second derivative of -6/7*l**2 + 24*l + 19/28*l**4 + 0 + 4/7*l**3 + 3/20*l**5. Factor z(p).
3*(p + 1)*(p + 2)*(7*p - 2)/7
Let o(l) = 27*l**3 - 193*l**2 + 283*l - 150. Let r(v) = 5*v**3 - 38*v**2 + 57*v - 30. Let b(n) = 4*o(n) - 22*r(n). Factor b(d).
-2*(d - 30)*(d - 1)**2
Let i = 2/275 + 31/3300. Let a(v) be the third derivative of -5/24*v**4 + 1/2*v**3 + 0*v + 4*v**2 + 0 + i*v**5 + 1/120*v**6. Factor a(n).
(n - 1)**2*(n + 3)
Let m(l) be the first derivative of -3*l**5/10 - 189*l**4/4 - 3969*l**3/2 + 252. Let m(x) = 0. Calculate x.
-63, 0
Factor 16/7*n**3 + 32/7*n + 2/7*n**4 + 40/7*n**2 + 0.
2*n*(n + 2)**2*(n + 4)/7
Let a(j) be the first derivative of -j**5/10 + j**4/6 + j**3/3 - j**2 + 15*j - 12. Let p(x) be the first derivative of a(x). Factor p(h).
-2*(h - 1)**2*(h + 1)
Let n(w) be the second derivative of -w**6/180 - w**5/30 + 5*w**4/36 + 7*w**3/9 + 5*w**2/4 - 26*w. Factor n(c).
-(c - 3)*(c + 1)**2*(c + 5)/6
Let s(t) = -3*t**3 + t**2 - 2*t. Let n(g) = 14*g**3 - 4*g**2 + 8*g. Let m(r) = -2*n(r) - 9*s(r). Find b, given that m(b) = 0.
-2, 0, 1
Let w(a) be the third derivative of -a**7/11340 + a**6/3240 - a**4/2 - 10*a**2. Let b(k) be the second derivative of w(k). Factor b(g).
-2*g*(g - 1)/9
Let w(t) be the second derivative of -t**4/30 + 9*t**2/5 - 113*t. Factor w(k).
-2*(k - 3)*(k + 3)/5
Solve 960*f + 977 + 225 - 41*f**3 + 72*f**2 - 2 - 7*f**3 + 3*f**4 = 0.
-2, 10
Let p(a) = 3 - 5 + 5*a - 4 + 2 - a**2. Let t be p(3). Factor 6*r**3 - 2*r**4 - 2*r**4 + 10*r**t - 2*r**5 + 4*r + 2*r**4.
-2*r*(r - 2)*(r + 1)**3
Let q(m) be the third derivative of -m**7/42 - 5*m**6/24 - 3*m**5/4 - 35*m**4/24 - 5*m**3/3 + 226*m**2. Factor q(w).
-5*(w + 1)**3*(w + 2)
Let g(f) be the second derivative of f**7/105 - f**5/5 - 2*f**4/3 - f**3 + 2*f**2 + 21*f. Let t(j) be the first derivative of g(j). Suppose t(i) = 0. What is i?
-1, 3
Determine f so that -12*f**3 - 9/4*f**2 - 3 + 21/4*f**4 + 12*f = 0.
-1, 2/7, 1, 2
What is h in -7605/2*h - 313*h**3 + 2197 - 1/2*h**5 + 1898*h**2 + 21*h**4 = 0?
1, 2, 13
Let f(j) be the second derivative of 5/3*j**6 - 9/2*j**5 + 12*j**3 - 13/3*j**4 - 8*j**2 + 17*j + 0. Let f(v) = 0. Calculate v.
-1, 2/5, 2
Let h(m) be the third derivative of 1/10*m**5 - 10*m**2 + 2/9*m**3 - 7/36*m**4 + 0*m + 1/315*m**7 + 0 - 1/36*m**6. Factor h(x).
2*(x - 2)*(x - 1)**3/3
Let x = -212 + 429/2. Determine o so that 7/4*o - 1/2 - x*o**3 - 1/4*o**2 = 0.
-1, 2/5, 1/2
Suppose -2*i + 1 = 3. Let t = i - -6. Factor -7*w**4 - 3*w**2 + 10*w**4 - 2*w + t*w - 3*w**3.
3*w*(w - 1)**2*(w + 1)
Let k be (13 + -13)*(0/3 - 1). Determine f so that k*f**4 - 1/4*f - 1/4*f**5 + 1/2*f**3 + 0 + 0*f**2 = 0.
-1, 0, 1
Suppose -g + 10 = 4*g. Let l = -90887/3 + 30311. Factor 80/3*z**2 + l*z + g - 32/3*z**3.
-2*(z - 3)*(4*z + 1)**2/3
Let h be 230/50 - (-2)/5. Factor 6*u**4 - 1092*u**5 + 1087*u**h + 9*u**4.
-5*u**4*(u - 3)
Suppose 10*a + 8 = -2. Let l be (-8 - 339/(-42))*(45 + a). Let -12/7 + 40/7*d**3 + 114/7*d**2 - l*d = 0. What is d?
-3, -1/4, 2/5
Let b(w) be the first derivative of -13*w**4/4 - 2*w**3 + 215. Factor b(u).
-u**2*(13*u + 6)
Let r(m) be the second derivative of 5*m**4/12 + 55*m**3/3 + 249*m. Factor r(o).
5*o*(o + 22)
Let g = 10 + -7. Find r such that -20*r - 2*r**3 + 16*r**2 - 3*r**3 - 4*r**3 + 5*r**g + 8 = 0.
1, 2
Let n(x) be the third derivative of 0*x + 1/60*x**6 + 1/180*x**4 + 0*x**3 - 15*x**2 - 1/175*x**7 + 0 - 7/450*x**5. Factor n(m).
-2*m*(m - 1)*(3*m - 1)**2/15
Suppose -3*g - 5 = -d, 0 = -4*g + 9*g + 5*d - 25. Let y(u) be the third derivative of 1/240*u**5 + 4*u**2 + 0 + 0*u**4 + 0*u + 1/480*u**6 + g*u**3. Factor y(c).
c**2*(c + 1)/4
Let m(o) be the first derivative of 91*o**5 + 425*o**4/2 + 105*o**3 - 50*o**2 - 20*o - 11. What is w in m(w) = 0?
-1, -2/13, 2/7
Let q(v) be the first derivative of -15/2*v**2 + 5*v**3 + 14 - 5/4*v**4 + 5*v. Find l, given that q(l) = 0.
1
Let z(l) = l**2 + 1. Let m(o) = 10*o**2 + 10*o + 15. Let q(p) = -60*p**2 - 60*p - 90. Let r(d) = 25*m(d) + 4*q(d). Let y(s) = -r(s) + 15*z(s). Factor y(w).
5*w*(w - 2)
Determine v, given that -11/2*v**2 - 21/2 + 1/2*v**3 + 31/2*v = 0.
1, 3, 7
Suppose -64*z + 60*z + 8 = 0. Let -9*p**2 + 4*p**z - 6*p + 8*p**2 = 0. What is p?
0, 2
Factor -2/13*b**3 + 144/13*b - 30/13*b**2 - 152/13.
-2*(b - 2)**2*(b + 19)/13
Let k(t) be the first derivative of 5*t**6/18 - 7*t**5/15 - 11*t**4/4 + 19*t**3/9 + 14*t**2/3 - 4*t - 253. What is h in k(h) = 0?
-2, -1, 2/5, 1, 3
Let x be (-1 - -12) + (25/(-2) - 1281/(-366)). Suppose 0 - 2/9*w**5 + 0*w - 4/9*w**x + 2/9*w**3 + 4/9*w**4 = 0. What is w?
-1, 0, 1, 2
Let m(h) be the first derivative of -18*h - 2/3*h**3 + 6*h**2 - 4. Solve m(v) = 0.
3
Let s = 335 + -637. Let q = -299 - s. Suppose 16/3*g**2 - 10/3*g + 2/3 - 8/3*g**q = 0. What is g?
1/2, 1
Let l(k) be the first derivative of -1/9*k**4 - 8/45*k**5 - 25 + k**2 + 1/27*k**6 + 0*k + 8/9*k**3. Factor l(t).
2*t*(t - 3)**2*(t + 1)**2/9
Find y, given that 128/3 - 14/3*y**4 - 80/3*y + 68/3*y**3 - 24*y**2 = 0.
-8/7, 2
What is b in 6*b + 2/7*b**2 - 44/7 = 0?
-22, 1
Determine m so that -1/12*m**2 - 1/4*m - 1/6 = 0.
-2, -1
Let g be 3/45*(1 + 8). Suppose 22*w + 3 = 3. Find b such that -3/5*b**3 + w + g*b - 3/5*b**2 + 3/5*b**4 = 0.
-1, 0, 1
Let a = -1325/6 + 17237/78. Factor 2/13*x**4 - a*x + 0 + 2/13*x**3 - 2/13*x**2.
2*x*(x - 1)*(x + 1)**2/13
Let p(i) = -2*i**3 + i**2 - i. Let r(j) = -9*j**3 + 22*j**2 + 15*j. Let n(y) = 4*p(y) - r(y). Factor n(h).
h*(h - 19)*(h + 1)
Let i(q) be the third derivative of -q**6/40 - 7*q**5/20 + 5*q**4/8 + 75*q**3/2 - 110*q**2. Suppose i(l) = 0. What is l?
-5, 3
Let c(y) be the second derivative of -y**5/30 + 49*y**4/9 - 2300*y**3/9 - 5000*y**2/3 - 185*y. Factor c(p).
-2*(p - 50)**2*(p + 2)/3
Let b(s) = -18*s - 2480. Let i be b(-138). Determine f, given that f**2 + 1/4*f**3 - f + 0 - 1/4*f**i = 0.
-2, 0, 1, 2
Let l = 25 + -29. Let t be (-3 - l)*12/2. Factor 2 + 5*v**2 - 6*v**2 + 3*v**2 - 2*v + t*v.
2*(v + 1)**2
Let r(g) = -3*g - 4*g + 2*g**2 - 4 - g. Let b(p) = -p**2 + 7*p + 3. Let w(d) = 4*b(d) + 3*r(d). Factor w(m).
2*m*(m + 2)
Let x(u) be the second derivative of u**4/24 - 5*u**3/4 + 13*u**2/2 + 7*u - 6. Factor x(r).
(r - 13)*(r - 2)/2
Let p(w) be the third derivative of w**8/2688 + 3*w**7/560 + 9*w**6/320 + 23*w**5/480 - w**4/8 - 3*w**3/4 - 145*w**2. Suppose p(c) = 0. Calculate c.
-3, -2, 1
Suppose -3*c + 0*c + 372 = 0. Let k = c - 124. Factor -16/5*m**3 - 28/5*m**4 - 8/5*m**5 + k + 16/5*m**2 + 0*m.
-4*m**2*(m + 2)**2*(2*m - 1)/5
Let j(f) = f + 14. Let g be j(-16). Let v(y) = -3*y**5 + 2*y**4 - y. Let l(q) = -4*q**5 + 3*q**4 - q**3 - q. Let u(n) = g*l(n) + 3*v(n). Factor u(d).
-d*(d - 1)**2*(d + 1)**2
Let v(g) = -g**3 + g + 2. Let p be v(-2). Suppose -12*l + 8*l + p = 0. Fact