*3 + 53*l**2 - 873*l + 3105. Let v(t) = 2*w(t) - z(t). What is p in v(p) = 0?
5, 25
Factor 377*j**3 - 202*j**3 - 14*j**2 - 176*j**3 - 33*j.
-j*(j + 3)*(j + 11)
Let k = -340 + 340. Let z(y) be the second derivative of 1/252*y**7 + 0*y**4 + k*y**3 + 1/180*y**6 + 0*y**5 + 0 + 0*y**2 + 35*y. Let z(s) = 0. What is s?
-1, 0
Let w(n) = 4302*n + 38718. Let m be w(-9). What is y in 1/2*y**2 + 1/2*y**4 + 0*y + y**3 + m = 0?
-1, 0
Let d be 12/(-1638)*12/100. Let s = 1298/2275 - d. Factor 0*k**3 + 2/7*k - 4/7*k**2 + 0 - 2/7*k**5 + s*k**4.
-2*k*(k - 1)**3*(k + 1)/7
Solve 1295*w**2 - 1290 + 11*w**4 - 747*w + 415*w**3 - 8*w**4 + 332*w - 8*w**4 = 0.
-3, -1, 1, 86
Let q(b) = -366*b - 368*b - 377*b + 1127*b - 14 - 3*b**2. Let d be q(4). Solve -1/3*p**d + 0*p + 1/3 = 0.
-1, 1
Factor 88 - 26/3*b**2 + 1/3*b**3 - 239/3*b.
(b - 33)*(b - 1)*(b + 8)/3
Factor -1170*n**2 - 3042*n - 2/3*n**4 - 54*n**3 + 0.
-2*n*(n + 3)*(n + 39)**2/3
Let j(f) be the first derivative of f**7/1680 - f**5/60 - 28*f**3 + 107. Let y(t) be the third derivative of j(t). Suppose y(p) = 0. Calculate p.
-2, 0, 2
Let d(a) be the third derivative of a**5/100 - 33*a**4/5 - 266*a**3/5 + 20*a**2 - 39*a. Suppose d(z) = 0. Calculate z.
-2, 266
Let s(b) be the first derivative of 2/27*b**3 + 22/9*b + 4/3*b**2 - 42. Factor s(k).
2*(k + 1)*(k + 11)/9
Let r(l) be the first derivative of -2*l**3/3 + 22*l**2 - 2640. Factor r(j).
-2*j*(j - 22)
What is z in 85*z - 600 - 5/4*z**2 = 0?
8, 60
Let v(t) be the second derivative of -1/20*t**6 + 0 - 14*t - 2*t**3 - 3/2*t**4 + t**2 - 9/20*t**5. Let y(q) be the first derivative of v(q). Factor y(p).
-3*(p + 2)**2*(2*p + 1)
Let o = 4/5 + 2/5. Suppose -18*g - 189 - 167 + 392 = 0. Factor -o*n - 4/5 - 2/5*n**g.
-2*(n + 1)*(n + 2)/5
Let x(w) be the first derivative of -w**5 - 15*w**4/2 - 5*w**3/3 + 60*w**2 - 80*w + 1538. Factor x(q).
-5*(q - 1)**2*(q + 4)**2
Suppose 7*u - 22*u + 90 = 0. Let y be (-300)/(-200) + (-7)/u. What is j in 4/3*j - 1 - y*j**2 = 0?
1, 3
Solve 145*l + 135*l**3 - 150*l**2 - 409 + 418*l**2 + 287*l**2 - 425 - l**4 = 0 for l.
-3, -2, 1, 139
Let a(v) be the second derivative of -v**6/90 + 47*v**5/6 - 2041*v**4 + 1897973*v**3/9 + 3869893*v**2/6 - 959*v + 1. Factor a(o).
-(o - 157)**3*(o + 1)/3
Let k(z) be the second derivative of -7/20*z**5 + 1 + 99*z + 1/15*z**3 + 11/20*z**4 + 0*z**2. Determine l, given that k(l) = 0.
-2/35, 0, 1
Let k be (2 + (-228)/9)*1*(-36)/96. Let j(d) be the second derivative of 0 - 1/4*d**5 - k*d**4 - 245/2*d**3 + d - 1715/2*d**2. What is w in j(w) = 0?
-7
Let v(m) be the second derivative of 45*m**5 + 227*m**4/3 + 4*m**3/3 - 4423*m. Factor v(h).
4*h*(h + 1)*(225*h + 2)
Let v(g) be the first derivative of 2*g**5/85 - 13*g**4/34 - 70*g**3/17 - 167*g**2/17 - 152*g/17 - 4309. What is l in v(l) = 0?
-4, -1, 19
Let j(a) be the second derivative of a**4/78 - 29*a**3/39 + 100*a**2/13 - 1344*a. Factor j(d).
2*(d - 25)*(d - 4)/13
Let b(u) be the second derivative of 992/25*u**6 + 533/15*u**4 + 1369/25*u**5 + 0 + 8/5*u**2 + 32/3*u**3 + 384/35*u**7 - 36*u. Find t, given that b(t) = 0.
-1, -2/3, -1/8
Let i(o) be the first derivative of 3*o**4/28 + 820*o**3/7 - 3*o**2/14 - 2460*o/7 + 1029. Factor i(a).
3*(a - 1)*(a + 1)*(a + 820)/7
Let a(t) be the first derivative of 3*t**4/16 - 5*t**3/4 + 9*t**2/8 + 116*t + 62. Let n(b) be the first derivative of a(b). Suppose n(x) = 0. Calculate x.
1/3, 3
Let z = 978 + -975. Let d be -1 - (-15)/z - (-76)/(-20). Factor -7/5*w**2 - 2/5*w + 0 - d*w**5 - w**4 - 9/5*w**3.
-w*(w + 1)**3*(w + 2)/5
Suppose -14 = -4*r - 2*i, 6*r = 2*r + 5*i - 7. Solve n**3 + 5*n**5 + 13*n**r - 36*n**3 - 22*n**2 + 39*n**2 = 0.
-3, 0, 1, 2
Let z(v) be the second derivative of -3*v**5/100 - 2*v**4/5 - 17*v**3/10 - 3*v**2 - 2*v - 11. Let z(k) = 0. What is k?
-5, -2, -1
Let j(t) = t + 1. Let d(q) = -1. Let f(i) = -6*d(i) + j(i). Let l be f(-4). Suppose -6 + 5 - z**2 + 3*z - 7*z - l = 0. What is z?
-2
Let f(x) = 13*x + 148. Let k(v) = 27*v + 309. Let m(w) = -7*f(w) + 3*k(w). Let i be m(-11). What is z in -7/4*z**2 - 5/4*z**3 + 2*z + i = 0?
-2, -2/5, 1
Let s(g) = 15*g**4 - 780*g**3 - 3230*g**2 - 5*g. Let n(a) = 22*a**4 - 1169*a**3 - 4846*a**2 - 7*a. Let f(w) = 5*n(w) - 7*s(w). Factor f(m).
5*m**2*(m - 81)*(m + 4)
Let f(k) be the second derivative of 3*k**5/100 + 41*k**4/20 - 22*k**3/5 - 126*k**2/5 - 1709*k. Factor f(h).
3*(h - 2)*(h + 1)*(h + 42)/5
Let a = 3008 + -3001. Let q(c) be the first derivative of 2/63*c**3 + 2/21*c**2 + a + 2/21*c. Factor q(z).
2*(z + 1)**2/21
Let h(n) be the first derivative of 3*n**6 - 672*n**5/5 + 1799*n**4 - 15784*n**3/3 - 6511*n**2 - 2312*n - 3700. Let h(b) = 0. Calculate b.
-1/3, 4, 17
Let f(p) be the first derivative of p**6/17 + 88*p**5/85 - p**4/2 - 20*p**3/17 + 399. Suppose f(g) = 0. What is g?
-15, -2/3, 0, 1
Solve 1215*j**2 + 17321 - 17321 - 3*j**3 - 957*j**2 = 0 for j.
0, 86
What is f in -28772*f**2 - 13924 - 41300*f - 11588*f**2 + 4351*f**3 - 5*f**4 + 465*f**4 - 16871*f**3 - 4*f**5 = 0?
-1, 59
Let x(b) = -2*b**3 + 4752*b**2 - 1507335*b + 159275098. Let w(p) = 15*p**3 - 33265*p**2 + 10551345*p - 1114925675. Let v(m) = -3*w(m) - 20*x(m). Factor v(d).
-5*(d - 317)**3
Let k(g) be the first derivative of 0*g**2 - 1/4*g**3 + 6*g - 24 - 5/24*g**4 + 1/20*g**5. Let v(i) be the first derivative of k(i). Factor v(m).
m*(m - 3)*(2*m + 1)/2
Suppose 117 = 19*a + 22. Let g(i) be the first derivative of 15 + 5/3*i**3 - 5/6*i**6 + 0*i**2 + 0*i - i**a + 5/4*i**4. Factor g(x).
-5*x**2*(x - 1)*(x + 1)**2
Let s(m) be the first derivative of -m**7/210 + m**5/12 - 2*m**3/3 + 55*m**2/2 - 27. Let u(n) be the second derivative of s(n). Find y, given that u(y) = 0.
-2, -1, 1, 2
Let f(j) be the third derivative of -j**2 + 1/390*j**5 + 18*j - 8/13*j**3 + 0 + 5/156*j**4. Solve f(c) = 0.
-8, 3
Let t(i) = 23*i**4 + 20*i**3 + 67*i**2 - 83*i + 3. Let p(z) = 8*z**4 + z**3 + z**2 - z + 1. Let g(b) = -3*p(b) + t(b). Determine j so that g(j) = 0.
-4, 0, 1, 20
Suppose 22*x + 6 = 23*x. Factor -2226*q**5 + 2231*q**5 + 4*q**4 - 10*q**2 + x*q**4 - 5*q**3.
5*q**2*(q - 1)*(q + 1)*(q + 2)
Let m be 3/((-27)/(-5462)) - 35/(-315). Let w = 1215/2 - m. Factor -w*b - 1/4 - 1/4*b**2.
-(b + 1)**2/4
Let i be (-643 - -636)/(35/(-15)). Find n, given that 1/10*n + 0 + 0*n**2 - 1/10*n**i = 0.
-1, 0, 1
Let n(u) = 8*u**3 + 18189*u**2 + 18181*u - 7. Let p(x) = -3*x**3 - 6064*x**2 - 6061*x + 2. Let r(g) = 2*n(g) + 7*p(g). Factor r(z).
-5*z*(z + 1)*(z + 1213)
Let u(p) = -7*p**3 + 76*p**2 + 192*p + 39. Let f be u(13). Factor 0*o**2 + 2/3*o**5 + f*o + 4/3*o**3 - 2*o**4 + 0.
2*o**3*(o - 2)*(o - 1)/3
Let j = -8853 + 8855. Let z(d) = 2*d**2 + d + 1. Let v(b) = -2 - 18*b**2 + 7*b**2 - 29*b**2 - 10*b. Let y(a) = j*z(a) + v(a). Determine i, given that y(i) = 0.
-2/9, 0
Let a(u) be the first derivative of -3*u**4 - 12 + 1/15*u**5 + 21/2*u**2 + 0*u + 54*u**3. Let m(d) be the second derivative of a(d). Factor m(l).
4*(l - 9)**2
Suppose 13*c - 33 = 578. Suppose 0 = 4*u - 3*y - 5, 5*u + c*y - 14 = 43*y. Factor -2/5*q**3 + 0 - 2*q**u - 8/5*q.
-2*q*(q + 1)*(q + 4)/5
Let u(a) = -6*a**3 + 18*a**2 + 71*a - 1. Let r be u(-6). Factor -77*o**2 - 128*o**3 + 13648*o**4 - 13644*o**4 - 6400*o + 8000 + r*o**2.
4*(o - 10)**3*(o - 2)
Let g be (648/(-12))/((-22)/16). Let m(k) be the first derivative of -24 + 12/11*k**3 + 108/11*k**2 + g*k + 1/22*k**4. Factor m(o).
2*(o + 6)**3/11
Factor 572/3*n + 0 - 1/3*n**2.
-n*(n - 572)/3
Let i(d) = 3*d**2 + 18*d. Let g be i(-13). Let f = g + -271. Determine r so that 0*r**f - 3*r**3 - 12 + 12*r + 3/4*r**4 = 0.
-2, 2
Factor -9345482*u - 359 + u**2 - 37 + 9345087*u.
(u - 396)*(u + 1)
Let q(y) = y. Let i be q(6). Let o(m) = -9*m**5 + 6*m**2 - 6*m. Let b(c) = 10*c**5 - 7*c**2 + 7*c. Let x(v) = i*b(v) + 7*o(v). Factor x(t).
-3*t**5
Let b(c) = c**3 - 2*c. Let m(t) = t**3 - 38*t**2 - 135*t + 170. Let s(q) = -2*b(q) + m(q). Find x, given that s(x) = 0.
-34, -5, 1
Let q(y) be the first derivative of y**4/6 + 26*y**3/9 - 205*y**2/3 + 1150*y/3 + 11190. Determine m, given that q(m) = 0.
-23, 5
Let u(q) = -q**2 + 313*q - 928. Let k be u(3). Suppose -5*g - 4*f + 5 = 0, -f - 48 + 18 = -5*g. Determine v, given that -152*v + 0 + 0 + 157*v - g*v**k = 0.
0, 1
Let b be (0/2 + 0)*(50/15 + -3). Let v(h) be the third derivative of 1/420*h**5 + 0*h**3 + 0*h**6 - 15*h**2 + b - 1/