- 1)*(s + 9)
Let s(l) be the first derivative of l**5/300 - l**4/60 + 11*l**2/2 - 22. Let a(u) be the second derivative of s(u). Suppose a(g) = 0. What is g?
0, 2
Solve 118/7*g - 38/7*g**2 - 12/7 = 0 for g.
2/19, 3
Let d = 2 + 2. Suppose -d*h = 5*q - 24, q - 4 - 1 = -h. Factor -7 + 8*c - q*c**2 + 3*c**2 - 9.
-(c - 4)**2
Find y such that -1/3*y**3 - 1/3*y**4 + 2 + 13/3*y + 7/3*y**2 = 0.
-2, -1, 3
Let j(z) = z**3 - z**2 - 3*z + 1. Suppose 63 = s - 4*s. Let l = -18 - s. Let f(x) = 3*x. Let c(i) = l*j(i) + 2*f(i). Factor c(u).
3*(u - 1)**2*(u + 1)
Suppose -18*q + 2 = -17*q. Let 4*s + 27 + s**2 - 24 + q*s + 2*s**2 = 0. What is s?
-1
Let f(a) = 4*a - 10 - 5*a**2 + 6*a**3 - 16*a**3 + 5*a**3 + 4*a**3. Let i be f(-6). Find o such that 1/5*o**i + 3/5*o - 2/5 + 1/5*o**4 - 3/5*o**3 = 0.
-1, 1, 2
Suppose -2*t + 6*t - 1 = -5*p, 0 = 3*p + 9. Factor 2/9*q**3 - 2/9*q + 2/9*q**2 + 0 - 2/9*q**t.
-2*q*(q - 1)**2*(q + 1)/9
Let m(w) be the first derivative of 4*w**3/3 - 2*w**2 - 8*w + 130. Factor m(d).
4*(d - 2)*(d + 1)
Let o(w) be the first derivative of w**5/20 - 3*w**4/4 + 4*w**3 - 10*w**2 + 12*w - 179. Factor o(l).
(l - 6)*(l - 2)**3/4
Let p(h) = -6*h**4 - 46*h**3 - 26*h**2 + 19*h - 15. Let k(m) = 3*m**4 + 23*m**3 + 13*m**2 - 9*m + 6. Let u(f) = 5*k(f) + 2*p(f). Solve u(j) = 0 for j.
-7, -1, 0, 1/3
Let p(o) = -15*o**2 + 66*o - 30. Let z be (9/6)/((-6)/16). Let u = z + 0. Let n(i) = -3*i**2 + 13*i - 6. Let l(y) = u*p(y) + 21*n(y). Factor l(v).
-3*(v - 2)*(v - 1)
Let h = 51923/7 + -7417. Factor 0 + h*j**2 + 4/7*j.
4*j*(j + 1)/7
Let z(g) be the first derivative of 5*g**4/4 + 40*g**3/3 + 89. Determine u so that z(u) = 0.
-8, 0
Let j(a) be the third derivative of 7*a**5/30 + 11*a**4/180 - 2*a**3/45 - 128*a**2. Determine w so that j(w) = 0.
-1/5, 2/21
Suppose 0 = 2*i + 5*y - 78, -3*y - 2 = -8. Find w such that -44*w**4 + 38*w**5 - 25*w**5 + 64*w**3 + 16*w**2 - 15*w**5 - i*w**5 = 0.
-2, -2/9, 0, 1
Let g(j) be the second derivative of j**5/15 - j**4/2 - 8*j**3/3 + 31*j**2/2 - j. Let a(s) be the first derivative of g(s). Determine h so that a(h) = 0.
-1, 4
Let d = -50 + 10. Let f = -118/3 - d. What is q in q**3 - f - 2/3*q**2 - 7/3*q = 0?
-1, -1/3, 2
Let s(a) be the first derivative of -3*a**4/16 + a**3/4 + 3*a**2/8 - 3*a/4 - 225. Factor s(o).
-3*(o - 1)**2*(o + 1)/4
Let n be ((-3)/(-4))/1 - (-28 - (-24020)/880). Determine q so that n + 2/11*q**2 - 18/11*q = 0.
1, 8
Let h(k) = 5*k**4 - 5*k**3 - k**2 + k + 4. Let w(j) be the first derivative of j**5/5 - j**4/4 + j + 26. Let z(s) = -h(s) + 4*w(s). Solve z(c) = 0.
-1, 0, 1
Let w(l) be the second derivative of -l**4/3 + 608*l**3/3 - 46208*l**2 - 2*l - 6. Factor w(b).
-4*(b - 152)**2
Let y(n) be the third derivative of -n**6/360 - n**5/60 - n**4/24 + n**3/6 + 4*n**2. Let j(x) be the first derivative of y(x). Factor j(k).
-(k + 1)**2
Let h(o) = o**3 - 14*o**2 + 15*o - 23. Let q be h(13). What is f in 16*f**2 - 17*f - 4*f**q - f**3 + 6*f + 8*f = 0?
0, 1/5, 3
Let p(a) = 9*a**3 + 3*a**2 - 12*a + 12. Let t(g) = -2*g**3 - 2*g**2 + g. Let j(v) = p(v) + 4*t(v). Factor j(i).
(i - 6)*(i - 1)*(i + 2)
Let i be (-24)/(2 - 6) + (5 - 9). What is p in -1/10*p**4 + 1/10*p**i - 1/5*p**3 + 0 + 1/5*p = 0?
-2, -1, 0, 1
Factor 4*b**2 - 1288*b**2 - 4*b**4 - 1024 - 4502*b**3 - 2176*b + 4366*b**3.
-4*(b + 1)**2*(b + 16)**2
Suppose 2*h = -5*v - 9, -h + 2 = -2*h. Let a be (-2 - v)*-6 + -3. Suppose w**5 - 2*w**a + 0*w**3 + 0*w**3 + w = 0. Calculate w.
-1, 0, 1
Let z = 33413/3 - 11137. Solve 0*s**4 + 0 + 2/3*s + 0*s**2 + z*s**5 - 4/3*s**3 = 0.
-1, 0, 1
Let y(v) be the second derivative of 2*v**7/21 + 8*v**6/5 - 76*v**5/5 + 146*v**4/3 - 78*v**3 + 68*v**2 - 3*v - 8. Determine z, given that y(z) = 0.
-17, 1, 2
Suppose 3 + 4*v**2 - 1/2*v**3 - 13/2*v = 0. Calculate v.
1, 6
Let k(m) be the first derivative of -1/3*m**4 + 0*m**3 - 2/5*m**5 + 11 + 0*m**2 + 0*m - 1/9*m**6. What is w in k(w) = 0?
-2, -1, 0
Let a be 12/(-10)*(-1995)/42. Let 116*v**2 - 28*v**3 - 12*v - a*v**3 - 20 + 109*v**2 - 8*v - 100*v**4 = 0. What is v?
-2, -1/4, 2/5, 1
Let i(t) be the second derivative of 0*t**2 + 0 + 1/15*t**5 - 6*t + 0*t**3 + 1/9*t**4. Factor i(q).
4*q**2*(q + 1)/3
Let k(y) = y**2 - 11*y - 12. Let z(t) = t**2 - 5*t - 6. Let m(f) = f**2 - 11*f - 2. Let b be m(11). Let h(x) = b*k(x) + 5*z(x). Factor h(g).
3*(g - 2)*(g + 1)
Let j(z) be the third derivative of z**6/480 + z**5/60 + 5*z**4/96 + z**3/12 + 184*z**2. Suppose j(x) = 0. Calculate x.
-2, -1
Determine h so that -39/2*h**2 + 20*h + 0 - 1/2*h**3 = 0.
-40, 0, 1
Suppose -232*v + 42 = -218*v. Let x(p) be the second derivative of -1/8*p**2 - 1/12*p**v - 1/48*p**4 + 5*p + 0. Factor x(u).
-(u + 1)**2/4
Let t be (0 + 0)/(-7 - (-81)/9). Let p(z) be the third derivative of -3*z**2 + 0*z**4 - 1/12*z**3 + 1/120*z**5 + t + 0*z. Suppose p(g) = 0. Calculate g.
-1, 1
Let c**3 + 728*c**2 - 40*c - 24 - 3*c**3 - 746*c**2 = 0. What is c?
-6, -2, -1
Let b(c) be the third derivative of c**8/3528 - c**7/2205 - c**6/252 + c**5/630 + 2*c**4/63 + 4*c**3/63 + 2*c**2 + c. Factor b(o).
2*(o - 2)**2*(o + 1)**3/21
Let v(g) be the first derivative of -g**5/5 + 3*g**4/2 + g**3/3 - 3*g**2 - 319. Factor v(z).
-z*(z - 6)*(z - 1)*(z + 1)
Suppose -f + 8 = -5*f - 4*h, 0 = -f - 3*h - 10. Let r(c) be the first derivative of 0*c + 2/15*c**3 + f - 1/5*c**2. Factor r(o).
2*o*(o - 1)/5
Let n(s) be the first derivative of s**6/10 + 9*s**5/20 - 2*s**3 + 5*s - 25. Let f(w) be the first derivative of n(w). Factor f(v).
3*v*(v - 1)*(v + 2)**2
Suppose 0*i + 2 = -2*i. Let w be i/(-3)*126/(-14). Let t(j) = j**2 - 4*j. Let l(d) = -1. Let o(x) = w*l(x) + t(x). Solve o(v) = 0 for v.
1, 3
Let o(h) = -16*h**2 - 81*h - 65. Let y(t) = -5*t**2 - 27*t - 22. Let v(d) = 2*o(d) - 7*y(d). Factor v(u).
3*(u + 1)*(u + 8)
Let p = 14 - 13. Let y be ((-20)/90)/(p/(-9)). Let 2 + 0*h**2 - 3*h**2 + 3*h + 3*h**y + h**2 = 0. What is h?
-2, -1
Let w be -7*(0 - ((-5)/7 - -1)). Factor 12*j**3 + 267*j**w + 8*j**3 + 5*j**4 - 247*j**2.
5*j**2*(j + 2)**2
Factor -2/5*n**3 + 2*n**2 - 48/5 + 4/5*n.
-2*(n - 4)*(n - 3)*(n + 2)/5
Let 5/2*g + 0 - 1/2*g**2 = 0. Calculate g.
0, 5
Let -30*w**2 - 75*w**2 + 5*w**4 + 27*w**3 + 0*w - 7*w**3 + 0*w = 0. Calculate w.
-7, 0, 3
Find y such that 0*y**4 - 5*y**2 + 7*y + 4*y**2 - 10*y - 2*y**5 + 5*y**3 + y**4 = 0.
-1, 0, 1, 3/2
Let q = -14 - 4. Let z be (-42)/q - (2 - 15/9). What is g in 4/5*g**3 + 2/5 + 2*g**z + 8/5*g = 0?
-1, -1/2
Let i = -184/39 + 96/13. Let v = -1909/6 - -643/2. Factor -i*x - 4/3*x**3 + 2/3 + v*x**2.
-2*(x - 1)**2*(2*x - 1)/3
Let s(b) = -4*b**2 - b - 1. Let p(x) = -15*x**2 - 40*x + 23. Let k(g) = -2*p(g) + 6*s(g). Determine n so that k(n) = 0.
-13, 2/3
Let g be 7*(-3)/(-84)*1/15. Let i(b) be the second derivative of 0 + 1/100*b**5 + g*b**4 - 1/150*b**6 + 0*b**2 - 1/30*b**3 - 6*b. Suppose i(q) = 0. What is q?
-1, 0, 1
Let g(u) be the second derivative of 0 + 6*u + 1/10*u**3 - 3/100*u**5 - 3/5*u**2 + 1/10*u**4. Find l, given that g(l) = 0.
-1, 1, 2
Let w(d) = d**2 - d. Let r(u) = u**3 + 84*u**2 - 175*u + 90. Let c(k) = -5*r(k) - 20*w(k). Factor c(q).
-5*(q - 1)**2*(q + 90)
Suppose -14*a + 1080 = a. Let w be 48/a*(-18)/(-4). Factor -2/3*c**2 - 2/15*c**4 + 4/15*c + 8/15*c**w + 0.
-2*c*(c - 2)*(c - 1)**2/15
Let n = 5 + -2. Let l(b) be the first derivative of -6*b - b**n + 3 + 6*b**2 + 0 - 6*b. Suppose l(d) = 0. What is d?
2
Let h(k) be the third derivative of k**8/672 + k**7/70 + 7*k**6/120 + 2*k**5/15 + 3*k**4/16 + k**3/6 - 77*k**2 + 2. Let h(z) = 0. What is z?
-2, -1
Let h be (-77)/(-22)*(2 - 0). Let -2*l**3 + h*l**3 - 3*l**5 + 10*l**4 + 5*l**5 + 3*l**5 = 0. Calculate l.
-1, 0
Factor -186/7*i**2 + 0 - 36/7*i + 66/7*i**3.
6*i*(i - 3)*(11*i + 2)/7
Factor 16/13 + 10/13*w**3 - 8/13*w - 2/13*w**4 - 12/13*w**2.
-2*(w - 2)**3*(w + 1)/13
Let 4/5*k - 2/5 - 2/5*k**2 = 0. Calculate k.
1
Let p(m) be the second derivative of m**7/3780 + m**6/180 + m**5/20 - 5*m**4/6 - 30*m. Let u(g) be the third derivative of p(g). Factor u(i).
2*(i + 3)**2/3
Suppose 0*j = -2*j + 3*o - 39, j + 3*o - 3 = 0. Let c be -3 + 4*j/(-8). Factor 12*d**3 + c*d**5 - 12*d**4 - 210*d**2 + 206*d**2 + d**5.
4*d**2*(d - 1)**3
Let h(t) be the second derivative of t**6/20 + 3*t**5/40 - 7*t**4/8 - 13*t**3/4 - 9*t**2/2 + 26*t - 1. Factor h(p).
3*(p - 3)*(p + 1)**2*(p + 2)/2
Let k(u) be the first deriv