Determine s, given that w(s) = 0.
-2, 1
Factor -149/8*w**3 + 25/2*w + 3/8*w**4 - 13/2*w**2 + 0.
w*(w - 50)*(w + 1)*(3*w - 2)/8
Suppose 41/2*x**3 + 92*x - 2*x**4 - 137/2*x**2 - 42 = 0. What is x?
1, 2, 21/4
Let m(z) be the first derivative of -8/11*z**4 + 64 - 49/11*z**2 + 12/11*z + 208/33*z**3. Factor m(w).
-2*(w - 6)*(4*w - 1)**2/11
Let j(z) = -81*z**3 + 151*z**2 - 90*z + 18. Let g(p) = p**2 + p - 1. Let y(l) = l + 3. Let r be y(-9). Let u(t) = r*g(t) - 3*j(t). What is o in u(o) = 0?
4/9, 1
Let y(n) be the second derivative of n**5/40 - 13*n**4/12 - 265*n**3/12 - 119*n**2/2 + 11*n + 8. Factor y(s).
(s - 34)*(s + 1)*(s + 7)/2
Let l(j) be the first derivative of 169/5*j + 13/5*j**2 + 1/15*j**3 + 89. Suppose l(y) = 0. What is y?
-13
Let d(o) be the second derivative of -o**4/30 - 163*o**3/15 - 162*o**2/5 + 806*o. Factor d(n).
-2*(n + 1)*(n + 162)/5
Let t(z) be the second derivative of -6/35*z**5 + 10/7*z**3 + 4/35*z**6 + 36/7*z**2 - 16/21*z**4 + 43*z - 2/147*z**7 + 0. Find f, given that t(f) = 0.
-1, 2, 3
Let y(s) = -9*s**2 + 4594*s - 1336336. Let n(z) = 80*z**2 - 41352*z + 12027024. Let c(i) = 5*n(i) + 44*y(i). Suppose c(d) = 0. Calculate d.
578
Let u be 3/(-9)*((-3 - -5) + -2). Suppose u = -11*c + 10*c + 2. Suppose -8*k**c - k**4 + 5 - k**2 + 6*k**4 - k**2 = 0. What is k?
-1, 1
Let b = 37624/28083 - 60/9361. What is u in 0 + 2/9*u**5 + 4/3*u**2 - 10/9*u - b*u**4 + 8/9*u**3 = 0?
-1, 0, 1, 5
Let s(a) be the first derivative of 9*a - 5 + 0*a**2 - 1/6*a**3 + 1/48*a**4. Let f(l) be the first derivative of s(l). Factor f(v).
v*(v - 4)/4
Factor 8864*v + 20308 + 306916*v**2 - 40638 + 20394.
4*(277*v + 4)**2
Let l(n) = -70*n**2 + 160*n + 120. Let z(r) = 35*r**2 - 89*r - 60. Let x(u) = -2*l(u) - 5*z(u). Factor x(b).
-5*(b - 4)*(7*b + 3)
Let a(w) = w + 7. Let o be a(-3). Let x = -1504 + 1522. Solve -20*p + 5*p**o - 17*p**2 - x*p**2 + 4*p**3 - 15*p**3 + p**3 = 0 for p.
-1, 0, 4
Let z = -1984 + 4118. Solve -z*d**4 + 2136*d**4 + 4*d + 8 - 6*d**2 - 8 = 0 for d.
-2, 0, 1
Solve 18*t - 147 + 0*t**2 - 163 + t**2 - 156 + 447 = 0 for t.
-19, 1
Let f be (-210)/14*(-16)/(-10). Let q be (-228)/f - 10/2. Suppose 3/4*b**2 - 3/4*b - q = 0. What is b?
-2, 3
Find m, given that 6*m**3 - 3*m**5 + 148*m + 129 + 151*m**4 - 22*m**4 - 151*m - 258*m**2 = 0.
-1, 1, 43
Let w(h) = -10*h + 7. Let m be w(-2). Let a = m + -11. Factor -2*u - 9 + 19 - a - 3*u**2 - 7*u.
-3*(u + 1)*(u + 2)
Let c(q) = -q - 7. Let i be c(-11). Let t = 6 - i. Factor 7*r**4 - 10*r + t*r - 2 + 0 + 15*r**2 + 9*r + 19*r**3.
(r + 1)**3*(7*r - 2)
Let i(b) be the second derivative of b**4/6 - 5*b**3/6 - 2*b**2 + 25*b. Let q be i(-1). Factor -64*a**q + 32*a**2 - 5*a + 86 - 122 + 65*a.
-4*(a + 1)*(4*a - 3)**2
Suppose -56*v + 107 = 21 - 26. Let u(x) be the second derivative of 0 - 1/36*x**4 + 4/9*x**3 + 29*x + 0*x**v. Solve u(q) = 0 for q.
0, 8
Let o(s) = 35*s**4 + 75*s**3 + 35*s**2 - 120*s - 85. Let i(m) = -5*m**4 - 11*m**3 - 5*m**2 + 17*m + 12. Let j(p) = -15*i(p) - 2*o(p). Factor j(g).
5*(g - 1)*(g + 1)**2*(g + 2)
Let y be ((45 - 24) + -20)*(-352)/(-55). Factor y*c + 2/5*c**4 + 0 - 24/5*c**2 + 0*c**3.
2*c*(c - 2)**2*(c + 4)/5
Let w(o) be the third derivative of 1/36*o**4 + 0*o**3 - o**2 - 1/60*o**6 + 0*o**5 + 2*o + 0 + 2/315*o**7. Determine l so that w(l) = 0.
-1/2, 0, 1
Determine t, given that -41 - 25 - 5*t**2 + 5291*t - 21 - 5201*t + 2 = 0.
1, 17
Let b(j) be the third derivative of j**8/672 + 13*j**7/140 + 169*j**6/80 + 2197*j**5/120 + 4*j**2 - 15. Factor b(a).
a**2*(a + 13)**3/2
Let m(t) be the second derivative of -56*t - 1/13*t**3 - 1/39*t**4 + 0 - 1/13*t**2. Let m(s) = 0. Calculate s.
-1, -1/2
Suppose -b = b + 4*t - 6, 23 = 3*b - t. Suppose -3*o + 7*o = 3*p - 18, -4*p - b = 5*o. Factor s + 2*s + 9*s**2 - 11*s**p - 6 + 5*s**2.
3*(s - 1)*(s + 2)
Determine g so that -1/3*g**2 - 95/3*g - 364/3 = 0.
-91, -4
Factor -1024 - 2/3*p**3 - 2240/3*p - 131/3*p**2.
-(p + 32)**2*(2*p + 3)/3
Let q(p) be the first derivative of 0*p - p**3 + 1 - 1/20*p**5 + 2*p**2 + 3/8*p**4. Let r(j) be the second derivative of q(j). Factor r(a).
-3*(a - 2)*(a - 1)
Let o(n) = -20*n - 12. Let a be o(-1). Let i = -22 + 36. Suppose -18*y**2 + 4*y**3 + i*y**4 - a*y**4 + 0 + 8 = 0. What is y?
-2, -2/3, 1
Factor -1370327 - 7344941 - 1567477 + 4224514 - 2*g**2 + 11504*g - 10484521.
-2*(g - 2876)**2
Let s be (-4 + 5 - 5)*-4. Suppose -s = 2*z - 12. Let v(n) = -3*n**4 + 12*n**2 - 3. Let g(o) = o**4 + o**2 + 1. Let h(w) = z*g(w) + v(w). Factor h(a).
-5*(a - 1)**2*(a + 1)**2
Let j = 311 - 309. Suppose -2 = -j*a + 2. Determine v so that a*v + 5/2 - 1/2*v**2 = 0.
-1, 5
Let j = 23 - -40. Solve -21 - 23 + j - 25 - v**2 + 5*v = 0 for v.
2, 3
Suppose 0 = -o - 18 + 20. Factor 4*p**2 - 21*p**2 + 6*p**o + 3*p**2 - 9*p**3 - p**4.
-p**2*(p + 1)*(p + 8)
Let c(j) = -2*j**2 - 53*j - 42. Let f(m) = -2*m**2 - 52*m - 44. Let z(n) = -2*n**2 + 17*n + 12. Let x be z(9). Let s(y) = x*f(y) - 2*c(y). Solve s(d) = 0.
-24, -1
Suppose 4 = -23*v - 12 + 16. Let j(x) be the second derivative of 1/3*x**4 + 29*x + v + 2*x**2 - 4/3*x**3. Find w, given that j(w) = 0.
1
Let k(b) = -35*b**3 + 64*b**2 + 386*b + 670. Let l(o) = 369*o**3 - 639*o**2 - 3861*o - 6699. Let r(x) = 21*k(x) + 2*l(x). Solve r(g) = 0.
-14, -4
Let c be 0*(578/(-34) + 16). Let 14*r**2 + 6*r**4 - 1/2*r**5 - 15*r**3 - 9/2*r + c = 0. What is r?
0, 1, 9
Let i be ((-3030)/2020)/((-2 - -4) + (-5)/2). Factor -5*k**2 + 1/2*k**i + 0 - 11/2*k.
k*(k - 11)*(k + 1)/2
Let x = 3836/3 - 1271. Let s = x - 13/3. Determine r so that -2/3*r**2 - 4*r - s = 0.
-5, -1
Let f(a) = -5*a**2 + 12250*a - 7503131. Let l(s) = -2. Let g(x) = -f(x) + 3*l(x). Suppose g(o) = 0. What is o?
1225
Suppose -5*s + 3*t - 54 = 0, -5*s - 100 = -217*t + 212*t. Factor 2/9*v**s - 86/9*v**2 + 0 + 0*v.
2*v**2*(v - 43)/9
Let n = 19277/38522 + -8/19261. Let -1/4 - 1/4*y**2 - n*y = 0. What is y?
-1
Let h(c) = 5*c**4 - 165*c**3 + 95*c**2 + 710*c + 445. Let k(a) = -3*a**4 + 82*a**3 - 48*a**2 - 356*a - 223. Let l(s) = -2*h(s) - 5*k(s). Factor l(u).
5*(u - 15)*(u - 3)*(u + 1)**2
Suppose -24 = -6*w + 2*w. Find y, given that w - y**2 - 6*y - y**2 + 2 = 0.
-4, 1
Solve 2/13*k**2 + 387200/13 - 1760/13*k = 0.
440
Let 188/5*j**3 + 376/5 - 112*j + 2/5*j**4 - 6/5*j**2 = 0. Calculate j.
-94, -2, 1
Let o = -48678 - -49039. Factor -o*v**2 - 130321/6 + 13718/3*v + 38/3*v**3 - 1/6*v**4.
-(v - 19)**4/6
What is b in -196*b**3 - 80*b**3 + 727*b**3 + 312*b**2 + 6*b**4 + 60*b**4 - 3*b**5 - 151*b**3 = 0?
-2, 0, 26
Let d(x) = 9*x**2 - 180*x + 129. Let h(u) be the second derivative of 1/12*u**4 - 3*u**3 + 18*u + 13/2*u**2 + 0. Let c(m) = 2*d(m) - 21*h(m). Factor c(j).
-3*(j - 5)*(j - 1)
Let u be (2*5/7)/(-4 + 312/42). Let o(g) be the first derivative of 5/2*g**2 + u*g**4 - 24 - 20/9*g**3 + 0*g. Determine m, given that o(m) = 0.
0, 1, 3
Let p be (8 + 183/(-24))*(-12)/(-18). Let 9/4*n**3 + 0 - 3/4*n**4 - p*n**5 + 0*n - 5/4*n**2 = 0. What is n?
-5, 0, 1
Let f = -172 + 176. Let t be f*1/24*3. Suppose 2*a + 5/2*a**2 + t*a**3 + 0 = 0. What is a?
-4, -1, 0
Let y be (-3231)/(-27) + (-16)/(-12). Suppose -h - 117 + y = q, 5*q - 5*h = 0. Factor 60/7*n - 2/7*n**q - 450/7.
-2*(n - 15)**2/7
Let d(q) be the second derivative of q**4/16 + 59*q**3/8 + 1960*q. What is h in d(h) = 0?
-59, 0
Let d(c) = 8*c + 4. Let u(t) = -t**2 - 31*t - 16. Let l be 1/2 - (-2)/((-8)/(-22)). Let h(q) = l*u(q) + 26*d(q). Factor h(y).
-2*(y - 4)*(3*y + 1)
Find b such that 0 + 3*b - 1/4*b**3 - 1/4*b**2 = 0.
-4, 0, 3
Let z be (-2)/(-10)*(-40)/(-96). Let f(w) be the first derivative of 5/8*w**2 - 13 - z*w**3 - 1/16*w**4 - 3/4*w. Factor f(h).
-(h - 1)**2*(h + 3)/4
Let m(k) be the second derivative of -k**5/60 - k**4/6 + 53*k**2/2 + 247*k. Let q(h) be the first derivative of m(h). Suppose q(u) = 0. What is u?
-4, 0
Let l(v) be the second derivative of -4/3*v**3 + 0 + 1/2*v**5 - 5/6*v**4 + 4*v**2 + 1/15*v**6 - 1/21*v**7 - 17*v. Determine g, given that l(g) = 0.
-2, -1, 1, 2
Let l = -575 + 575. Suppose 32*k - 55 = -55. Factor -4/5*b**4 + l*b**3 + 0*b + k + 0*b**2.
-4*b**4/5
Determine r, given that 6*r**2 + 524*r + 119*r + 561 + 482*r = 0.
-187, -1/2
Let u(x) be the second derivative of -x**6/15 + x**5/5 + x**4/6 - 2*x**3/3 + 169*x + 1. Factor u(r).
-2*r*(r - 2)*(r - 1)*(r + 1)
Let k be (532/(-42))/(2/(-3)). Suppose -4*w - k = -5*j, 2*j 