s**q + 4/11 - 100/11*s**3 = 0 for s.
2/7, 1
Let l(p) = 13*p**2 + 44*p + 29. Let v(x) = -11*x**2 + 18*x**2 - 9*x**2 - 14 - 23*x - 5*x**2. Let j(c) = 4*l(c) + 7*v(c). What is o in j(o) = 0?
-3, -2
Suppose 172/7*h + 1058/7*h**2 + 338/7*h**4 - 1220/7*h**3 - 352/7 + 4/7*h**5 = 0. Calculate h.
-88, -1/2, 1, 2
Let z(v) be the second derivative of -9/2*v**3 - 1/20*v**6 + 0*v**2 - 23*v - 9/20*v**5 - 5 + 25/8*v**4. Let z(p) = 0. Calculate p.
-9, 0, 1, 2
Let b(i) be the second derivative of i**5/10 - 32*i**4/3 + 380*i**3 - 3600*i**2 - 38*i - 6. Suppose b(o) = 0. What is o?
4, 30
Let q = 338/3 + -337/3. Let x = -5575 + 16726/3. Find i, given that -x*i**3 + 0*i + 0 + q*i**2 = 0.
0, 1
Factor 0 + 22/3*q**2 - 2/9*q**3 - 364/9*q.
-2*q*(q - 26)*(q - 7)/9
Suppose 55 = 4*w + w. Let c(i) = -15*i - 82. Let u be c(-6). Let w + u + 19 + 10*f - 13 + f**2 = 0. What is f?
-5
Let b(p) = p**3 + 17*p**2 - 116*p - 130. Let z be b(-22). Suppose 0 = 2*k + k - 6. Find j such that 150*j - k*j**3 + j**z + 3*j**2 - 150*j = 0.
0, 2
Let v(l) = -3*l**2 + 50*l - 172. Let d be v(5). Let o(b) be the second derivative of -25/2*b**2 + 10/3*b**d - 4*b + 5/12*b**4 + 0. Find p, given that o(p) = 0.
-5, 1
Let z(o) be the first derivative of 33*o - 5/2*o**2 - 3/20*o**5 - 34 + 19/6*o**3 - 11/12*o**4. Let y(w) be the first derivative of z(w). Factor y(g).
-(g - 1)*(g + 5)*(3*g - 1)
Let s be (7/(112/36))/(6/(-16)). Let d be ((-4)/s)/((-20)/18 + 2). Factor 3/8*q**2 + d + 9/8*q.
3*(q + 1)*(q + 2)/8
Let u = 123 - 72. Let o = u + -47. Factor o + 4*b**2 + 2*b - 22*b + 5*b + 7*b.
4*(b - 1)**2
Let g(r) be the first derivative of -r**8/560 + r**7/140 + 52*r**3/3 + 2*r + 23. Let q(a) be the third derivative of g(a). Find u such that q(u) = 0.
0, 2
Let c be (-54)/45*(-2 - (-7 + 0)). Let v be 15/(120/32) + c/(-21). Factor v*h + 0 + 6/7*h**2.
6*h*(h + 5)/7
Suppose 0 = -5*o, -12 = -0*n - 3*n - 3*o. Suppose -32*k = -694 + 374. Factor 2*p**3 + k*p - 8*p - 1 - 4*p + 4*p**n - 3*p**4.
(p - 1)*(p + 1)**3
Let g(r) be the first derivative of -2*r**6/3 + 84*r**5/5 + 216*r**4 + 1856*r**3/3 - 1012. Solve g(d) = 0.
-4, 0, 29
Let k(d) be the third derivative of -5/336*d**8 + 0*d + 0*d**3 + 1/24*d**6 + 0*d**5 + 0 + 0*d**7 + 0*d**4 + 45*d**2. Factor k(v).
-5*v**3*(v - 1)*(v + 1)
Suppose 710 = -5*n + 3*t + 2*t, 3*t = 5*n + 700. Let i = 139 + n. Factor 4*k**4 + 2*k**5 + 39*k**2 - 39*k**i.
2*k**4*(k + 2)
Let f = 2410697/7 - 344385. Solve 14*z - 4*z**2 + 0 + f*z**3 = 0 for z.
0, 7
Let j(y) be the third derivative of -y**6/480 - 11*y**5/120 + y**4/2 + 5*y**2 - 149*y + 5. Find b, given that j(b) = 0.
-24, 0, 2
Let v(h) be the first derivative of 1/3*h**3 + 20*h - 105 + 9/2*h**2. Factor v(u).
(u + 4)*(u + 5)
Let d(o) be the second derivative of -1/21*o**3 + 1/294*o**7 + 1/70*o**6 + 0*o**2 + 1/140*o**5 + 0 - 1/28*o**4 - 4*o. Find p such that d(p) = 0.
-2, -1, 0, 1
Let -496109 + 496109 + 70*d**4 + 104*d**3 - 5*d**5 - 70*d**2 + 245*d - 344*d**3 = 0. Calculate d.
-1, 0, 1, 7
Suppose 0 = -13*c - 7*c + 700. Factor 43*q**3 - 4*q**4 - q**4 + 10*q**2 + q**4 - c*q**3 + 2*q**2.
-4*q**2*(q - 3)*(q + 1)
Factor 4536/5*s**2 + 8748*s + 2/5*s**4 + 164/5*s**3 + 39366/5.
2*(s + 1)*(s + 27)**3/5
Let u be ((-145)/(-116))/(2/16). Factor 4*o**4 + 98*o**5 + o**4 - 184*o**5 + 91*o**5 - u*o**3.
5*o**3*(o - 1)*(o + 2)
Suppose -2*h - 28 = -4*u + h, -5*h = -u + 24. Suppose -t = -4*p - u, 2*t + 0 = 3*p + 3. Factor 0*q + t*q - 3*q**2 - 3*q - 3*q.
-3*q*(q + 2)
Let s(z) be the first derivative of 2*z**3/15 - 207*z**2/5 + 412*z/5 - 1057. Factor s(j).
2*(j - 206)*(j - 1)/5
Let b(q) be the third derivative of 11*q**6/2340 - 23*q**5/780 + q**4/78 + 22*q**3/3 - 2*q**2 - 28*q. Let i(k) be the first derivative of b(k). Factor i(u).
2*(u - 2)*(11*u - 1)/13
Let v be 2 - -2 - 0/5. Suppose 0 = -4*k - 4*d + v, 4*k + d - 6 = -d. What is l in k*l - l**2 + 0*l**2 + 9 - 6 = 0?
-1, 3
Factor 72/19*p - 4/19*p**4 - 120/19*p**2 + 0 - 46/19*p**3.
-2*p*(p + 6)**2*(2*p - 1)/19
Let b = -24 - -31. Suppose 0 = z - 3*w - 2, b*z + 2*w = 2*z + 10. Determine g, given that 125/2 + 7*g**3 - 30*g**z + 25*g - 1/2*g**4 = 0.
-1, 5
Suppose -9*z + 5*z - 5*i = -15, 3*z - 19 = 4*i. Suppose -46 = -z*p - 36. Suppose 38/3*n**2 + p*n**4 + 22/3*n + 26/3*n**3 + 4/3 = 0. What is n?
-2, -1, -1/3
Let m(n) be the second derivative of n**4/12 - 4*n**3/3 - 93*n. Let k be -3 + 3 + (-2)/(-2). Let l(v) = v. Let z(x) = k*m(x) + 4*l(x). Factor z(j).
j*(j - 4)
What is a in 7/3*a**2 - 1/6*a**3 + 11/3 - 35/6*a = 0?
1, 2, 11
Let y(d) be the third derivative of -63*d**2 + 0*d + 0 + 1/390*d**5 + 0*d**3 - 5/156*d**4. Factor y(c).
2*c*(c - 5)/13
Factor 56*o**3 - 224*o + 370*o - 116*o**2 - 322*o - 4*o**4.
-4*o*(o - 11)*(o - 4)*(o + 1)
Let g(i) = -8*i**2 + 2023*i - 1973. Let b(u) = 5*u**2 - 1350*u + 1315. Let d(p) = 7*b(p) + 5*g(p). Determine t so that d(t) = 0.
1, 132
Let k(j) be the second derivative of -j**5/20 - j**4/12 + j**2/2 + 33*j. Let f(t) = -8*t**3 - 28*t**2 + 2*t + 28. Let v(d) = f(d) - 6*k(d). Factor v(l).
-2*(l - 1)*(l + 1)*(l + 11)
Suppose 8 = -0*t + 4*t. Factor 0*i**2 - 27*i + 2*i**t + 45*i.
2*i*(i + 9)
Let d(n) = -n**3 - n**2. Let m(o) = 2 - 2 + 16*o + o**3 + 8*o + 10*o**2. Let q(f) = 4*d(f) + m(f). Factor q(a).
-3*a*(a - 4)*(a + 2)
Let o(b) be the first derivative of b**5/15 - 13*b**4/6 - 115*b**3/9 - 74*b**2/3 - 20*b + 1323. Let o(u) = 0. Calculate u.
-2, -1, 30
Let n = -547 + 552. Suppose -2*s - n*d - 4 = 0, 3*s = s - 3*d. Factor 0 + 1/2*p**2 - 1/2*p**4 - 1/2*p**s + 1/2*p.
-p*(p - 1)*(p + 1)**2/2
Let h(n) be the second derivative of n**7/21 + 2479*n**6/60 + 95323*n**5/10 - 433379*n**4/12 + 144926*n**3/3 - 96721*n**2/4 - 88*n - 6. Solve h(v) = 0.
-311, 1/4, 1
Let o be (-26)/(-273)*(130/(-52) + 17/4). Solve 0 - 1/6*q + o*q**3 + 0*q**2 = 0 for q.
-1, 0, 1
Suppose 5*t = -20, -t = 3*i - 0 - 29. Suppose 20 = i*h - 13. Factor -2/17*s**5 + 14/17*s + 4/17*s**h - 4/17*s**4 + 16/17*s**2 + 4/17.
-2*(s - 2)*(s + 1)**4/17
Suppose 4*w + r - 15 = 0, 2*w = -17*r + 12*r + 21. Factor 25/3 - 1/3*x**4 - 10/3*x - 8*x**2 + 10/3*x**w.
-(x - 5)**2*(x - 1)*(x + 1)/3
Let h(z) = -z**2 - 255*z - 503. Let x be h(-2). Let v(d) be the first derivative of -2*d - 3/4*d**2 - 17 + 1/6*d**x. Factor v(l).
(l - 4)*(l + 1)/2
Let y = -80367 + 80370. Factor 972*i - 162*i**2 + 0 - 126*i**y - 50/3*i**4 - 2/3*i**5.
-2*i*(i - 2)*(i + 9)**3/3
Let i(v) be the second derivative of -4/21*v**3 + 0*v**2 - 1/14*v**4 + 11*v + 1 + 1/14*v**5 + 1/35*v**6 - 1/147*v**7. Suppose i(m) = 0. What is m?
-1, 0, 1, 4
Factor -5*m**4 - 9*m**3 - 40*m**2 - 25*m - 12*m**2 - 26*m**3 - 39*m**2 + 36*m**2.
-5*m*(m + 1)**2*(m + 5)
Let p(b) be the first derivative of -b**3 + 42*b**2 - 588*b - 293. Suppose p(y) = 0. Calculate y.
14
Let m(f) = 4*f**2 - 1. Let a(j) = -13*j**2 + 100*j + 4307. Let y(l) = a(l) + 2*m(l). Factor y(g).
-5*(g - 41)*(g + 21)
Let o = 7/50963 - -203831/152889. Let -o - 8/3*m + 5/12*m**4 - 4/3*m**2 + 1/12*m**5 + 1/3*m**3 = 0. What is m?
-2, -1, 2
Let b = 182 - 265. Let o = b - -80. Let w(y) = 5*y**2 + 20*y + 47. Let p(v) = 16*v**2 + 60*v + 140. Let x(s) = o*p(s) + 10*w(s). Let x(t) = 0. Calculate t.
-5
Let q = 71 - 71. Suppose -4*c = 4*d - d - 138, q = 5*d - 3*c - 259. What is g in -5*g**4 - d*g - 30*g**3 - 35 + 42*g + 38*g + 40*g**2 = 0?
-7, -1, 1
Suppose 0 = 3*p + x, 29*p = 33*p + x. Let r(y) be the second derivative of 2/33*y**4 + 1/165*y**6 + 15*y + 0 + 2/55*y**5 + 0*y**2 + p*y**3. Factor r(k).
2*k**2*(k + 2)**2/11
Factor 2/3*y**3 + 4 + 4*y**2 + 22/3*y.
2*(y + 1)*(y + 2)*(y + 3)/3
What is h in 112 - 408*h + 75*h**2 + 8*h**4 - 2*h**5 - 18*h**2 + 25*h**4 + 348*h**2 + 50*h**2 - 190*h**3 = 0?
1/2, 1, 4, 7
Factor 0 - 306*p**4 + 0*p - 5/2*p**5 - 18849/2*p**3 - 3721*p**2.
-p**2*(p + 61)**2*(5*p + 2)/2
Let t(p) be the second derivative of 7/5*p**5 - 15 - 2/3*p**3 + 2/3*p**4 + 9*p + 0*p**2 + 8/15*p**6. Factor t(l).
4*l*(l + 1)**2*(4*l - 1)
Let y(s) be the third derivative of -5*s**8/672 - 23*s**7/84 + s**6/24 + 23*s**5/12 - 5*s**4/48 - 115*s**3/12 - 2782*s**2. Suppose y(l) = 0. What is l?
-23, -1, 1
Let d(i) be the first derivative of -i**6/21 + 82*i**5/35 - 220*i**4/7 + 800*i**3/21 + 1323. What is g in d(g) = 0?
0, 1, 20
Let z(b) be the third derivative of 3*b**7/175 - 613*b**6/300 + 5236*b**5/75 - 289*b**4/15 - 1195*b**2. Factor z(r).
2*r*(r - 34)**2*(9*r - 1)/5
