r z(w).
2*w**2*(w + 1)**2/5
Determine g, given that -25000 + 2*g**3 + 3685*g - 121*g**2 + 2315*g - 89*g**2 = 0.
5, 50
Let a = -966 + 968. Let f(i) be the first derivative of 5/14*i**4 - 21 + 0*i - 8/7*i**3 + 4/7*i**a. Factor f(o).
2*o*(o - 2)*(5*o - 2)/7
Let f = -417/7 - -60. Let t be 6/(-84) + ((-187)/(-154))/17. What is k in -6/7*k**2 + t - f*k - 3/7*k**3 = 0?
-1, 0
Suppose -12*f = -13*f - 8. Let g be (-71)/f + -5 + (-2)/(-16). Let 29*b + g*b**2 - 2*b**2 + 8 - 37*b = 0. What is b?
2
Let t = -21 + 29. Suppose 2*i + 2 + t = 0. Let r(g) = g - 1. Let k(a) = -5*a**2 - 10*a + 5. Let c(f) = i*r(f) - k(f). Factor c(v).
5*v*(v + 1)
Let w(z) be the second derivative of 3*z**5/140 - 73*z**4/14 + 145*z**3/14 - 3274*z. Factor w(h).
3*h*(h - 145)*(h - 1)/7
Let p(b) be the second derivative of b**5/20 - 3*b**4/4 + 10*b**3/3 + 1084*b. Let p(v) = 0. What is v?
0, 4, 5
What is v in -52/9*v**3 + 286/9 + 2/9*v**4 - 620/9*v + 128/3*v**2 = 0?
1, 11, 13
Suppose p - 3*p - 80 = -5*l, -19 = -l + p. Suppose -2 + 6 = 2*z + 2*k, 0 = 5*z + k - l. Solve -3*c**4 - 36*c**2 + 11*c + 12*c - 4 + 18*c**z - 5 + 7*c = 0.
1, 3
Factor 0*g - 5/3*g**5 - 4/9*g**3 + 0*g**2 + 0 + 17/9*g**4.
-g**3*(3*g - 1)*(5*g - 4)/9
Let b(a) = -51*a - 119. Let i be b(-3). Suppose -i*o = -29*o - 10. Factor 2/3*p**o + 6 + 4*p.
2*(p + 3)**2/3
Let m(y) be the first derivative of -2*y**3/3 + 16*y**2 + 72*y + 2784. What is r in m(r) = 0?
-2, 18
Let l(t) = 4*t**2 + 2*t + 2. Let p be l(0). Let g = 391/2 - 195. Solve -5/2 - g*n**p + 3*n = 0 for n.
1, 5
Let s = -70 - -114. Suppose -4*y + 40 = -0*a + 2*a, -2*y + 5*a + s = 0. Factor 26*i**4 + 19*i - 2*i**2 + 6*i**3 + y*i**3 + 10*i**5 - 23*i.
2*i*(i + 1)**3*(5*i - 2)
Let n(c) = -56*c**3 - 410*c**2 - 1073*c + 491. Let b(g) = 27*g**3 + 205*g**2 + 536*g - 242. Let y(i) = -13*b(i) - 6*n(i). Solve y(x) = 0.
-10, -4, 1/3
Let s(p) be the first derivative of 1/2*p**2 - 90 + 0*p - 1/6*p**3. Factor s(t).
-t*(t - 2)/2
Let m(r) be the second derivative of 0 - 63*r - 13/24*r**4 - 11/12*r**3 - 1/8*r**5 - 3/4*r**2. What is p in m(p) = 0?
-1, -3/5
Let q(w) be the second derivative of 0 - 18*w - 1/135*w**6 - 5/18*w**4 - 1/10*w**5 - 7/27*w**3 + 0*w**2. Suppose q(r) = 0. What is r?
-7, -1, 0
Determine f, given that -16/5*f + 4/3*f**2 + 0 + 26/15*f**3 + 2/15*f**4 = 0.
-12, -2, 0, 1
Let k(u) be the first derivative of -2*u**6/3 + 4*u**5 - u**4 - 68*u**3/3 + 44*u**2 - 32*u + 2993. Determine j, given that k(j) = 0.
-2, 1, 4
Suppose -6*d + 11 = -1. Suppose -w - d*w = 2*o - 135, 0 = 5*w + 2*o - 221. Factor -w*l + 4 - 2*l**2 + 21*l + 20*l.
-2*(l - 1)*(l + 2)
Let f(p) be the first derivative of -2*p**5/65 + 216*p**4/13 - 7244*p**3/3 + 92880*p**2/13 - 92450*p/13 + 9284. Suppose f(h) = 0. What is h?
1, 215
Factor 18*r + 17/3*r**2 + 1/3*r**3 - 24.
(r - 1)*(r + 6)*(r + 12)/3
Let 126 + 93/5*r + 3/5*r**2 = 0. Calculate r.
-21, -10
Let v(w) be the first derivative of 10/3*w**3 + 1/2*w**4 + 4*w**2 + 0*w + 90. Factor v(u).
2*u*(u + 1)*(u + 4)
Let i(y) = -6*y**2 + 40*y - 102. Let z(u) = 38*u - 10179 - 31*u**2 + 162*u + 9668. Let d(m) = m. Let j be d(-2). Let l(o) = j*z(o) + 11*i(o). Factor l(x).
-4*(x - 5)**2
Factor -37 - 1/3*d**2 - 40/3*d.
-(d + 3)*(d + 37)/3
Let p be (22 + -4)/((9 - 10)*-1). Let r be 8 - (-3 + (p - 9)). Let 108*t**4 - 48*t**3 + 0*t + 16/3*t**r + 0 = 0. What is t?
0, 2/9
Let f(h) = -57*h**3 - 487*h**2 - 1085*h - 256. Let z(l) = -113*l**3 - 971*l**2 - 2169*l - 512. Let i(o) = 7*f(o) - 3*z(o). What is v in i(v) = 0?
-4, -4/15
Let q(l) be the third derivative of -l**8/336 - 11*l**7/210 - 19*l**6/120 + 43*l**5/60 + 5*l**4/6 - 16*l**3/3 - 266*l**2 - 2*l - 3. Find o, given that q(o) = 0.
-8, -4, -1, 1
Let l(v) be the third derivative of -v**7/2520 + v**5/40 - 55*v**3/6 + 3*v**2 - 2. Let k(w) be the first derivative of l(w). Factor k(t).
-t*(t - 3)*(t + 3)/3
Let c(a) = 5*a**3 + a**2 - 3. Let u be c(2). Suppose -u - 7 = -2*t. Factor -4 - 2*n**4 - 2*n**4 + 8*n**2 + 24*n - t*n.
-4*(n - 1)**2*(n + 1)**2
Suppose 4*g = 2*u + 16, 41*g - 43*g - 4 = 5*u. Let j(w) be the second derivative of 0 + 10*w**2 - 7*w + 5/12*w**4 + 25/6*w**g. Factor j(b).
5*(b + 1)*(b + 4)
Solve 107/3*d - 1/6*d**2 + 436/3 = 0.
-4, 218
Factor 35 - 348 + 75*k**3 - 5*k**4 - 187 - 395*k**2 + 825*k.
-5*(k - 5)**2*(k - 4)*(k - 1)
Let n(f) be the first derivative of -3*f**4/4 - 25*f**3 - 129*f**2/2 + 207*f - 1341. Solve n(l) = 0 for l.
-23, -3, 1
Suppose 215 = 11*t - 6*t. Suppose 0 = 6*a + 19 - t. Solve -5*n**3 + 24*n**4 - 3*n**2 + a*n**2 - 20*n**4 = 0 for n.
0, 1/4, 1
Let w(t) = 361*t**4 + 18*t**3 + t**2. Let q(d) = -2*d**4 + d**2. Let o(l) = q(l) - w(l). Factor o(c).
-3*c**3*(121*c + 6)
Let a(d) = 15*d**4 + 54*d**3 + 174*d**2 + 186*d - 6. Let b(o) = -17*o**4 - 53*o**3 - 169*o**2 - 185*o + 7. Let s(h) = 7*a(h) + 6*b(h). Factor s(t).
3*t*(t + 2)**2*(t + 16)
Let y(q) be the first derivative of 42 + 0*q - 1/8*q**4 + 13/2*q**2 - 11/6*q**3. Determine x so that y(x) = 0.
-13, 0, 2
Let d = 342826/21 - 48970/3. Determine y, given that -436/7*y**3 - 416/7*y - 124/7*y**4 - 80/7 - 660/7*y**2 - d*y**5 = 0.
-5, -2, -1, -1/3
Let l be (-13)/(65/(-6))*(-232)/(-957)*11. Factor -4*w + 2/5*w**4 + 8/5*w**3 - 6/5*w**2 + l.
2*(w - 1)**2*(w + 2)*(w + 4)/5
Let a(p) be the first derivative of p**4/18 + 4*p**3/9 + p**2 + 8*p/9 + 1121. Factor a(i).
2*(i + 1)**2*(i + 4)/9
Let g(c) = -12*c**2 - 34*c - 154. Let p(k) = 7*k**2 + 2*k + 1. Let o(j) = -g(j) - 2*p(j). Let o(u) = 0. What is u?
-4, 19
Let g = 41 + -42. Let m be (9*3/(-36))/(g/12). Factor 15 - 12*z - m*z**2 - 3*z**2 + 17*z**2 - 8*z**2.
-3*(z - 1)*(z + 5)
Let p(b) be the first derivative of b**3/2 - 465*b**2/2 + 72075*b/2 + 799. Let p(g) = 0. Calculate g.
155
Factor -27/5*o**3 - 31008/5*o - 1833/5*o**2 + 3468/5.
-3*(o + 34)**2*(9*o - 1)/5
Let i(w) be the second derivative of w**5 + 95*w**4/8 - 685*w**3/12 - 45*w**2/2 + 2184*w - 2. Determine k so that i(k) = 0.
-9, -1/8, 2
Suppose -35 + 183 = 4*d. Let -7 + 7*n**2 - 17*n**2 - 3*n + 28*n - 5*n**3 + d = 0. Calculate n.
-3, -1, 2
Let p(x) be the third derivative of x**8/4032 + x**7/1008 - x**6/12 - 23*x**5/12 - 24*x**2 - 2*x. Let c(s) be the third derivative of p(s). Factor c(f).
5*(f - 3)*(f + 4)
Let w = 13482/5 + -13458/5. Solve w*r**3 + 0*r - 6*r**2 + 6/5*r**4 + 0 = 0 for r.
-5, 0, 1
Let o(a) be the third derivative of 0 + 12*a + 3/40*a**6 + 3/2*a**3 + 5/8*a**4 - 11/20*a**5 + 2*a**2. Factor o(k).
3*(k - 3)*(k - 1)*(3*k + 1)
Let k be (-1 - (0 - 1))*6/(-6). Suppose k = -5*u - 0*u + 15. Factor -4*i + 4*i**4 - 2*i**3 - 11*i**u + i**3 + 12*i**2.
4*i*(i - 1)**3
Let m(g) be the third derivative of g**6/120 - 16*g**5/15 - 11*g**4/2 + 764*g**2 - g. Factor m(i).
i*(i - 66)*(i + 2)
Let w(v) be the first derivative of v**4 + 840*v**3 + 198450*v**2 - 731. Factor w(l).
4*l*(l + 315)**2
Let f(a) = 11*a**3 + 111*a**2 + 132*a + 219. Let l be f(-9). Factor 1/2*c**l + 0*c**2 - 3/4*c**4 + 0*c + 0.
-c**3*(3*c - 2)/4
Let p(k) be the second derivative of 1/50*k**5 + 0 - 2/15*k**4 + 6/5*k**2 + 1/15*k**3 - 29*k. Determine m, given that p(m) = 0.
-1, 2, 3
Let v = 12214/17217 - 932/1913. Factor -v + 0*u + 2/9*u**2.
2*(u - 1)*(u + 1)/9
Let s(y) be the third derivative of 1/112*y**8 + 0*y**3 + 2/5*y**5 + 0*y**4 - 1/10*y**6 - 19 - 1/35*y**7 + 0*y - 2*y**2. Solve s(b) = 0 for b.
-2, 0, 2
Let k(h) be the second derivative of h**4/28 - 5*h**3/7 - 144*h**2/7 - 96*h - 3. Determine o, given that k(o) = 0.
-6, 16
Let w(c) = 18*c + 4. Let d be w(0). Factor 3*i - 13*i - 58 + 30 - i**2 + d.
-(i + 4)*(i + 6)
Let h = 41/2 - 20. Let k = 10/13871 + 13811/83226. Factor -2/3*s + k*s**2 + h.
(s - 3)*(s - 1)/6
Let s(h) be the second derivative of h**6/40 - 21*h**5/16 - 151*h**4/16 - 193*h**3/8 - 117*h**2/4 + 163*h + 3. Suppose s(j) = 0. What is j?
-2, -1, 39
Suppose 2*y = 10*y + 2872. Let n = -356 - y. Find j, given that -6/7*j**2 - 2/7 + 2/7*j**n + 6/7*j = 0.
1
Let w(l) be the first derivative of l**3/6 + 93*l**2/2 - 188*l + 2872. Find n such that w(n) = 0.
-188, 2
Suppose b = 3*w - 7, 1 = 4*w - 5*w + 2*b. Factor 55*k**2 - 71*k**2 - 3*k**w + 5*k**3 + 14*k.
2*k*(k - 7)*(k - 1)
Let d(j) be the second derivative of -j**4/4 - 427*j**3/2 - 639*j**2 + 252*j. Let d(z) = 0. What is z?
-426, -1
Factor -5/2*d**3 + 1/2*d**4 - 2 + 5/2*d + 3/2*d**2.
(d - 4)*(d - 1)**2*(d + 1)/2
Let z be (1066/(-656))/((-5)/(-