1*r - 2)/3
Factor -514/9*c - 130/3 + 8/9*c**2.
2*(c - 65)*(4*c + 3)/9
Let g be (-8)/((5 - (-65)/(-15))*-3). Let l(p) be the third derivative of -1/9*p**3 - 5/18*p**5 + 0*p + 0 + 5/18*p**g - 13*p**2. Let l(q) = 0. Calculate q.
1/5
Let w(q) be the first derivative of 615*q**3 + 1847*q**2/2 + 2*q + 562. Factor w(c).
(c + 1)*(1845*c + 2)
Suppose 99*b + 147*b**3 + 59*b - 9*b + 2*b**4 - 8*b**4 + 5*b**4 + 297*b**2 = 0. What is b?
-1, 0, 149
Let w be 9/((-9)/4) + 89. Let y = 152 - w. Factor -8*v**3 + y*v - 2*v**3 - 62*v + 5*v**5.
5*v*(v - 1)**2*(v + 1)**2
Let p(t) be the second derivative of -t**5/20 - 349*t**4/6 - 121801*t**3/6 + 200*t - 6. Suppose p(u) = 0. Calculate u.
-349, 0
Let w(c) be the first derivative of c**3/12 + 49*c**2/4 - 102*c + 2423. Factor w(u).
(u - 4)*(u + 102)/4
Let -1308*w**5 - 192 + 1272*w**5 + 2004*w**2 - 212*w**4 + 132*w**3 + 1294*w + 210*w = 0. What is w?
-4, -1, 1/9, 3
Let v(h) be the first derivative of 5*h**4/16 + 425*h**3/4 + 635*h**2/4 + 994. What is b in v(b) = 0?
-254, -1, 0
Let y be (-34)/(-4) - (-2)/(-18)*(-117)/26. Let p(r) be the second derivative of y*r + 0 + 4/3*r**3 + 0*r**2 + 1/6*r**4. Find h, given that p(h) = 0.
-4, 0
Suppose -410*w - 1571 = -442*w + 1629. Factor 120 + 70/3*j**2 - 5/3*j**3 - w*j.
-5*(j - 6)**2*(j - 2)/3
Let l = -5276 + 10577/2. Let s(h) be the first derivative of 11 + 29*h**2 - 130/3*h**3 - 6*h - l*h**4. Factor s(x).
-2*(x + 3)*(5*x - 1)**2
Let j be (-5)/(-6) + (36 - 20723/690). Solve -44/5*c + 2*c**4 - j*c**2 - 16/5 + 2/5*c**3 + 2/5*c**5 = 0 for c.
-4, -1, 2
Let i(n) be the second derivative of n**5/4 + 35*n**4/12 - 5*n**3/6 - 35*n**2/2 + 6*n - 38. Suppose i(c) = 0. What is c?
-7, -1, 1
Let d = 134 - 160. Let n be (126/d - -3) + (-16)/(-8). Find j such that -n - 128/13*j**3 - 24/13*j - 96/13*j**2 = 0.
-1/4
Suppose -18*p = -20*p + 38. Solve -2 + 25*g**2 - 27 + g**3 - p + g**3 + 20*g + g**2 = 0.
-12, -2, 1
Let a(p) be the second derivative of -242/3*p**2 - 22/9*p**3 + 265*p - 1/36*p**4 + 0. Suppose a(l) = 0. What is l?
-22
Let z(j) be the third derivative of j**7/1680 - 17*j**6/960 + 7*j**5/80 + j**4/48 - 7*j**3/6 - 170*j**2 + 2*j + 1. Factor z(g).
(g - 14)*(g - 2)**2*(g + 1)/8
Let i(y) be the first derivative of -4*y**5/25 + 14*y**4 + 572*y**3/15 + 144*y**2/5 + 6518. Factor i(n).
-4*n*(n - 72)*(n + 1)**2/5
Let a(g) be the third derivative of g**7/1050 - 17*g**6/50 + 3399*g**5/100 + 10609*g**4/60 - g**2 + 2253*g. Factor a(o).
o*(o - 103)**2*(o + 2)/5
Let d = -11/747 - -19931/747. Factor 64/3*y**5 - 20/3*y**3 + 10/3*y - 25/3*y**2 - 1/3 + d*y**4.
(y + 1)**2*(4*y - 1)**3/3
Suppose -4*y + 39*y = -140. Let v(u) = -10*u**2 - 16*u - 24. Let o(n) = 8*n**2 + 16*n + 24. Let b(l) = y*o(l) - 3*v(l). Factor b(m).
-2*(m + 2)*(m + 6)
Suppose 4*q + x + 6 = 17, -4*q + 5 = -x. Suppose -q*a = -n - 3 - 5, a = n + 6. Factor 0*u - a + 3/2*u**2 - 1/2*u**3.
-(u - 2)**2*(u + 1)/2
Let i be 6 + (-224)/16 - (-14)/24*14. Solve 7/3*l**2 - 11/6*l - l**3 - 1/6*l**4 + i*l**5 + 1/2 = 0 for l.
-3, 1
Let j(c) be the second derivative of 1/90*c**6 + 13/36*c**4 + 38*c + 0*c**2 - 1 + 2/15*c**5 + 1/3*c**3. Factor j(k).
k*(k + 1)**2*(k + 6)/3
Let s(o) be the third derivative of o**5/60 - 11*o**4/3 - 155*o**3/2 + 54*o**2 - 2. Find g such that s(g) = 0.
-5, 93
Determine z, given that 21/4*z**2 + 153/4*z - 87/2 = 0.
-58/7, 1
Let x(b) be the third derivative of -28*b - 3*b**2 + 3/20*b**5 - b**3 + 1/40*b**6 + 0 - 1/8*b**4 - 1/70*b**7. Factor x(g).
-3*(g - 2)*(g - 1)*(g + 1)**2
Let a(g) = 2*g**2 - 27*g - 207. Let q be a(-6). Suppose 30 = q*l - 24. Factor -2/7*b + 20/21 - 2/21*b**l.
-2*(b - 2)*(b + 5)/21
Suppose -3*j + 4*w = -71, 5*j + 57*w - 60*w - 100 = 0. Factor -35/2 + j*s + 1/2*s**2.
(s - 1)*(s + 35)/2
Let s(m) be the first derivative of 1/10*m**5 - 1/6*m**4 + 1/18*m**3 + 0*m**2 - 19 + 0*m. Factor s(q).
q**2*(q - 1)*(3*q - 1)/6
Suppose -3*i + 3 = -3*l, -4*i + 43 = 11*l + 54. Factor -10/7*c**3 + 2/7*c**4 + 0*c + i + 0*c**2.
2*c**3*(c - 5)/7
Let w = 9613 - 9613. Suppose -x + 0*x + 4 = 3*v, 3*v = 3*x + 12. Find z, given that w*z + 1/2 - 1/2*z**v = 0.
-1, 1
Find t such that -2/13*t**4 - 376710/13*t**2 - 1734/13*t**3 + 0 - 374978/13*t = 0.
-433, -1, 0
Let t(j) be the third derivative of -j**7/560 + j**6/80 + 9*j**5/80 + 5*j**4/16 + 7*j**3/16 + 134*j**2 - 1. Factor t(o).
-3*(o - 7)*(o + 1)**3/8
Let g(d) = 2*d**2 - 15*d - 3. Let m(s) = 7*s**2 - 59*s - 11. Suppose 102 = -5*y + 4*j, -120 = 6*y - y + 5*j. Let v(t) = y*g(t) + 6*m(t). Factor v(w).
-2*w*(w + 12)
Let r(y) be the second derivative of 25*y**4/12 + 95*y**3/6 + 42*y**2 - 18*y - 32. Factor r(g).
(5*g + 7)*(5*g + 12)
Let y(n) be the first derivative of 5*n**2/2 + 48*n - 1. Let a be y(-9). Determine m, given that 12*m**2 - 2*m**a + 46*m + 2*m + 64 - 3*m**3 + 6*m**3 = 0.
-4
Let r be 52/390 + 105591/16155. Let u = -1/359 + r. Factor 20/3*b**2 + u + 2*b**3 - 46/3*b.
2*(b - 1)*(b + 5)*(3*b - 2)/3
Let v = -1443 - -1448. Let x(i) be the third derivative of 0*i**3 + 1/180*i**v - 1/72*i**4 - 12*i**2 + 0*i + 0. Factor x(u).
u*(u - 1)/3
Suppose -k - 4*o = 14, 4*k + 3 = -4*o - 5. Factor 3*i**k - 65 - 3*i**2 - 31 - 4*i**2 - 56*i.
-4*(i + 2)*(i + 12)
Let -880/7*k + 584/7 - 2/7*k**3 + 298/7*k**2 = 0. Calculate k.
1, 2, 146
Let k be ((-4)/18*-24)/((-3)/(-549)). Let d = k - 976. Determine u so that 3/5*u**3 + 0*u + d + 1/5*u**2 = 0.
-1/3, 0
Let z be 21/63*(23 - 23). Factor 5/4*a**2 - 1/2*a + z.
a*(5*a - 2)/4
Let s(d) = -d**3 + 425*d**2 - 46224*d + 90732. Let h(b) = -2*b**3 + 851*b**2 - 92447*b + 181466. Let p(u) = 3*h(u) - 5*s(u). Factor p(m).
-(m - 213)**2*(m - 2)
Let a(x) = 2*x**2 + 303*x + 2830. Let g be a(-10). Factor -10/9*s**4 - 2*s**3 - 14/9*s**2 - 4/9*s - 2/9*s**5 + g.
-2*s*(s + 1)**3*(s + 2)/9
Let z(j) = -2*j**2 - 1. Let i(o) = -12*o**3 + 9*o**3 - 11*o - 13*o**3 + 8 - 3*o**2 + 36*o**2 + 4*o**4. Let v(d) = i(d) + 6*z(d). Let v(l) = 0. What is l?
1/2, 1, 2
Let j(t) = 116*t + 12879. Let h be j(-111). Suppose -54/11 - 108/11*v**h + 42/11*v**4 + 102/11*v + 12/11*v**2 + 6/11*v**5 = 0. Calculate v.
-9, -1, 1
Let a(u) be the first derivative of -2*u**3/39 + 1606*u**2/13 + 3214*u/13 + 5750. Factor a(i).
-2*(i - 1607)*(i + 1)/13
Let p be -1 - (-12)/4*(-3)/(-9). Suppose -45*b + 180 = -p*b. Determine v so that 0 - 284/5*v**b + 32/5*v**2 - 10*v**3 - 42*v**5 + 8/5*v = 0.
-1, -2/5, -2/7, 0, 1/3
Factor 161*f**3 + 26*f + 1834*f + 5*f**4 + 633*f**3 + 3725*f**2 + 297*f**3 + 779*f**3.
5*f*(f + 1)**2*(f + 372)
Let y(m) be the third derivative of -1/60*m**6 - 1/504*m**8 + 0*m**3 + 3*m**2 + 0*m - 1/18*m**5 + 1/63*m**7 - 20 + 1/9*m**4. Find r such that y(r) = 0.
-1, 0, 1, 4
Let b = -4559/6 + 760. Let n(t) be the first derivative of -17 + b*t + 10/9*t**3 + 3/4*t**2. Factor n(d).
(4*d + 1)*(5*d + 1)/6
Let y(x) be the first derivative of 33/10*x**5 + 2*x**3 + 6*x**2 + 0*x - 27/4*x**4 - 133 - 1/2*x**6. Determine z so that y(z) = 0.
-1/2, 0, 2
Let c be -2 - -1 - (798/57 + (-20 - -2)). Solve -4/11*x**c + 0 + 2/11*x**4 - 2/11*x**2 + 4/11*x = 0 for x.
-1, 0, 1, 2
Let i(w) be the first derivative of -w**4/8 + 17*w**3/3 - 33*w**2/4 - 334. Solve i(y) = 0.
0, 1, 33
Let v(x) be the first derivative of x**6/6 + 4*x**5/5 - 23*x**4/2 - 196*x**3/3 - 147*x**2/2 - 800. What is c in v(c) = 0?
-7, -3, -1, 0, 7
Let f be ((-6)/15 + (-48)/(-180))*(15 + -20). What is i in f*i**2 + 6*i - 20/3 = 0?
-10, 1
Let x(j) be the third derivative of -j**6/240 - 15*j**5/8 + j**2 + 1474. Factor x(q).
-q**2*(q + 225)/2
Solve -36*i**3 - 3*i**4 + 199 - i + 183 - 111*i**2 - 17*i - 380 + 166 = 0.
-7, -4, -2, 1
Let m(o) = o**3 + 21*o**2 + 8*o + 31. Let j be m(-20). Factor -326*g + 10 - 4*g**2 + 24*g**2 + 25*g**3 + j*g.
5*(g - 1)*(g + 2)*(5*g - 1)
Let q(a) be the third derivative of a**8/30240 - 2*a**7/945 + a**5/4 + 7*a**4/24 + a**2 - 68. Let l(f) be the third derivative of q(f). Factor l(c).
2*c*(c - 16)/3
Let j be 0 + 1/7 + 5561/469. What is t in -17*t**2 - 21 - 24 + 111*t - j*t**3 - 61*t**2 + 24*t**4 - 3*t**5 + 3 = 0?
-2, 1, 7
Let c(o) be the first derivative of -23/3*o**2 + 2/3*o**3 - 16/3*o - 65. Suppose c(y) = 0. What is y?
-1/3, 8
Let c(n) be the second derivative of 1/10*n**6 - 1/2*n**3 - 9/20*n**5 + 10 + 3/4*n**4 - 6*n + 0*n**2. Factor c(p).
3*p*(p - 1)**3
Factor -40*k + 99/5*k**3 + 0 + 102/5*k**2 - 1/5*k**4.
-k*(k - 100)*(k - 1)*(k + 2)/5
Let o(l) 