f -3*u**5/40 + 3*u**4/4 - 24*u**2 - 2*u - 278. Factor v(i).
-3*(i - 4)**2*(i + 2)/2
Suppose 128*b - 214*b = 0. Let z(c) be the third derivative of -29*c**2 + b*c + 1/40*c**6 + 0 + 1/10*c**5 + 0*c**3 + 1/8*c**4. What is j in z(j) = 0?
-1, 0
Suppose -m = -5*a + 23, -12 = -23*m + 22*m - 2*a. Let y(g) be the third derivative of 0*g - 1/36*g**4 + 0 + 2*g**m + 0*g**3 - 1/180*g**5. Factor y(h).
-h*(h + 2)/3
Let w(n) be the first derivative of -n**4/16 - 3289. Solve w(j) = 0 for j.
0
Let c = -455215 + 455217. Let 178/9*x - 20/3 + 6*x**3 + 2/9*x**4 - 58/3*x**c = 0. Calculate x.
-30, 1
Let c(w) = 3*w**2 + 400*w - 14455. Let i(h) = 5*h**2 + 606*h - 21683. Let l(u) = 8*c(u) - 5*i(u). Factor l(z).
-(z - 85)**2
Let g(d) = -2*d - 1. Let c(w) = w. Let z(k) = -3*c(k) - 2*g(k). Let y be z(3). Factor h**2 + y*h + 6*h**2 - 2*h**2.
5*h*(h + 1)
Determine i, given that 29 - 59/2*i**2 + 27/2*i - 27/2*i**3 + 1/2*i**4 = 0.
-2, -1, 1, 29
Let v(g) be the third derivative of -g**7/420 - 29*g**6/120 + 61*g**5/30 - 31*g**4/6 + 178*g**2. Find n such that v(n) = 0.
-62, 0, 2
Let i(t) be the first derivative of -18*t + 3/2*t**2 + 20 + t**3. Factor i(w).
3*(w - 2)*(w + 3)
Let s(x) be the second derivative of -x**4/54 - 34*x**3/3 + 307*x**2/9 + 6816*x. Factor s(a).
-2*(a - 1)*(a + 307)/9
Suppose 5*v = 3*r + 76, -2*v = -3*v + r + 14. Let q be 51/v + 3 + 104/(-18). Solve -1/9*x**2 - 1/9*x + q = 0 for x.
-2, 1
Factor -28/3 - 67/3*y - 17*y**2 - 1/3*y**4 - 13/3*y**3.
-(y + 1)**2*(y + 4)*(y + 7)/3
Find s such that 5*s**3 - 620*s + 30*s**2 - 99*s**2 - 71*s**2 - 135 - 505 = 0.
-2, 32
Let u(f) = f**3 - 39*f**2 - 80*f - 72. Let y be u(41). Solve -5*k**5 + 13*k + 1 - y*k**3 + 2*k + 137*k**4 - 117*k**4 - 20*k**2 - 1 = 0 for k.
-1, 0, 1, 3
Let d = -2/5627 + 11260/16881. Let n be 4/(-16) - 13/(-4). Determine w so that 0 - 4/3*w + d*w**n - 2/3*w**2 = 0.
-1, 0, 2
Let m be (-1 - 21/5)*-5. Suppose -152*o + 139*o + m = 0. What is g in 2/5*g**o - 2/5*g + 0 = 0?
0, 1
Let f be (0/3 - 1)/((-3)/66). Suppose 2*r = -9*r + f. Factor -7*s - 8*s**r - 16 + 71*s**4 - 68*s**4 - 25*s + 8*s**3.
(s - 2)*(s + 2)**2*(3*s + 2)
Let z = 753 - 728. Factor z*p**2 - 3011 - 20221 + 23*p**2 - 51*p**2 - 528*p.
-3*(p + 88)**2
Let u(p) = 2*p**3 - 20*p + 20. Let k be u(1). Let h(o) be the third derivative of 1/60*o**5 + 0*o**3 + 0 + 14*o**k + 0*o + 0*o**4. Solve h(v) = 0.
0
Let d(f) be the second derivative of -2*f**6/75 - 2*f**5/25 + f**4/5 + 8*f**3/15 - 8*f**2/5 + 21*f + 45. Factor d(i).
-4*(i - 1)**2*(i + 2)**2/5
Let w(z) be the third derivative of -z**6/120 - 13*z**5/5 - 77*z**4/6 - 68*z**2 - 16. Solve w(l) = 0 for l.
-154, -2, 0
Suppose -k = -4*q - 25, 3*k + 23*q = 26*q + 21. Let 3/4*g**2 - k - g + g**3 + 1/4*g**4 = 0. What is g?
-2, -1, 1
Let o be ((-51)/(24531/(-148)))/(14/(-273)*3*-3). Factor -34/3*x + o*x**3 + 6 + 14/3*x**2.
2*(x - 1)**2*(x + 9)/3
Let y be -3 - ((-9)/(-9)*1 - 40/5). Let d(j) be the second derivative of y*j + 2/5*j**5 + 1/3*j**4 + 0*j**3 + 0*j**2 + 2/15*j**6 + 0. Factor d(g).
4*g**2*(g + 1)**2
Let x be ((-4)/10)/((-4)/20)*2. Suppose -15 = -x*k - k. Factor 3*s**5 - 3*s**4 - 6*s**3 + 6*s**k - 6*s**3.
3*s**3*(s - 2)*(s + 1)
Let i = 9173/9 - 1019. Let g = 13 - 13. Factor 0*s + i*s**2 + g.
2*s**2/9
Let l(q) = 7*q**3 + 4*q**2 - 18*q + 3. Let i = -509 - -512. Let f(w) = 8*w**3 + 4*w**2 - 16*w + 4. Let r(o) = i*f(o) - 4*l(o). Determine z so that r(z) = 0.
-3, 0, 2
Let d(m) be the second derivative of -49*m**6/780 - 21*m**5/65 - 5*m**4/13 - 8*m**3/39 + 69*m**2/2 + 7*m. Let r(q) be the first derivative of d(q). Factor r(z).
-2*(z + 2)*(7*z + 2)**2/13
Let k(l) be the first derivative of -l**5/6 - 35*l**4/2 - 4855*l**3/18 - 1435*l**2 - 2130*l + 7817. Solve k(v) = 0.
-71, -6, -1
Let s be 295/(-354)*(-24)/10. Let a(z) be the third derivative of -6*z**s - 5/8*z**4 + 0*z + z**3 + 0 + 1/5*z**5 - 1/40*z**6. Factor a(x).
-3*(x - 2)*(x - 1)**2
Let j(z) = z**2 + 13*z + 20. Let p be j(-12). Suppose -7*x + 30 = p*x. Solve -3*i**x + 9*i + 6*i**3 + 5*i**4 - 2*i**4 + 0*i - 15*i = 0 for i.
-2, -1, 0, 1
Let l(z) = -16*z**2 + 7*z + 18. Suppose -2*s + 2 - 12 = 4*k, 4*s - 19 = 5*k. Let q(p) = 7*p**2 - 3*p - 9. Let h(u) = k*l(u) - 7*q(u). Let h(o) = 0. What is o?
-3, 3
Suppose 234/7*f - 1220/7 + 2/7*f**2 = 0. What is f?
-122, 5
Let b(a) be the first derivative of -3*a**5/5 + 69*a**4/4 + 804*a**3 + 7770*a**2 + 13200*a + 5633. Determine u so that b(u) = 0.
-10, -1, 44
Let o = -883 + 888. Let x(u) = -14*u**3 - 15*u**2 - 14*u + 5. Let j(s) = 12*s**3 + 16*s**2 + 16*s - 4. Let v(z) = o*j(z) + 4*x(z). Factor v(w).
4*w*(w + 2)*(w + 3)
Let v(p) be the second derivative of -p**4/16 + 81*p**3/4 + 3841*p. Factor v(c).
-3*c*(c - 162)/4
Let m be (-3)/2 + (1/(-2) - 1). Let z be (-1 - 1) + 3 - m. Solve c - 4*c**3 + c**5 - 8*c**2 - z*c**4 + 8*c**4 - c**3 + 3*c**3 + 4 = 0.
-4, -1, 1
Let p(z) be the second derivative of -25/21*z**3 + 46/7*z**2 - 135*z + 1/42*z**4 + 0. Let p(j) = 0. Calculate j.
2, 23
Suppose -24924*y = -24947*y + 15548. Let r(o) be the first derivative of -41 + 4/3*o**3 + y*o - 52*o**2. Solve r(h) = 0.
13
Let p(o) = -22*o**3 - 52*o**2 - 150*o - 88. Let r(y) = 30*y**3 + 68*y**2 + 200*y + 118. Let u(t) = 11*p(t) + 8*r(t). Factor u(q).
-2*(q + 1)**2*(q + 12)
Let i be (1 + 1 + -5)*(0 - 3). Suppose 9 = 3*f - 3*w, 4*f + 7*w - 10 = i*w. Factor -2 - d**f - 11/3*d.
-(d + 3)*(3*d + 2)/3
Let b(r) be the third derivative of -r**5/108 + 791*r**4/72 + 475*r**3/27 + 118*r**2 - 3*r. What is i in b(i) = 0?
-2/5, 475
Let m(n) be the first derivative of -4*n**5/5 - 14*n**4 + 4*n**3/3 + 28*n**2 - 1071. Suppose m(f) = 0. What is f?
-14, -1, 0, 1
Solve -65170*z**2 + 495*z - 170*z + 65175*z**2 - 1750 = 0.
-70, 5
Let h(g) = -g**3 + 2*g**2 - 3*g + 1. Let x(b) = 6*b**4 + 12*b**2 - 32*b + 6. Let m(q) = -8*h(q) + x(q). Determine c, given that m(c) = 0.
-1, -1/3, 1
Factor 3118/3*m - 2430481/3 - 1/3*m**2.
-(m - 1559)**2/3
Let f(m) be the second derivative of m + 4/3*m**4 + 0*m**2 - 6 - 4/5*m**5 + 2/15*m**6 + 0*m**3. Factor f(x).
4*x**2*(x - 2)**2
Let d(l) be the second derivative of 1/3*l**3 + 20*l - 5/4*l**2 + 1/24*l**4 + 2. Factor d(x).
(x - 1)*(x + 5)/2
Let p(g) be the first derivative of -1/9*g**3 + 2/3*g**2 - 54 - 4/3*g. Find a such that p(a) = 0.
2
Factor 0*a + 312/5*a**3 - 2/5*a**5 - 72/5*a**4 + 0 - 64*a**2.
-2*a**2*(a - 2)**2*(a + 40)/5
Let x be 147 - (0/2 + 1). Suppose -3*r - k = -6*r + x, 3*r = 5*k + 154. Factor -25 + r - 4*p - p**2 - 24 + 2*p.
-(p + 1)**2
Determine b so that 83*b + 126*b**3 + 125*b + 12*b**2 + 36*b**3 - 237 + 93 - 4*b**4 - 234*b**3 = 0.
-18, -2, 1
Suppose -l - 2*w + 6 + 1 = 0, -2*l + 15 = 5*w. Suppose l*p - 4 = 2*a + 3, a - 19 = -5*p. Factor 2/13*r + 0*r**2 - 4/13*r**3 + 0 + 0*r**a + 2/13*r**5.
2*r*(r - 1)**2*(r + 1)**2/13
Let w(m) be the second derivative of m**6/195 + 12*m**5/65 + 9*m**4/13 - 360*m**3/13 + 2025*m**2/13 + 1415*m. Factor w(k).
2*(k - 3)**2*(k + 15)**2/13
Let n be (-75)/(-24) + 188/32 + -6. Suppose 5 = 5*s - 10. Find f, given that -f**3 - n*f - 2*f**s + 3*f**3 - 9*f**2 - 6*f**3 = 0.
-1, -1/2, 0
Let w(s) = -2*s**3 - s**2 - s + 1. Let f(o) = 10*o**3 + 19*o**2 + 28*o + 7. Let l(v) = -f(v) - 4*w(v). Factor l(t).
-(t + 1)**2*(2*t + 11)
Determine s, given that 2/13*s**2 + 842/13 + 844/13*s = 0.
-421, -1
Let u be 0/((-12)/(30/5)). Determine i, given that 4*i**4 - 10 - 55*i**2 - 65*i**2 + 10 - 52*i**3 + u*i**4 = 0.
-2, 0, 15
Let c(j) be the third derivative of -j**7/2415 - 17*j**6/1380 - 2*j**5/115 + 17*j**4/69 + 64*j**3/69 - j**2 - 478*j. Find z, given that c(z) = 0.
-16, -2, -1, 2
Let z(l) be the first derivative of l**6/24 - 13*l**5/10 + 27*l**4/2 - 81*l**3/2 - 729*l**2/8 + 1988. Factor z(y).
y*(y - 9)**3*(y + 1)/4
Suppose 24/7*g**2 + 3/7*g**3 - 27/7*g + 0 = 0. What is g?
-9, 0, 1
Let d = 110139815/28014 + -272048/69. Let b = 117/58 - d. Factor -196 - 376*q**2 - b*q**4 - 4/7*q**5 - 760/7*q**3 - 476*q.
-4*(q + 1)**2*(q + 7)**3/7
Let x = -29 - -42. Suppose -30 = 3*o - x*o. Find f, given that 0*f + 191*f**2 + 8*f - 4 - 196*f**2 + f**o = 0.
1, 2
Let i = 84 + -82. Let j be 23/207*0 + (-9)/(-4). Factor 9/4*s**3 + 3/2 - 6*s**i + j*s.
3*(s - 2)*(s - 1)*(3*s + 1)/4
Let h(z) = -7979*z + 4. Let x be h(0). Find k, given that -16/9 - 2/9*k**5 + 14/9*k**3 + 2/3*k**x - 14/9*k**2 - 4*k = 0.
-1, 2, 4
Solve 0*z + 432*z**3 + 0 - 1095/2*z**4