 - 7/8*g**2 + 5/8*g**n.
-g*(g - 3)*(g - 1)**2/8
Let c(f) be the second derivative of -f**4/18 + 2*f**3 - 24*f**2 - 8*f - 2. What is u in c(u) = 0?
6, 12
Let a = -1585 + 1541. Let b be 460/a + 4 - -7. Factor 0 + 0*f**2 - 6/11*f**3 + b*f.
-6*f*(f - 1)*(f + 1)/11
Let v be 335/80 - (627/(-176))/(-19). Let c(q) be the first derivative of -50*q - 92/3*q**3 + 6*q**v - 2/5*q**5 + 42 + 60*q**2. Factor c(g).
-2*(g - 5)**2*(g - 1)**2
Let k(v) = -2*v + 12. Let n(m) = -3*m + 11. Let b(c) = 4*k(c) - 3*n(c). Let y be b(-7). Factor 6*d**2 - y*d**2 - 3*d**2 - 10*d.
-5*d*(d + 2)
Let d = 1 - -1. Suppose i - 3*b = 2*b + 3, d*i = -b + 6. Factor 6*f**3 + i*f**4 + 1 - 1 + 83*f**2 - 80*f**2.
3*f**2*(f + 1)**2
Let k = -145391 + 581565/4. Suppose 0 - k*q**2 + 2*q = 0. What is q?
0, 8
Suppose -552*a + 354*a**2 + 1895*a**2 + 7 - 287*a**3 + 1620*a**4 - 3007*a**3 + 19*a**2 + 9 = 0. What is a?
1/30, 2/3
Find f, given that -230/7 - 228/7*f + 2/7*f**2 = 0.
-1, 115
Suppose 8*i = 59*i - 102. Factor -3*n**5 + 40*n**4 + 50*n**4 - 141*n**4 - 189*n**3 + 243*n**i.
-3*n**2*(n - 1)*(n + 9)**2
Let z(j) = -2*j**3 + 21*j**2 + 21*j - 106. Let v = 850 - 839. Let q be z(v). Factor -16/5*d + 8/5*d**2 + 12/5*d**3 + 2/5*d**5 - 2*d**q + 0.
2*d*(d - 2)**3*(d + 1)/5
Let u(p) = -7*p**4 + p**3 + p**2 - p - 1. Let n(r) = -24*r**4 - 33*r**3 + 9*r**2 + 33*r - 13. Let q(y) = -n(y) + 4*u(y). Find f such that q(f) = 0.
-1, 1/4, 1, 9
Let k be 205/595 + -10 + (-68)/(-7). Let q(l) be the first derivative of 6 + 2/51*l**3 - 2/85*l**5 + 0*l - 1/34*l**4 + k*l**2. Factor q(n).
-2*n*(n - 1)*(n + 1)**2/17
Let x(q) be the second derivative of -q**6/180 - 17*q**5/120 + q**4/24 + 49*q**3/36 - 17*q**2/6 - 1157*q. Factor x(w).
-(w - 1)**2*(w + 2)*(w + 17)/6
Let r(d) be the first derivative of 3/16*d**2 - 1/4*d + 62 - 1/24*d**3. Let r(g) = 0. Calculate g.
1, 2
Factor -3/5*x**2 - 39/5*x - 66/5.
-3*(x + 2)*(x + 11)/5
What is a in 512/3 + 3136*a - 361*a**3 + 7778/3*a**2 + 35/3*a**4 = 0?
-1, -2/35, 16
Let q(i) be the third derivative of i**8/1680 + i**7/168 - i**6/180 + i**4/24 + 17*i**3/6 - 75*i**2. Let w(f) be the second derivative of q(f). Factor w(o).
o*(o + 4)*(4*o - 1)
What is q in -786*q - 833*q - 1988 + 1928*q - 3*q**2 - 607*q + q**2 = 0?
-142, -7
Let w(q) = 19*q**3 + 3*q**2 - q - 1. Let u be w(1). Suppose 0*g - 4*g = -u. Suppose -6*s**4 + 0*s**5 + 3*s**g + 3*s**4 = 0. What is s?
0, 1
Let b(x) be the first derivative of 32/7*x + 80 - 8/21*x**3 + 24/7*x**2 + 2/21*x**6 + 0*x**5 - x**4. Suppose b(h) = 0. Calculate h.
-2, -1, 2
Suppose 0 = 3*t + 4*c + 28, 4*t + 6*c - 9*c + 29 = 0. Let k be t/(-6) - 40/30. Factor 0 - 1/9*a**3 + k*a**2 + 1/9*a.
-a*(a - 1)*(a + 1)/9
Suppose 0 = 3*w + 2*u - 128, -2*w + 162 - 78 = u. Suppose -6*k = -w + 28. Solve -8/5*v**4 + 0 + 2*v**3 + 2/5*v**5 + 0*v - 4/5*v**k = 0.
0, 1, 2
Let p(z) be the first derivative of -37/3*z**3 + 0*z + 0*z**2 - 1/3*z**4 - 43 + 1/18*z**6 - 1/10*z**5. Let g(v) be the third derivative of p(v). Factor g(m).
4*(m - 1)*(5*m + 2)
Let v = 112914 - 112912. Suppose 2/7*p**v + 20/7 - 22/7*p = 0. Calculate p.
1, 10
Let r be (2/6)/((-27)/(-72) - (-10)/(-30)). Solve 12*x - 1/2*x**4 - 1/2*x**2 - 3*x**3 - r = 0 for x.
-4, 1
Let s be (-5)/((-90)/(-4)) - (-116)/36. Factor 156 - s*n**2 - 9*n - 156.
-3*n*(n + 3)
Let s(x) be the first derivative of 8*x**5/5 + 41*x**4/4 + 61*x**3/3 + 31*x**2/2 + 3*x + 2293. Factor s(k).
(k + 1)**2*(k + 3)*(8*k + 1)
Let m(r) = -r**2 + 2*r - 76. Let q be m(0). Let t be 10/(-28) + 2 + 38/q. Let 6/7 + t*p + 2/7*p**2 = 0. Calculate p.
-3, -1
Let o(n) = -2563*n - 135837. Let f be o(-53). Factor 32/7*x**f + 0*x + 4/7*x**3 + 0.
4*x**2*(x + 8)/7
Suppose 5*v - 3 = 5*r + 2, -5*r - 5*v = -5. Suppose r = -3*a - 3 + 24. Let -27*q**2 - 185*q + 545*q + 100 + a*q**2 + 55*q**2 = 0. Calculate q.
-10, -2/7
Let s(g) be the second derivative of 7*g**5/4 + 3275*g**4/4 - 21355*g**3/3 + 5700*g**2 + 15*g - 257. Let s(d) = 0. What is d?
-285, 2/7, 4
Suppose 0 = -0*m - 2*m + v + 2, 5*m - 4 = 3*v. Let l = -121/69 - -163/23. Solve -32*y + l*y**m + 0 - 2/9*y**3 = 0.
0, 12
Let a be (-16)/(-7) + ((-414)/1449)/((-3)/(-3)). Let q = 9/10 - 3/20. Determine i, given that -3/4*i**5 - 3*i**a - 3*i**4 - 9/2*i**3 - q*i + 0 = 0.
-1, 0
Let d(a) = -a**3 - 9*a**2 + 8*a + 6. Let p be d(-10). Let i = p - 22. Factor -i*v + v**2 + 32 + v**2 - 12*v.
2*(v - 4)**2
Let z(t) be the third derivative of 0*t**3 + t**2 + 0 + 0*t + 1/280*t**6 + 13/56*t**4 - 1/10*t**5. Find m, given that z(m) = 0.
0, 1, 13
Suppose 0 = -n + 16*n - 28710. Let w = 9714/5 - n. Let -w - 4/5*l**2 + 48/5*l = 0. What is l?
6
Let j(x) = 7*x**2 - 117*x + 102. Let s(z) = z**2 - z - 4. Let l(k) = -k**3 + 47*k + 13. Let q be l(7). Let m(i) = q*j(i) + 2*s(i). Factor m(h).
-5*(h - 22)*(h - 1)
Let j = 40 - 36. Determine y so that -27*y**3 + 3*y + 4*y**2 - 1629*y**4 + 5*y**2 + 1560*y**j - 36*y**5 = 0.
-1, -1/4, 0, 1/3
Let t(i) = i**3 - 139*i**2 + 411*i + 6. Let z(m) = -4*m**3 + 557*m**2 - 1646*m - 22. Let x(q) = 22*t(q) + 6*z(q). Find d such that x(d) = 0.
0, 3, 139
Let a be (-5)/(-15)*(11 - (-3)/(-1)). Let t(j) be the first derivative of 32/3*j + 2 + 2/9*j**3 - a*j**2. Find g, given that t(g) = 0.
4
Let l = 16 - 14. Factor -983*q + 983*q - 26*q**l - 2*q**3.
-2*q**2*(q + 13)
Let u be 2 + (-2 + 0 - 6 - (-571 - -563)). Let 8/3*a**u + 2/9*a**4 - 20/9*a + 2/3 - 4/3*a**3 = 0. What is a?
1, 3
Suppose 20*r**3 + 2/7*r**4 - 2/7*r**5 + 100/7*r**2 + 54 - 618/7*r = 0. Calculate r.
-7, -3, 1, 9
Find d, given that 0*d + 0 - 1/4*d**3 + 85/4*d**2 = 0.
0, 85
Let q(u) be the second derivative of -u**5/15 + 17*u**4/9 + 77*u**3/6 + 30*u**2 - 32*u + 1. Factor q(l).
-(l - 20)*(2*l + 3)**2/3
Let g(m) = 17*m**2 + 3611*m + 903. Let x(t) = 35*t**2 + 7220*t + 1805. Let z(o) = 5*g(o) - 3*x(o). Determine d, given that z(d) = 0.
-180, -1/4
Determine c so that 0 + 1/3*c**3 + 4*c + 8/3*c**2 = 0.
-6, -2, 0
Let v(w) be the second derivative of 155/6*w**3 + 199*w - 2 + 5/12*w**4 + 0*w**2. Determine n so that v(n) = 0.
-31, 0
Let j(d) = -26 - 18*d + 117 + 8*d - 3*d. Let y be j(7). Let 1/4*i**2 + y + 1/2*i = 0. What is i?
-2, 0
Let n(y) be the first derivative of y**4/48 - 14*y**3/9 - 31*y**2/2 + 2039. Solve n(b) = 0 for b.
-6, 0, 62
Factor -32076*o**3 - 1932*o + 180*o**2 - 80 - 2036 + 32072*o**3.
-4*(o - 23)**2*(o + 1)
Let b = -2080 - -2082. Let w(m) be the third derivative of 11*m**b + 0 - 1/20*m**5 + 2*m**3 + 0*m + 3/8*m**4. Find h, given that w(h) = 0.
-1, 4
Factor 5/2*w + 1/8*w**2 + 19/8.
(w + 1)*(w + 19)/8
Factor 229*u + 2*u**3 + 177*u - 52*u**2 - 166*u.
2*u*(u - 20)*(u - 6)
Let j(r) be the third derivative of -11*r**6/420 - 8*r**5/105 + 17*r**4/21 + 16*r**3/3 + 4622*r**2. Suppose j(q) = 0. Calculate q.
-2, 28/11
Let k(x) = 7*x + 28. Let g be k(-3). Factor 6*f + 4*f**2 - 3*f - 2*f + g*f + 4.
4*(f + 1)**2
Find r such that -674/5*r - 672/5 - 2/5*r**2 = 0.
-336, -1
Let q(v) be the first derivative of 5*v**3/3 - 50*v**2 + 180*v - 1242. Factor q(p).
5*(p - 18)*(p - 2)
Factor 0 + 676/9*i**2 - 4/9*i**3 + 0*i.
-4*i**2*(i - 169)/9
Suppose -159*l**2 - 33708*l - 1/4*l**3 - 2382032 = 0. What is l?
-212
Let q(k) be the third derivative of k**6/80 + 7*k**5/40 + k**4/4 - 3*k**3 - 654*k**2 + 1. Find a such that q(a) = 0.
-6, -2, 1
Solve -80/3 - 4/9*p**5 + 70/9*p**4 - 40*p**3 + 610/9*p**2 - 76/9*p = 0 for p.
-1/2, 1, 3, 4, 10
Let m(p) be the second derivative of -p**4/108 + 1637*p**3/54 + 91*p**2 - 70*p. Let m(l) = 0. What is l?
-1, 1638
Let a(b) = b + 1. Let z be a(1). Let p = -4313 - -4319. Factor 2*l**2 + p*l**z + 15*l - 3 + 4*l**2 + 6.
3*(l + 1)*(4*l + 1)
Solve 57/4*s**2 + 132 - 3/4*s**3 - 78*s = 0 for s.
4, 11
Let f(n) be the third derivative of n**8/112 + 24*n**7/35 - 15*n**6/4 + 38*n**5/5 - 51*n**4/8 - 2209*n**2. Solve f(w) = 0.
-51, 0, 1
Let m(j) be the third derivative of j**8/84 - 2*j**7/15 - 2*j**6/15 + 52*j**5/15 + 8*j**4 + 2586*j**2. Let m(q) = 0. What is q?
-2, -1, 0, 4, 6
Let f(n) be the second derivative of -49*n**6/10 - 8211*n**5/2 - 3829837*n**4/4 - 1090890*n**3 - 467046*n**2 + 979*n. Factor f(q).
-3*(q + 279)**2*(7*q + 2)**2
Let y(a) be the third derivative of a**5/180 + 91*a**4/36 + 8281*a**3/18 + 134*a**2 - 3. Find s such that y(s) = 0.
-91
Let s(r) = -12*r**3 + 35*r**2 - 86*r + 68. Let p(m) = -7*m**3 + 18*m**2 - 42*m + 32. Let v(h) = -5*p(h) + 3*s(h). Suppose v(a) 