*r**2.
-2*r**2*(r + 1)**2
Factor -15/4*m**4 - 75/2*m**3 - 145*m**2 - 1/8*m**5 - 240*m - 144.
-(m + 2)**3*(m + 12)**2/8
Let a = 21/40 - 1/40. Suppose -30*y - 14 + 74 = 0. Find l such that -1/2*l**3 + 1/2*l**y + a*l - 1/2 = 0.
-1, 1
Suppose 3*s + 8 + 4 = 0, 0 = d + 3*s + 4. Suppose 3 = -d*p + 19. Determine x so that -3*x**2 + 6*x - 2*x + 4 + 4*x**p - 8*x = 0.
2
Determine t, given that 3/5*t**4 - 2*t**3 + 9/5*t**2 - 2/5*t + 0 = 0.
0, 1/3, 1, 2
Let x(d) be the first derivative of 0*d + 5 + d**4 + 0*d**2 + 16/3*d**3. Factor x(a).
4*a**2*(a + 4)
Let f(g) be the first derivative of -g**6/6 + 3*g**5/4 + 5*g**4/12 - 5*g**3/2 - 45*g + 31. Let x(a) be the first derivative of f(a). Factor x(l).
-5*l*(l - 3)*(l - 1)*(l + 1)
Let q(a) be the third derivative of a**5/90 + 55*a**4/36 + 202*a**2. Factor q(t).
2*t*(t + 55)/3
Let g(i) be the second derivative of i**5/60 + 5*i**4/36 - i**3/18 - 5*i**2/6 - 4*i - 2. Factor g(t).
(t - 1)*(t + 1)*(t + 5)/3
What is z in 316/11*z - 12482/11 - 2/11*z**2 = 0?
79
Let a = 2717/3390 - 1/678. Solve -a*p + 0 + 4/5*p**3 - 14/5*p**4 + 14/5*p**2 = 0.
-1, 0, 2/7, 1
Let k(g) be the third derivative of g**9/45360 - g**8/1680 + g**7/140 - g**6/20 + g**5/12 + 18*g**2. Let l(i) be the third derivative of k(i). Factor l(z).
4*(z - 3)**3/3
Let j(k) = -12*k**2 + 99*k + 51. Let d(a) = 3*a**2 - 25*a - 12. Let c(g) = 15*d(g) + 4*j(g). Factor c(q).
-3*(q - 8)*(q + 1)
Let r(l) be the third derivative of 0*l + 0 + 1/60*l**6 - 4/3*l**3 - 1/6*l**5 - 29*l**2 + 2/3*l**4. Factor r(j).
2*(j - 2)**2*(j - 1)
Factor 0 - 3/4*a**2 - 15/2*a.
-3*a*(a + 10)/4
Suppose 3*c - 35 = -2*c. Let r(s) = 4 - 5 + 5 - 2*s**3 - c*s + 8*s**2. Let q(v) = -v. Let w(b) = 6*q(b) + 2*r(b). Let w(x) = 0. Calculate x.
1, 2
Let s be (5/35)/(7/2 - 111/37). Factor -s*t**2 - 12/7*t - 18/7.
-2*(t + 3)**2/7
Factor 0*c + 0*c**2 + 0 + 5*c**3 - 50/3*c**5 + 35/3*c**4.
-5*c**3*(c - 1)*(10*c + 3)/3
Find j such that 14*j**3 - 5*j + 53*j**3 + 80*j**2 + 5*j**3 - 2*j**5 + 12*j**4 + 5*j = 0.
-2, 0, 10
Suppose 10 = -5*b - 3*j, -3*j = -3*b - j - 6. Let i be (28/(-49))/(b/7). Factor -d**i - 2*d**4 + 0*d**2 + 2*d**4 + d**4.
d**2*(d - 1)*(d + 1)
Suppose -4*b - 71 = 5*h, 2*b + 20 + 38 = -4*h. Let w(k) = k + 20. Let a be w(h). Factor -4*r - 4*r**3 + 2*r**2 + r**2 + a*r**2.
-4*r*(r - 1)**2
Let p = -8239/183 + 42/61. Let d = 49 + p. Determine y so that 6*y**4 + 16*y - 8/3 + 38/3*y**3 - d*y**5 - 82/3*y**2 = 0.
-2, 2/7, 1
Suppose 759*u + 32 = 767*u. Factor 0 + 1/4*v**2 + 1/4*v**3 - 1/4*v**u - 1/4*v.
-v*(v - 1)**2*(v + 1)/4
Suppose 0 = -20*v - 8*v + 56. Let q(k) be the third derivative of -1/12*k**4 - 2*k**v - 1/15*k**5 + 0*k + 2/3*k**3 + 0 + 1/60*k**6. Factor q(s).
2*(s - 2)*(s - 1)*(s + 1)
Let 0*p**2 - 2*p**2 + 76*p + 20*p**2 - 10*p**2 + 1444 - 7*p**2 = 0. What is p?
-38
Let a(s) be the second derivative of -5/3*s**4 - 15*s + 1/4*s**5 + 0 - 5*s**2 + 25/6*s**3. Let a(n) = 0. What is n?
1, 2
Let c(v) = -2*v**3 + 72*v**2 - 70*v. Let s be c(35). Determine w so that 0 - 2/3*w**2 + s*w**3 + 1/3*w - 1/3*w**5 + 2/3*w**4 = 0.
-1, 0, 1
Let s(x) = -x - 3 + 0 + 2. Let m be s(-5). Suppose 15*n**4 - n**3 - 4*n**m - 8*n**4 - 2*n**4 = 0. What is n?
0, 1
Let l(c) be the third derivative of c**7/168 - c**5/24 - c**3 + 8*c**2. Let t(q) be the first derivative of l(q). Factor t(i).
5*i*(i - 1)*(i + 1)
Let z(k) = 2*k**2 + k - 1. Let h(j) = 3*j**4 - 43*j**3 + 183*j**2 - 231*j - 244. Let w(b) = h(b) + 6*z(b). Solve w(g) = 0.
-2/3, 5
Let y(b) be the third derivative of b**7/280 - 31*b**6/160 - 33*b**5/80 + 31*b**4/32 + 4*b**3 + b**2 - 35. Find i such that y(i) = 0.
-1, 1, 32
Let i be ((-1131)/(-550) - 2) + 36/450. Let x(q) be the first derivative of 2/3*q**3 + 12/11*q**2 + 8/11*q + i*q**4 - 2. Factor x(g).
2*(g + 1)*(g + 2)*(3*g + 2)/11
Let f(h) be the third derivative of 0 + 0*h - 1/12*h**5 - 10/3*h**3 - 5/6*h**4 + 20*h**2. Determine x, given that f(x) = 0.
-2
Let m(b) be the third derivative of b**7/735 + 4*b**6/105 + 13*b**5/35 + 4*b**4/3 + 7*b**3/3 + b**2 + 77*b. Factor m(r).
2*(r + 1)**2*(r + 7)**2/7
Let f(s) = 4*s**4 - 12*s**3 + 29*s**2 - 21*s - 3. Let g(w) = w**4 - w - 1. Let v(p) = 5*f(p) - 15*g(p). Factor v(h).
5*h*(h - 9)*(h - 2)*(h - 1)
Suppose 3 = 5*c - 4*g - 3, -13 = -4*c - 5*g. Factor 3*n**c + 3*n - 18*n**3 - 3 - 16*n**3 + 31*n**3.
-3*(n - 1)**2*(n + 1)
Let b(q) be the second derivative of -7*q - 4/9*q**3 + 0 + 4/3*q**2 + 1/18*q**4. Factor b(a).
2*(a - 2)**2/3
Solve -92/5*y + 16/5 - 58/5*y**3 - 166/5*y**2 = 0 for y.
-2, -1, 4/29
Let z(h) = -1. Let l(t) = t + 1. Let m(d) = l(d) + z(d). Let g be m(3). What is p in -3/2*p**2 - g + 9/2*p = 0?
1, 2
Let q = -18 - -18. Let d be 8/(q + 8/4). Factor 0 + 2/11*j**3 + 2/11*j**d - 2/11*j**5 + 0*j - 2/11*j**2.
-2*j**2*(j - 1)**2*(j + 1)/11
Let l(i) be the first derivative of 4*i**5/85 - 15*i**4/34 - 58*i**3/51 + 18*i**2/17 - 384. Solve l(q) = 0 for q.
-2, 0, 1/2, 9
Let c(f) be the first derivative of f**4/10 + 4*f**3/3 + 5*f**2 - 414. Factor c(w).
2*w*(w + 5)**2/5
Let d(j) be the second derivative of j**6/90 - j**5/60 - j**4/6 + 2*j**3/9 + 4*j**2/3 - 46*j. Suppose d(s) = 0. Calculate s.
-2, -1, 2
Let w(l) be the first derivative of 5/12*l**3 - 11 + l**2 + l + 1/16*l**4. Factor w(t).
(t + 1)*(t + 2)**2/4
Factor 2*t**4 + t**4 + 91 + 99*t**2 + 33*t**3 - 253 + 27*t.
3*(t - 1)*(t + 3)**2*(t + 6)
Let z(g) be the third derivative of g**7/1365 + g**6/390 - 2*g**5/65 - 10*g**4/39 - 32*g**3/39 + 73*g**2. Determine r so that z(r) = 0.
-2, 4
Let u = -11 - -14. Factor -7*s**3 + 1 + s**2 + 8*s**3 - 3*s - 2*s**4 + 0*s**4 + 2*s**u.
-(s - 1)**2*(s + 1)*(2*s - 1)
Factor -6/7*f**2 - 4/7*f**3 + 16/7*f - 6/7.
-2*(f - 1)*(f + 3)*(2*f - 1)/7
Let h(o) be the third derivative of 1/120*o**5 + 1/224*o**8 + 0*o**3 - 1/80*o**6 + 0*o - 1/420*o**7 + 0*o**4 + 12*o**2 + 0. Suppose h(t) = 0. What is t?
-1, 0, 1/3, 1
Let d be (1617/22)/21 - 2/2. Factor d*s + 1 + 2*s**2 + 1/2*s**3.
(s + 1)**2*(s + 2)/2
Let w(z) = 2*z**5 + 3*z**4 + z**3 + z - 2. Let x(r) = -7*r**5 - 65*r**4 + 233*r**3 - 240*r**2 - 3*r + 6. Let j(v) = -3*w(v) - x(v). Let j(b) = 0. Calculate b.
-60, 0, 2
Let w be (-117)/(-18) + (-3)/2. Solve 3*f**2 + w*f**2 + 4*f**3 - 289 + 289 = 0.
-2, 0
Let a(m) = -29*m**4 - 218*m**3 - 404*m**2 - 7*m + 7. Let g(d) = -20*d**4 - 145*d**3 - 270*d**2 - 5*d + 5. Let x(q) = 5*a(q) - 7*g(q). Factor x(f).
-5*f**2*(f + 2)*(f + 13)
Let i be (-3 + -1)*(-7 + 2). Suppose 0 = -5*h + 5*z - i, 7*h = 4*h + 5*z - 20. Factor 2/7*d + h + 2/7*d**2.
2*d*(d + 1)/7
Let b(h) = -h**2 + 8*h - 10. Let x be (69/46)/(2/(-4)). Let v(t) = -2*t**2 + 8*t - 10. Let c(l) = x*v(l) + 4*b(l). Find y, given that c(y) = 0.
-5, 1
Suppose 24*v - 85 = 11. Let i(h) be the first derivative of -2/15*h**3 + 0*h + 0*h**2 - 3 - 1/10*h**v. Factor i(x).
-2*x**2*(x + 1)/5
Let a(j) be the first derivative of j**3/15 - 3*j**2/5 + 9*j/5 - 179. Factor a(g).
(g - 3)**2/5
Let k(h) be the first derivative of 1/4*h**3 + 0*h + 0*h**2 - 12 + 1/16*h**4. Factor k(i).
i**2*(i + 3)/4
Solve -61/9*g - 1/9*g**3 + 32/9*g**2 + 10/3 = 0.
1, 30
Find d, given that -22*d**2 + 36*d**2 + 132*d + 46*d**2 + 9*d**3 - 13*d**3 + 68 = 0.
-1, 17
Let c(h) = 2*h**4 + 8*h**3 - 4*h + 4. Let i(o) = 2*o**4 + 7*o**3 - 3*o + 3. Let m(l) = 3*c(l) - 4*i(l). Factor m(k).
-2*k**3*(k + 2)
Suppose -3*c + 2*n = -7, -n - n - 4 = 0. Suppose -5*o + c = -14. Determine r, given that -3*r**4 + 2*r - 4*r**3 - 5*r**3 + o*r**2 + 5*r**3 - 2*r**2 = 0.
-1, 0, 2/3
Let k be (6 + 6 - 12)/(-2). Factor 0 - 1/5*t**2 + k*t.
-t**2/5
Let z(o) = o + 2. Let j be z(3). Let d be 18/30 + 22/j. Factor 3*i**3 - 6*i**4 + 3*i**4 - 3*i**4 + 3*i**d.
3*i**3*(i - 1)**2
Let b(r) = r**2 - r + 1. Let l(p) = p**3 + 11*p**2 - 26*p + 1. Let c be l(-13). Let i(j) = -j**2 - 4*j + 7. Let g(y) = c*i(y) + 2*b(y). Factor g(a).
(a - 3)**2
Let 121/9 - 22/3*v + v**2 = 0. What is v?
11/3
Let v(c) be the second derivative of -c**7/84 - 3*c**6/20 - 19*c**5/40 - c**4/8 + 5*c**3/3 + 3*c**2 + 27*c + 1. Suppose v(b) = 0. What is b?
-6, -2, -1, 1
Determine u so that 153*u**5 - 15699*u**2 + 690*u**4 + 18 + 31999*u**2 - 15568*u**2 + 201*u + 1086*u**3 = 0.
-2, -1, -1/3, -3/17
Let q(m) = 2*m**3 + 2*m**2 - 2*m + 1. Let r(l) = -5*l**3 - 6*l**2 + 5*l - 2. Let u = -29 + 37. Let c(a) = u*q(a) + 3*r(a). Factor c(i).
(i - 2)*(i - 1)*(i + 1)
Let k = 218 + -210. Let t be (k/14