- 78*k**2 + 606. Suppose s(o) = 0. What is o?
-4, 0, 13
Let t(p) be the first derivative of 4*p**2 + 8/5*p**5 + 4 + 28/3*p**3 + 7*p**4 + 0*p. Factor t(l).
4*l*(l + 1)*(l + 2)*(2*l + 1)
Let a(m) = -2*m**3 - 36*m**2 - 36*m - 32. Let r be a(-17). Let w(g) = g**2 - 3. Let q be w(3). Factor q*h**2 + 2*h**3 + 2*h**3 - 2*h**r + h**4.
h**2*(h + 2)**2
Factor 0 + 24/13*v**3 + 0*v**2 - 16/13*v**4 + 0*v + 2/13*v**5.
2*v**3*(v - 6)*(v - 2)/13
Let o be ((-4)/(-6))/(14/168). Suppose -g - o = -5*g. Find d such that g*d**3 + 7*d**4 + 6*d**2 + 4*d + 3*d**3 - d**3 + 1 - 6*d**4 = 0.
-1
Solve -3/2*n**5 - 30*n**2 - 21/2*n**4 + 0 - 27*n**3 - 12*n = 0.
-2, -1, 0
Suppose 0 = -2890*k + 2916*k. Let -1/10*c + 1/10*c**3 + 0 + k*c**2 = 0. Calculate c.
-1, 0, 1
Suppose -590*p + 622*p - 64 = 0. Let c(d) be the third derivative of p*d**2 + 3*d**3 + 0 + 0*d - 5/8*d**4 + 1/20*d**5. Find q, given that c(q) = 0.
2, 3
Find j, given that 1900097*j**2 - 674273*j**2 + 10555010367 - 119979263 + 184690816*j + 4*j**4 + 102*j**3 + 3514*j**3 = 0.
-226
Let r = 1628 - 8137/5. Factor -3/5*m**2 + r*m**3 + 1/5*m + 0 - 1/5*m**4.
-m*(m - 1)**3/5
Let g(t) = -6*t**2 - t + 5. Let h = 85 - 89. Let v(m) = -5*m**2 - m + 4. Let q(f) = h*g(f) + 5*v(f). Factor q(i).
-i*(i + 1)
Let f(v) be the second derivative of v**7/420 - v**6/240 - v**5/60 + 11*v**2/2 - 12*v. Let w(y) be the first derivative of f(y). Factor w(n).
n**2*(n - 2)*(n + 1)/2
Let c = 721645/9 - 79985. Let g = 198 - c. Solve -g*y**2 + 4/9 - 2/9*y = 0 for y.
-2, 1
Suppose -3 = 2*j - 33. Suppose 2*h = -3*h + j. Let -2/5*l**4 + 0 + 0*l + 2/5*l**2 + 2/5*l**5 - 2/5*l**h = 0. Calculate l.
-1, 0, 1
Let q = 497970 - 547269358/1099. Let h = -2/157 - q. Solve -4/7*m**2 + 2/7*m**5 + 4/7*m**3 - h + 6/7*m**4 - 6/7*m = 0.
-1, 1
Let f(l) be the third derivative of l**6/120 + l**5/5 + 2*l**4 + 4*l**3/3 - 14*l**2. Let q(t) be the first derivative of f(t). Solve q(k) = 0 for k.
-4
Let v(a) be the second derivative of a**4/108 + 19*a**3/27 + 361*a**2/18 + 29*a. Suppose v(x) = 0. What is x?
-19
Let g(c) be the first derivative of 2*c**6/3 - 4*c**5/5 - 1. Factor g(p).
4*p**4*(p - 1)
Let g(i) be the second derivative of i**7/126 + i**6/15 + i**5/12 - i**4/3 - 506*i. Factor g(o).
o**2*(o - 1)*(o + 3)*(o + 4)/3
Let k(a) be the first derivative of -3*a**4/4 + 29*a**3 - 585*a**2/2 - 675*a + 159. Suppose k(m) = 0. Calculate m.
-1, 15
Suppose -3*s = -3*f - 6, 93*s = -3*f + 94*s + 4. Let j(n) be the third derivative of n**2 + 1/28*n**4 + 0 + 0*n + 0*n**f + 1/280*n**6 + 3/140*n**5. Factor j(i).
3*i*(i + 1)*(i + 2)/7
Let l(w) be the first derivative of -w**6/18 + 2*w**5/3 - 25*w**4/12 - 205. Factor l(c).
-c**3*(c - 5)**2/3
Let n(s) be the second derivative of -s**4/12 + 238*s**3/3 - 28322*s**2 + s - 71. What is a in n(a) = 0?
238
Let d(p) be the second derivative of -7/30*p**5 + 0 - 1/60*p**6 + 8*p + p**2 - 5/4*p**4 - 3*p**3. Let k(v) be the first derivative of d(v). Factor k(z).
-2*(z + 1)*(z + 3)**2
Suppose 4*m - 5*q = 530, 0 = -3*m - 4*q + 5*q + 392. Let p = 135 - m. Suppose -15/7*u**4 + 15/7*u**3 - 3/7*u**p + 75/7*u**2 + 48/7 - 120/7*u = 0. Calculate u.
-4, 1
Let f(o) be the first derivative of -o**6/9 + 2*o**5/3 - 7*o**4/6 + 2*o**3/3 + 6. Suppose f(w) = 0. What is w?
0, 1, 3
Let b(a) be the first derivative of 14*a**5/25 + 33*a**4/10 + 12*a**3/5 - 8*a**2/5 - 450. What is g in b(g) = 0?
-4, -1, 0, 2/7
Let a(w) be the first derivative of -5/13*w**2 + 10 + 1/26*w**4 - 6/13*w - 2/39*w**3. Factor a(m).
2*(m - 3)*(m + 1)**2/13
Suppose -c + 3 = -g, 0*g - 30 = 5*c + 4*g. Let y be (-2)/(-16)*10 - c/(-2). Factor y*w**2 - 1/2*w + 1/4.
(w - 1)**2/4
Let h(p) = -2*p**4 - 12*p**3 - 26*p**2 + 4. Let f(b) = -2*b**2 + 1. Let j(n) = -4*f(n) + h(n). Factor j(t).
-2*t**2*(t + 3)**2
Let t = 7/2875 - -183979/8625. Suppose 32/3*o + t + 4/3*o**2 = 0. What is o?
-4
Let f(l) = -4*l**2 - 21*l - 9. Let u be f(-5). Let r be 4/(-7)*u/(-16)*-1. Let r - 2/7*b + 1/7*b**2 = 0. Calculate b.
1
Let y(a) = 7*a**2 + 42*a + 80. Let f(c) = -50*c**2 - 295*c - 560. Let v(g) = 2*f(g) + 15*y(g). What is h in v(h) = 0?
-4
Let k(r) be the first derivative of 2*r**6/15 + 4*r**5/5 + 5*r**4/3 + 4*r**3/3 + 2*r + 8. Let j(z) be the first derivative of k(z). Factor j(a).
4*a*(a + 1)**2*(a + 2)
Let a(g) = g**2 - 7*g + 6. Suppose 7 = 6*k - 5*k. Let i be a(k). Factor 8*o - 3*o + 16*o**4 - 7*o**5 - 4*o**3 + i*o - 67 - 14*o**2 + 65.
-(o - 1)**3*(o + 1)*(7*o - 2)
Determine x so that 19*x - 75 + 211*x + x**2 - 220*x = 0.
-15, 5
Let d(x) be the third derivative of x**5/12 + 40*x**4/3 + 2560*x**3/3 + 307*x**2. Determine m, given that d(m) = 0.
-32
Let v be -10 + 1656/162 + (3 - 6) + 3. Determine x, given that -32/9*x + v*x**2 + 128/9 = 0.
8
Determine v so that 8/9*v + 0 + 2/3*v**2 - 2/9*v**3 = 0.
-1, 0, 4
Let c = -950/3 + 318. Let n(t) be the first derivative of 2*t + 8 - c*t**3 - 7/2*t**2. Factor n(a).
-(a + 2)*(4*a - 1)
Let l be 608/(-44) + (-2)/11. Let j = l + 25. Factor -12*t**3 + j*t**3 - 4*t**2 + 0*t**3 - 4*t.
-t*(t + 2)**2
Let i(d) be the third derivative of d**5/90 - d**3/9 + 73*d**2. Factor i(j).
2*(j - 1)*(j + 1)/3
Let f = 15427/21 - 5133/7. Factor -1/3*g**2 + 0 - f*g.
-g*(g + 4)/3
Factor 7/2*u - 1/2*u**2 - 5.
-(u - 5)*(u - 2)/2
Let n be -711*(-3)/12*1. Let u = -176 + n. Suppose 1/2*f**2 + 0*f + u*f**3 + 0 + 3/2*f**4 = 0. Calculate f.
-2/3, -1/2, 0
Let m(z) = -3*z + z + 0*z - 5. Let v be m(-4). Determine x, given that -10*x - x**2 - 4 - 4*x**2 - 12*x**2 - 5*x**v - 6*x = 0.
-2, -1, -2/5
Let q(x) be the first derivative of 8 - 2/9*x**6 - 2/3*x**4 - x**5 - 4/3*x + 2*x**2 + 19/9*x**3. Find z such that q(z) = 0.
-2, -1, 1/4, 1
Let f = 5712 - 74226/13. Find v, given that -f*v**2 + 8/13*v**3 - 8/13*v + 0 = 0.
-1/4, 0, 4
Let g = -119 - -367/3. Let d(a) be the first derivative of 8/5*a**5 - g*a**3 + 5 - 3*a**2 + 3/2*a**4 + 2*a. Factor d(b).
2*(b - 1)*(b + 1)**2*(4*b - 1)
Let n = 3/80 + 551/240. Factor -n*p**4 - p - 13/3*p**2 + 0 - 17/3*p**3.
-p*(p + 1)**2*(7*p + 3)/3
Let i(s) = -s**2 + 8*s + 12. Let f be i(9). Factor -18*a**4 - 10*a**2 - 34*a**f - a**3 + 13*a**4 - 20*a**4.
-5*a**2*(a + 1)*(5*a + 2)
Let h(z) = -5*z**2 - 24*z + 86. Let m(s) = -2*s**2 - 12*s + 42. Let d(u) = 3*h(u) - 7*m(u). Let d(a) = 0. Calculate a.
6
Let p = -1/3606 - -7217/18030. Factor -4/5*q + 2/5*q**2 + 0 + p*q**3.
2*q*(q - 1)*(q + 2)/5
Solve 20*p + 114*p + 42*p**2 + 36*p**2 - 276 + 61*p + 3*p**3 = 0 for p.
-23, -4, 1
Let p(q) be the third derivative of q**5/105 + q**4/21 + 5*q**2 - 2. Factor p(r).
4*r*(r + 2)/7
Suppose 501*s**3 + 38640*s**2 - 556*s + 2*s**4 + 341 + 55*s**3 - 38983 = 0. What is s?
-139, -1, 1
Suppose 5*d = -k + 30, -4*k - 5*d = -78 + 48. Find u such that 0 + k*u**3 + 1/4*u**2 - 1/4*u**4 + 0*u = 0.
-1, 0, 1
Determine u, given that -3/8*u**4 + 21/4*u**3 - 9/2*u**2 + 39/8 - 21/4*u = 0.
-1, 1, 13
Let n = -37 - -41. Let x be (-1)/(-5)*n/10*5. Suppose -x*g + 0 + 2/5*g**2 = 0. What is g?
0, 1
Let w be (178/(-1602))/(2/(-3)). Find y such that -w*y - 1/12*y**2 - 1/12 = 0.
-1
Let j be ((-8)/21)/((-58)/203). Suppose j*u**2 + 0 - 4/3*u = 0. Calculate u.
0, 1
Let x(c) be the first derivative of -15*c**6/13 + 456*c**5/65 - 4*c**4 - 704*c**3/39 - 16*c**2/13 + 128*c/13 - 579. Solve x(m) = 0 for m.
-2/3, 2/5, 2, 4
Suppose -11*i - 19 = 25. Let n(x) = -4*x**3 + 11*x**2 - 15*x + 13. Let s(l) = 4*l**3 - 12*l**2 + 16*l - 12. Let q(k) = i*n(k) - 5*s(k). Solve q(h) = 0 for h.
1, 2
Let n(j) = 2*j**2 - 23*j - 12. Let p be n(12). Let b(w) be the third derivative of -w**2 - 1/144*w**4 + p + 0*w - 1/18*w**3 + 1/360*w**5. Factor b(y).
(y - 2)*(y + 1)/6
Find k such that -81/7 - 3/7*k**2 - 36/7*k = 0.
-9, -3
Let y be (-10 + -2)/(-12) + -1. Factor -1/5*x**3 + y - 3/5*x + 4/5*x**2.
-x*(x - 3)*(x - 1)/5
Let n(s) = -3*s**3 + 65*s**2 - 177*s - 245. Let p(d) = 65*d**3 - 1430*d**2 + 3895*d + 5390. Let a(j) = 45*n(j) + 2*p(j). Find c, given that a(c) = 0.
-1, 7
Let l(x) be the first derivative of -9/14*x**6 - x**3 + 0*x - 4 + 3/5*x**5 + 33/28*x**4 - 3/7*x**2. Find q such that l(q) = 0.
-1, -2/9, 0, 1
Let s(g) be the first derivative of -g**5/100 - g**4/40 + g**3/30 + g - 25. Let u(v) be the first derivative of s(v). Factor u(t).
-t*(t + 2)*(2*t - 1)/10
Suppose -i + 7*i = 144. Factor 4*y**4 + i*y**2 - 3*y**2 - 16*y**3 - 7*y**2 - 2*y**2.
4*y**2*(y - 3)*(y - 1)
Let y(s) be the t