 Suppose -x*d = -d - 27. Suppose d*j**4 + 9*j**2 - 5*j**4 - 25*j**2 = 0. What is j?
-2, 0, 2
Suppose 0*x - 6 = -3*x. Suppose x*v**2 + v**2 - 53 + 9*v + 59 = 0. What is v?
-2, -1
Let j be -1*(0 + -1 + 2). Let a(l) = l. Let k(r) = -3*r**4 + 9*r**3 - 9*r**2 + 6*r. Let t(c) = j*k(c) + 3*a(c). Factor t(p).
3*p*(p - 1)**3
Suppose -6*r + 17 + 7 = 6. Factor 5/6*w + 2/3*w**r - 3/2*w**2 + 0.
w*(w - 1)*(4*w - 5)/6
Let g(d) be the second derivative of 0*d**2 - 1/90*d**4 - 1/150*d**5 + 0 + 1/225*d**6 + 0*d**3 - 2*d + 1/315*d**7. Factor g(x).
2*x**2*(x - 1)*(x + 1)**2/15
Let f(h) be the second derivative of 2*h**7/21 - 3*h**5/5 + 2*h**4/3 + 21*h + 1. Suppose f(d) = 0. Calculate d.
-2, 0, 1
Let p(z) be the third derivative of z**6/280 + z**5/10 - 174*z**2. Factor p(b).
3*b**2*(b + 14)/7
Let p(g) be the first derivative of -10*g**3/9 - 8*g**2/3 - 48. Factor p(s).
-2*s*(5*s + 8)/3
Determine c, given that -14113 + 3*c**2 + 9*c + 14113 = 0.
-3, 0
Let w = 1/4086 - -673/32688. Let c(d) be the third derivative of -w*d**3 - 9*d**2 + 0 + 1/480*d**5 - 1/192*d**4 + 0*d + 1/960*d**6. Factor c(y).
(y - 1)*(y + 1)**2/8
Let y(k) = -6*k**2 - 7*k - 1. Let w(q) = -5*q**2 - 7*q. Let z(v) = -7*w(v) + 6*y(v). Factor z(t).
-(t - 6)*(t - 1)
Let g(t) = 70*t**2 - 365*t + 685. Let i = -80 - -38. Let n = i - -38. Let p(q) = 5*q**2 - 26*q + 49. Let h(k) = n*g(k) + 55*p(k). Factor h(r).
-5*(r - 3)**2
Determine g, given that 0 - 3/4*g - 1/4*g**3 - g**2 = 0.
-3, -1, 0
Let x(w) be the first derivative of -2/35*w**5 + 1/7*w**2 - 2/7*w + 4/21*w**3 - 5 - 1/7*w**4 + 1/21*w**6. What is r in x(r) = 0?
-1, 1
Suppose 4*s - 10 = -3*b, -9*b - 3*s = -14*b + 7. Determine j, given that 4/21 - 2/7*j + 2/21*j**b = 0.
1, 2
Let z(s) = 2*s**5 + 2*s**4 + s**2 + 4*s. Let h(i) = -5*i**5 - 4*i**4 - 3*i**2 - 9*i. Let q(u) = -6*h(u) - 14*z(u). Find f, given that q(f) = 0.
-1, 0, 1
Let j = -672 - -677. Let b(q) be the second derivative of -3/2*q**4 - 3/2*q**2 + 2*q**3 + 0 + 3/5*q**j - 1/10*q**6 - 3*q. Find r such that b(r) = 0.
1
Let v = -92 + 340/3. Suppose 3*f - 14 = -j, -12 = 4*j - 2*f - 3*f. Factor v - 32/3*t + 4/3*t**j.
4*(t - 4)**2/3
Determine u so that 1/4*u**3 + 20*u - 19 - 23/4*u**2 = 0.
2, 19
Let s(y) be the third derivative of 13*y**2 - 35/24*y**4 + 0*y + 0*y**3 + 1/24*y**6 + 0 - 1/2*y**5. Find i, given that s(i) = 0.
-1, 0, 7
Let z(y) be the first derivative of -y**3/2 - 3*y**2 - 9*y/2 - 637. Suppose z(n) = 0. Calculate n.
-3, -1
Suppose -b + 0*l + 3 = -4*l, 2*l + 12 = 2*b. Suppose 3*q + 5*g + b = -4, q - 4*g - 19 = 0. Find m, given that -5/3*m**2 - 1/3*m**q - 8/3*m - 4/3 = 0.
-2, -1
Let p(v) be the first derivative of 10*v**3/3 - 32*v**2 + 24*v + 79. Factor p(n).
2*(n - 6)*(5*n - 2)
Let u(n) = -n**2 - 18*n + 39. Let o be u(-20). Let p be 6 - -1*(-2 + o). Suppose 0*v + 0*v**4 + 0*v**2 - 2/7*v**5 + 0 + 0*v**p = 0. What is v?
0
Determine o, given that 35/2*o - 245/4 - 5/4*o**2 = 0.
7
Let i(h) be the third derivative of -1/24*h**4 + 0 + 0*h + 1/240*h**6 - 1/120*h**5 + 6*h**2 + 0*h**3. Factor i(f).
f*(f - 2)*(f + 1)/2
Let a = 12/120373 - -135524770/152753337. Let y = 2/1269 + a. Factor 0 + 18*r**3 - 8*r**2 + y*r.
2*r*(9*r - 2)**2/9
Let o(r) be the second derivative of r**6/75 + 3*r**5/10 + 34*r**4/15 + 4*r**3 - 144*r**2/5 - 152*r. Factor o(n).
2*(n - 1)*(n + 4)*(n + 6)**2/5
Let i**3 - 7/3*i - 10/3 + 14/3*i**2 = 0. What is i?
-5, -2/3, 1
Suppose -5*u + 5 = -10. Factor -16*f**2 + f**3 - f**5 - 16*f**4 - 15*f**u + 10*f**4 - 2 - 9*f.
-(f + 1)**4*(f + 2)
Suppose -5*y + 664 = -4*x, 3*x = -2*y + 191 + 93. Let j be y/40 - (1 + 2) - 0. What is o in 0 + 1/5*o**2 - j*o = 0?
0, 2
Suppose 5*u = -20, p + 13 = -u - 3*u. Find g, given that -2*g + g**3 - g**5 - 4 + 8*g**2 - 4*g**4 + 3*g**p - g**5 = 0.
-2, -1, 1
Factor -2/5*w**2 - 1568/5 + 112/5*w.
-2*(w - 28)**2/5
Suppose 15*q - 38*q + 0*q = -92. Find k, given that -q*k + 1/2*k**2 + 8 = 0.
4
Let j = 15721 + -15719. Find z such that 1/7*z**j + 3/7*z - 4/7 = 0.
-4, 1
Let r(o) = o**3 + 15*o**2 + 19*o + 10. Let y be r(-14). Let b be y/75*(1 - (-8)/(-3)). Factor 0 - 16*s**3 + 8*s**2 + 40/3*s**4 - 4*s**5 - b*s.
-4*s*(s - 1)**3*(3*s - 1)/3
Factor 318/7*s + 8427/7 + 3/7*s**2.
3*(s + 53)**2/7
Let r(n) = n + 33. Let v be r(-30). Let a = -80 + 82. Factor 2/3*q**a - 4/3*q**v + 4/3*q - 2/3*q**4 + 0.
-2*q*(q - 1)*(q + 1)*(q + 2)/3
Let v(d) be the third derivative of d**8/10080 - d**7/280 + 2*d**5/15 - 25*d**2. Let q(r) be the third derivative of v(r). Factor q(m).
2*m*(m - 9)
Let 21*j - 12*j**4 - 6 + 18*j**2 - 89*j**3 - 104*j**3 + 172*j**3 = 0. What is j?
-2, -1, 1/4, 1
Factor 52/3*k**3 + 4/3 + 16/3*k**4 + 28/3*k + 20*k**2.
4*(k + 1)**3*(4*k + 1)/3
Let l(y) be the first derivative of y**5/10 + 7*y**4/8 + 17*y**3/6 + 17*y**2/4 + 3*y - 218. Find r such that l(r) = 0.
-3, -2, -1
Let v = -96 + 48. Let k = v + 50. Factor -k*h - 2/3*h**2 - 4/3.
-2*(h + 1)*(h + 2)/3
Suppose -195*k + 328 + 62 = 0. Factor 2/7*a**k + 0 - 8/7*a.
2*a*(a - 4)/7
Suppose 3*j - 5*u = 26, -4*j = -4*u + u - 20. Suppose -2*y - y + 6 = 0. Factor y*a - 4*a**5 + 8*a**3 - 5*a + j*a - 3*a.
-4*a*(a - 1)**2*(a + 1)**2
Let l(i) = -i**2 + 8*i + 3. Let a be l(8). Let x**2 - x**4 + 12*x**3 + x**a + 6*x**3 - x - 18*x**3 = 0. What is x?
-1, 0, 1
Let g be (-6)/5 - (-1938)/665. Let p be 240/28*2/6. Factor g*c**4 + 6/7*c + p*c**2 + 2/7*c**5 + 24/7*c**3 + 0.
2*c*(c + 1)**3*(c + 3)/7
Let y(j) = -3*j**5 - 3*j**4 + 8*j**3 + 8*j**2 - 5*j + 5. Let n(r) = r**3 + r**2 - r + 1. Let x(w) = 5*n(w) - y(w). Factor x(b).
3*b**2*(b - 1)*(b + 1)**2
Suppose -3*c + c + 4*o + 12 = 0, 5*c + 4*o - 16 = 0. Suppose 5*q + j = 60, 5*q - c*j = 32 + 53. Factor -q*g**2 - 38*g**2 + 144*g - 308*g**2 - 16 + 35*g**2.
-4*(9*g - 2)**2
Let j = -1787/36 - -218593/4284. Let h = -12/119 + j. Factor -6/7 + 3/7*g**3 + 0*g**2 - h*g.
3*(g - 2)*(g + 1)**2/7
Let n = 7/3 + -2. Let y(s) be the third derivative of 0*s - 3*s**2 + 3/8*s**4 - 1/5*s**5 - n*s**3 + 1/24*s**6 + 0. Factor y(m).
(m - 1)**2*(5*m - 2)
Suppose 0*j - 4*j - n = -21, -20 = -5*j + 5*n. Factor 2*c**4 + 4*c**j + 16*c**2 - 7*c**4 - 7*c**4.
4*c**2*(c - 2)**2*(c + 1)
Let j(d) be the first derivative of -d**6/16 + 27*d**5/40 + 9*d**4/16 - 95*d**3/4 + 225*d**2/16 + 3375*d/8 + 112. Solve j(x) = 0 for x.
-3, 5
Let m(w) be the second derivative of 1/78*w**4 - 1/13*w**2 - 14*w + 0 - 1/39*w**3 + 1/130*w**5. Factor m(x).
2*(x - 1)*(x + 1)**2/13
Suppose 0*v + 36 = 4*v. Suppose 15 = 3*h + v. Factor -2*x**2 - 3*x**h + 6*x**4 + 8*x + 3*x**5 - 7*x**2 + 4*x - 9*x**3.
3*x*(x - 1)**2*(x + 2)**2
Let g(r) = 2 - 4 + 7 + r. Let b be g(-3). Factor -3*x - 4*x + b*x**2 + 9*x - x**2.
x*(x + 2)
Let k be (-2)/(-2) - (2 + -10 + 89). Let z = -78 - k. Suppose 3/4 + 0*l**z + 3/2*l - 3/2*l**3 - 3/4*l**4 = 0. Calculate l.
-1, 1
Let j be (4 - (-24)/(-3)) + 6. Let b be 2/9 - 4/(-18). Factor b - 2/9*o + 2/9*o**3 - 4/9*o**j.
2*(o - 2)*(o - 1)*(o + 1)/9
Let v = 11553/2 + -5769. Factor 21/2*k + v*k**2 + 3/2*k**3 + 9/2.
3*(k + 1)**2*(k + 3)/2
Let a(h) = h**2 - 19*h + 3. Let y be a(18). Let z be (3/y)/(4/(-4)). Solve 0*t + 0 - z*t**2 = 0.
0
Let h = 363/5 - 72. Find r such that 0*r**3 + 3/5*r**4 + h - 6/5*r**2 + 0*r = 0.
-1, 1
Let g = -447/7 - -64. Let t be ((-36)/66)/(585/(-2145)). Let -4/7*v**t - g + 4/7*v = 0. Calculate v.
1/2
Let f(j) be the second derivative of -j**7/126 - j**6/45 + j**4/18 + j**3/18 + 175*j. Find c such that f(c) = 0.
-1, 0, 1
Determine v so that 8 - 31/2*v**2 + 4*v + 7/2*v**3 = 0.
-4/7, 1, 4
Let w(n) = 2*n**2 - 3*n + 18. Let p be w(-6). Factor -52*s**2 + p - 8*s + 55*s**2 + 44*s.
3*(s + 6)**2
Let b(h) be the second derivative of h**5/190 - 25*h**4/114 + 200*h**3/57 - 500*h**2/19 - 237*h. Find k, given that b(k) = 0.
5, 10
Suppose -3*o - 18 = 4*r, 4*o - 20 = -167*r + 169*r. Factor 1/3*i**o - 4/3 + i.
(i - 1)*(i + 4)/3
Suppose 2*q - 15 = -q, -2*q + 4 = 3*h. Let x be -2 - (h - (-1 + 5/4)). Find i such that -x*i - 1/4*i**2 + 1/2 = 0.
-2, 1
Suppose -9/2*r**3 - 24 + 69/2*r**2 + 15*r = 0. Calculate r.
-1, 2/3, 8
Let l be (6/(-4))/(-28 - -22). Let y(t) be the second derivative of 0 - 1/20*t**5 + 1/2*t**2 + l*t**4 + 2*t - 1/2*t**3. Factor y(r).
-(r - 1)**3
Factor 81/2 - 3/2*b**2 + 39*b.
-3*(b - 27)*(b + 1)/2
Let w(r) be the first derivative of -5*r**4/4 + 50*r**3/3 - 85*r**2/2 + 40*r + 64. Factor w(x).
-5*(x - 8)*(x - 1)**2
Let l(g) be the s