 - 5*p**2 - 8*p**2 + 18*p**2 = 0.
-2, 1
Let l be 93/(-217) + (-13)/(-14). Factor l*b - 1 + 1/2*b**2.
(b - 1)*(b + 2)/2
Let 6/7 + 2/7*y**3 - 6/7*y**2 - 2/7*y = 0. What is y?
-1, 1, 3
Determine l, given that -17*l**2 + 32*l**2 - l**3 + 117*l + 180 - 65 + 74 = 0.
-3, 21
Let u(k) be the second derivative of -2*k + 1/9*k**2 - 5/54*k**3 + 1/60*k**5 - 1/27*k**4 + 0. Factor u(j).
(j - 2)*(j + 1)*(3*j - 1)/9
Let d(n) = 2*n**2 - 16*n + 2. Let c be d(8). Factor -5*q - 2*q - q + 0*q + 28*q**c.
4*q*(7*q - 2)
Let q = 133 - 129. Let b be 3/q + -1 + (-28)/(-48). Find j such that -2/3 - b*j + 2/3*j**2 + 1/3*j**3 = 0.
-2, -1, 1
Let b(w) = -w**3 - 2*w**3 + 4 + 5 + 4*w**3 - 3*w**2 - 6*w. Let m be b(4). Let a(v) = -v**2 - v - 1. Let t(i) = -i. Let q(n) = m*a(n) + t(n). Solve q(j) = 0.
-1
Let v(m) be the third derivative of 28*m**2 + 1/480*m**5 + 0*m + 1/96*m**4 + 1/48*m**3 + 0. Find r such that v(r) = 0.
-1
Let b be (0 - 106)*(-15)/210 - 5. Determine a, given that 12/7*a**3 + 2/7 - 12/7*a - b*a**4 + 16/7*a**2 = 0.
-1, 1/3, 1
Let i(v) be the first derivative of -124/3*v**3 + 9 - 32*v**2 - 11*v**4 + 16*v. Factor i(f).
-4*(f + 1)*(f + 2)*(11*f - 2)
Let l = 14061/11 - 1277. Suppose -12*z + 124 - 40 = 48. Suppose -14/11*f**4 + l*f**2 + 0 + 4/11*f**z - 4/11*f = 0. What is f?
-1, 0, 2/7, 1
Let y(q) = -7*q**4 - 41*q**3 - 27*q**2 + 29*q + 28. Let g(j) = -8*j**4 - 42*j**3 - 26*j**2 + 28*j + 27. Let m(n) = 6*g(n) - 7*y(n). Solve m(v) = 0 for v.
-34, -1, 1
Let w = 5123/4 - 1280. Suppose -3/2*s + 9/4*s**3 + 0 - 3/4*s**4 + w*s**2 - 3/4*s**5 = 0. What is s?
-2, -1, 0, 1
Suppose -1998*g + 3972*g = 1996*g - 66. Suppose -1/8*o**g + 0 + 3/8*o**4 + 1/2*o**5 + 0*o**2 + 0*o = 0. Calculate o.
-1, 0, 1/4
Let n = 20 - 57. Let o = 40 + n. Determine c so that -9*c**2 + o + 3 + 6*c**2 + 3 - 6*c = 0.
-3, 1
Let i(k) be the third derivative of k**7/5544 + 7*k**6/7920 + k**5/660 - k**4/3 + 8*k**2. Let v(n) be the second derivative of i(n). Factor v(x).
(x + 1)*(5*x + 2)/11
Suppose -4*q + 2*d = -0 - 12, -3*q - 5*d + 22 = 0. Let 5*c**2 - 5*c**q + 36*c**3 + 2*c**5 + 3*c**5 - 41*c**3 = 0. What is c?
-1, 0, 1
Let b(s) be the first derivative of s**7/70 - s**6/40 - 3*s**5/20 + s**4/8 + s**3 - s**2/2 - 8. Let d(o) be the second derivative of b(o). Solve d(r) = 0.
-1, 1, 2
Let m(h) = 2*h**2 - 113*h + 602. Let b(s) = 15*s**2 - 905*s + 4815. Let p(k) = 3*b(k) - 25*m(k). Determine z, given that p(z) = 0.
11
Let f(h) be the first derivative of -1029*h**6/4 + 1323*h**5 - 903*h**4/2 + 508*h**3/9 - 8*h**2/3 + 557. What is k in f(k) = 0?
0, 2/21, 4
Let l(k) = k**3 - k + 1. Let g(y) = -9*y + 0 + y**3 - 5*y**2 - 2 + 1 + 3*y**3. Let i(h) = -g(h) - l(h). Solve i(o) = 0 for o.
-1, 0, 2
Let w(x) be the first derivative of 0*x + 1/200*x**6 + 0*x**3 - 1/40*x**4 + 0*x**5 - 3/2*x**2 + 3. Let b(u) be the second derivative of w(u). Factor b(t).
3*t*(t - 1)*(t + 1)/5
Let n = -1055 + 4221/4. Factor 0 - w**2 - n*w**4 + w**3 + 0*w.
-w**2*(w - 2)**2/4
Let m(r) be the third derivative of -3/20*r**6 - 1/8*r**4 + 0*r + 0*r**3 + 0 - 1/5*r**5 + 13*r**2 - 1/112*r**8 - 2/35*r**7. Let m(p) = 0. Calculate p.
-1, 0
Let a(c) be the third derivative of 0 - 1/80*c**5 - 1/160*c**6 + 0*c**3 + 9*c**2 + 0*c + 1/16*c**4. Solve a(u) = 0 for u.
-2, 0, 1
Let k = 92 + -8. Let n be (-24)/k - (-73)/35 - 1. Solve 12/5*s - n*s**4 + 8/5 - 4/5*s**2 - 12/5*s**3 = 0 for s.
-2, -1, 1
Factor -172*t - 36 + 319*t - 4*t**4 + 32*t**3 - 179*t + 40*t**2.
-4*(t - 9)*(t - 1)*(t + 1)**2
Let r(v) be the second derivative of -v**8/840 - v**7/210 - 4*v**3/3 - 6*v. Let l(s) be the second derivative of r(s). Factor l(w).
-2*w**3*(w + 2)
Let l(u) be the second derivative of -u**4/120 - u**3/10 + 128*u. Factor l(s).
-s*(s + 6)/10
Let u(p) be the second derivative of -8*p**7/63 - 14*p**6/15 - 17*p**5/15 + 17*p**4/9 + 14*p**3/3 + 8*p**2/3 - 238*p. Solve u(y) = 0.
-4, -1, -1/4, 1
Let p(l) be the third derivative of 0 + 0*l + 10*l**2 - 1/90*l**5 + 1/9*l**4 + 5/9*l**3. Find s, given that p(s) = 0.
-1, 5
Let g(p) = -5*p. Let u be g(-2). Suppose -5*o - 9 = -94*i + 92*i, 2*i - 5 = o. Let -16*y + 66*y - i + 70*y - u - 153*y**2 = 0. Calculate y.
2/17, 2/3
Let r = -183 + 188. Suppose r*g - 5*a = -1 - 4, -2*a + 22 = 3*g. Factor -6/5*z**2 - 2/5*z**g + 2/5*z + 6/5*z**3 + 0.
-2*z*(z - 1)**3/5
Let s be 500/715 - 80/520. Suppose 4/11 + 28/11*p**4 + 2*p + s*p**5 + 52/11*p**3 + 48/11*p**2 = 0. Calculate p.
-1, -2/3
Let m(d) be the second derivative of d**7/336 + 77*d**6/240 - 159*d**5/80 + 241*d**4/48 - 323*d**3/48 + 81*d**2/16 + 19*d + 4. Suppose m(n) = 0. Calculate n.
-81, 1
Let h be 1 - 5/((-5)/2). Suppose h*i - 6 = -0*i. Suppose -i + 0*x**2 - 4*x - x**2 + 2*x - x = 0. Calculate x.
-2, -1
Suppose u = 10 - 14. Let d(m) = m**2 - 5*m - 4. Let s(t) = t**2 - 4*t - 3. Let g(z) = u*s(z) + 3*d(z). Solve g(l) = 0.
0, 1
Suppose -6*a - 147 = -477. Find y such that -50*y - 648*y**4 - 142*y**2 - 92*y**2 - 270*y**5 - 4 - 576*y**3 - a*y**2 + 45*y**2 = 0.
-1, -2/5, -1/3
Let i(q) be the first derivative of 12 - 1/2*q - 2/5*q**5 + 1/8*q**6 + 0*q**4 + 5/6*q**3 - 3/8*q**2. Find m, given that i(m) = 0.
-1, -1/3, 1, 2
Let n(k) = 22*k**4 + 48*k**3 + 142*k**2 + 132*k + 28. Let j(u) = 9*u**4 + 19*u**3 + 57*u**2 + 53*u + 11. Let v(c) = 12*j(c) - 5*n(c). Find h such that v(h) = 0.
-2, -1
Let r(z) be the second derivative of -z**3 + 0*z**2 + 0 - 7/4*z**4 + 26*z - 9/20*z**5. Factor r(n).
-3*n*(n + 2)*(3*n + 1)
Let f(v) be the second derivative of -v**7/840 + v**6/120 + v**5/5 + 3*v**4/2 + 30*v. Let z(x) be the third derivative of f(x). Factor z(s).
-3*(s - 4)*(s + 2)
Let g be (-60)/(-16) + 2891/(-980). What is z in 2/5 + 2/5*z**2 - g*z = 0?
1
Let w(u) be the third derivative of 0*u**4 - 1/20*u**5 + 0*u**3 + 27*u**2 + 0 - 1/70*u**7 + 0*u - 1/20*u**6. Factor w(n).
-3*n**2*(n + 1)**2
Suppose -3*a - 113 = y, 2*y + 251 = 2*a - 3*a. Let g be (-2)/15*(y + -12). What is w in g*w + 54*w**4 + 8/3 + 26/3*w**2 - 84*w**3 = 0?
-2/9, 1
What is r in 20*r**4 + 4*r**5 + 1420*r**3 + 58*r + 88*r**2 - 1556*r**3 + 108*r - 108 - 34*r = 0?
-9, -1, 1, 3
Suppose -k + 15 = 5*r, -2*k - 5*r = -9 - 1. Let m = -2 - k. Factor -9*p**2 - 7*p + m + 2*p - p.
-3*(p + 1)*(3*p - 1)
Let h(s) = -6*s - 12. Let g be 1/(((-21)/9)/7). Let f be h(g). Factor -5*o**2 + 2*o - 5*o + 2*o + f*o**2.
o*(o - 1)
Let o = -145/8 + 149/8. Let 11/8*w**3 - 5/4*w**2 - o*w**4 + 3/8*w + 0 = 0. What is w?
0, 3/4, 1
Let x(r) be the first derivative of 2*r**3/21 - 4*r**2/7 + 8*r/7 - 40. Suppose x(s) = 0. What is s?
2
Factor 2/7*d**3 + 2*d**2 + 0 - 16/7*d.
2*d*(d - 1)*(d + 8)/7
Suppose -3*s - 40 = v, 5*s - 3*v + 59 = -3. Let j be (1*4)/(15 + s) - 0. Find c, given that -2/5*c**j + 6/5*c - 4/5 = 0.
1, 2
Suppose -8697 = 19*x - 8697. Factor -3/8 + x*p + 3/8*p**2.
3*(p - 1)*(p + 1)/8
Suppose 73 + 306 = 5*g - 3*f, 2*f - 290 = -4*g. Factor -76*x**4 - 4*x**3 + g*x**4 + x**2 - 3*x**2 + 0*x**2.
-2*x**2*(x + 1)**2
Let k be (-2)/(0 - -2)*0. Suppose 0 = 4*m - k*m - 8. Let -9*f**m + 5*f + 7*f + f**2 + 4*f**2 = 0. What is f?
0, 3
What is c in 8/7*c**5 - 46/7*c**4 + 128/7*c + 24/7 - 36/7*c**3 + 122/7*c**2 = 0?
-1, -1/4, 2, 6
Let k(b) = -2*b + 26. Let i be k(11). Find x such that -x**2 + 42*x + i - 42*x = 0.
-2, 2
Let s(p) = 4*p + 13. Let r be s(-10). Let w be (r/45 + 0)/(-3*1). Determine g, given that 0 + 0*g + w*g**3 + 1/5*g**2 = 0.
-1, 0
Suppose 7*f - 46 + 18 = 0. Let u(w) be the first derivative of 0*w + 2*w**5 + 4/3*w**6 - 1/3*w**3 + 0*w**2 + 1/4*w**f + 6. Find h, given that u(h) = 0.
-1, -1/2, 0, 1/4
Let v(h) be the second derivative of -1/66*h**4 + 1/33*h**3 + 0 + 0*h**2 + 25*h. Factor v(a).
-2*a*(a - 1)/11
Factor 225/2*a**2 + 15*a**3 + 0*a + 0 + 1/2*a**4.
a**2*(a + 15)**2/2
Let i be (-5)/(-4) - 53/(-212). Factor 9 - 21/2*u + i*u**2.
3*(u - 6)*(u - 1)/2
Let c(f) = f**3 + 20*f**2 - 19*f + 47. Let w be c(-21). Suppose -1 + 23*q**3 - 24*q**3 - q**2 + w + 4*q = 0. Calculate q.
-2, -1, 2
Suppose -3*c = 4*s - 9, -3*s = -s + 2*c - 4. Solve 6/11*k**s + 6/11*k**4 + 0 + 0*k + 2/11*k**2 + 2/11*k**5 = 0 for k.
-1, 0
Let u(w) be the second derivative of w**5 + 2*w**4/3 - 10*w**3/3 - 4*w**2 - 15*w. Find z such that u(z) = 0.
-1, -2/5, 1
Let u = 236 + -233. Let x(c) be the first derivative of 2 + 1/3*c**u + 2*c + 3/2*c**2. Determine g, given that x(g) = 0.
-2, -1
Determine m, given that 1/3*m**2 + 31/3 + 