 1
Let b(j) = -135*j**2 + 270*j + 55. Let f(o) = 5*o**2 - 10*o - 2. Let t(h) = -2*b(h) - 55*f(h). Factor t(d).
-5*d*(d - 2)
Let j(r) be the second derivative of -1/6*r**4 - r**2 + 0 + 3*r - 2/3*r**3. Factor j(g).
-2*(g + 1)**2
Let l(i) = -i. Let t(h) = -h + 4. Let d(o) = -2*o - 9. Let p be d(-6). Let g be t(p). Let f(q) = q**2 - 6*q + 1. Let m(s) = g*f(s) - 4*l(s). Solve m(v) = 0.
1
Let d(u) be the second derivative of -4*u + 0*u**4 + 0 + 0*u**2 + 1/3*u**3 + 1/1440*u**6 + 0*u**5. Let g(w) be the second derivative of d(w). Factor g(p).
p**2/4
Suppose 32*f = 46*f. Find x such that 0*x + 4/5*x**2 - 2/5 + f*x**3 - 2/5*x**4 = 0.
-1, 1
Find v, given that -2137 - 21*v**4 - 39*v + 2131 - 42*v**3 - 81*v**2 - 27*v**3 = 0.
-1, -2/7
Let j = 259 - 1033/4. Let -j*r**2 + 0 - 1/4*r**3 - 1/2*r = 0. What is r?
-2, -1, 0
Determine h, given that -18 + 3*h**5 + 21 + 3*h - 2*h**2 - 4*h**2 + 3*h**4 - 6*h**3 = 0.
-1, 1
Suppose -1 = -3*x + 8. Let r be 0/((-3)/(x - 6)). Factor 0 + r*q - 1/3*q**2 - 1/3*q**3.
-q**2*(q + 1)/3
Let i be (2 - 1)*(5 - 3). Let k(x) be the first derivative of -1/2*x**i + 1/4*x**4 - 1/2*x + 1/10*x**5 + 0*x**3 + 1. Factor k(z).
(z - 1)*(z + 1)**3/2
Let v = 1/294 - -583/1470. Factor -v*n**2 - 2/5*n + 0.
-2*n*(n + 1)/5
Let l = -162018/5 + 32303. Let b = l - -101. Solve 0 + b*o**4 + 0*o**2 + 0*o + 2/5*o**3 = 0 for o.
-1, 0
Let q be 32/14 - (-2)/(-7). Suppose 3*b - 11 + q = 0. Find g, given that -b*g**4 - g**4 + 5*g**4 = 0.
0
Let h(t) be the second derivative of -1/2*t**3 + 0 - 1/4*t**4 + 0*t**2 + t. Find z, given that h(z) = 0.
-1, 0
Let d(n) = 4*n**2 - 16*n + 28*n - 2 - n**3 - 14*n. Let k be d(2). Solve -1/3*h**k + 0 - 1/3*h**3 + 0*h = 0.
-1, 0
Let h be (-5)/(-10) - (-61)/(-2). Let n be 20/h - (-52)/42. Factor -2/7*j**3 + 4/7 + 2/7*j - n*j**2.
-2*(j - 1)*(j + 1)*(j + 2)/7
Let f = 4 - 0. Suppose 5*y = -3*g + 4*g - 22, 0 = -f*y - 16. Factor -v**g + 8*v + 2 + 6 + 3*v**2.
2*(v + 2)**2
Let g be (-1)/(2/2) + 4. Let s(v) = -4*v**2 - 38*v + 86. Let r(a) = -a**2 - 13*a + 29. Let q(b) = g*s(b) - 10*r(b). Suppose q(j) = 0. What is j?
4
Let s(i) be the first derivative of 2*i**5/15 - i**4/6 - 2*i**3/9 + i**2/3 - 6. Factor s(l).
2*l*(l - 1)**2*(l + 1)/3
Factor 0 - 4/3*p**3 - 4/3*p**2 + 0*p.
-4*p**2*(p + 1)/3
Factor 13*y**3 + 3*y**3 + 72*y**3 + 14 + 4*y**5 + 2 + 32*y**4 + 68*y + 112*y**2.
4*(y + 1)**4*(y + 4)
Solve 3*j**2 - 6*j + 3*j + j = 0 for j.
0, 2/3
Let v(p) = -p**5 - 13*p**4 + 10*p**3 + 10*p**2 - 13*p + 7. Let s(z) = -12*z**4 + 9*z**3 + 9*z**2 - 12*z + 6. Let h(u) = 4*s(u) - 3*v(u). What is w in h(w) = 0?
-1, 1
Let l(o) be the second derivative of o**5/130 + o**4/39 + o**3/39 - o. Factor l(f).
2*f*(f + 1)**2/13
Suppose -7*q = -8*q. Factor q*h**2 + 0*h - 4/7*h**3 + 2/7*h**4 + 0.
2*h**3*(h - 2)/7
Let x be 6/1*(-5)/((-30)/4). Let z(r) be the second derivative of 0 - 1/9*r**3 + 1/18*r**x - r + 0*r**2. Factor z(u).
2*u*(u - 1)/3
Find z such that 12*z + 96*z**2 + 246*z**3 + 34*z**4 + 50*z**4 - 33*z**3 = 0.
-2, -2/7, -1/4, 0
Let x(m) be the first derivative of -1/10*m**6 - 11/10*m**4 + 4/5*m**3 + 14/25*m**5 - 2/5*m - 1 + 1/10*m**2. Determine o so that x(o) = 0.
-1/3, 1, 2
Let j(u) = u**3 + 3*u**2 + 2*u + 2. Let d be j(-2). Let 4/5*i**d - 2/5 + 2/5*i = 0. What is i?
-1, 1/2
Let 283*g**3 - 281*g**3 - 2*g**4 + 3*g**4 + g**2 = 0. What is g?
-1, 0
Let g(v) be the second derivative of 2*v**7/21 + 2*v**6/15 - v**5/5 - v**4/3 + 43*v. Let g(i) = 0. What is i?
-1, 0, 1
Suppose 0 = g + 3*g - 16. Suppose -3*p = -33 + 33. Factor -2/9*d**g + 2/9*d**2 + 0*d + p + 0*d**3.
-2*d**2*(d - 1)*(d + 1)/9
Let x(k) = -k**5 + k**3 + 2*k. Let g(v) = v**4 + v**3 + v. Suppose 7 - 2 = 5*h. Let b(j) = h*x(j) - 2*g(j). Suppose b(m) = 0. Calculate m.
-1, 0
Suppose -2*j = 4, -660 = 5*g + 2*j + 3*j. Let h be (-32)/g - (-20)/130. Factor 6*b + 18/5 + 14/5*b**2 + h*b**3.
2*(b + 1)*(b + 3)**2/5
Let a = 17 + -14. Let v be (2/5)/((-6)/(-10)). What is l in 4/3*l**2 + 0 - 2/3*l - v*l**a = 0?
0, 1
Let t = 6784/3 + -2291. Let b = t - -30. Factor -2/3*f**3 + b*f**4 + 0*f + f**5 + 0 + 0*f**2.
f**3*(f + 1)*(3*f - 2)/3
Let c(k) be the second derivative of -k**5/200 - k**4/60 + 29*k. What is f in c(f) = 0?
-2, 0
Let r(p) be the first derivative of -p**4/26 + 7*p**2/13 - 12*p/13 - 13. Factor r(i).
-2*(i - 2)*(i - 1)*(i + 3)/13
Let o(i) be the second derivative of -i**5/60 + 11*i**4/36 - 21*i + 2. Suppose o(k) = 0. Calculate k.
0, 11
Suppose 12 = -3*p + 6*p. Let x(w) be the second derivative of -25/42*w**p - 1/7*w**2 + 0 - 3*w + 10/21*w**3. Suppose x(h) = 0. What is h?
1/5
Let b be 1*8/6*(-3)/(-6). Factor -4/3 + 2/3*q**2 + b*q.
2*(q - 1)*(q + 2)/3
Let z(u) be the third derivative of 0*u**3 + 1/135*u**5 + 0*u - 3*u**2 + 0 - 1/1512*u**8 + 0*u**6 - 2/945*u**7 + 1/108*u**4. Factor z(b).
-2*b*(b - 1)*(b + 1)**3/9
Suppose 4 = c - 0*c. Suppose c*b - 4*w + 8*w = 0, -4*b - 3*w = -5. Determine t so that 22*t**5 - t**b + 26*t**2 + 49*t**3 - 9*t**2 + 55*t**4 + 2*t = 0.
-1, -1/3, -2/7, 0
Let o(j) be the first derivative of -j**5 - 5*j**4/4 + 10*j**3 + 10*j**2 - 40*j + 39. Factor o(a).
-5*(a - 2)*(a - 1)*(a + 2)**2
Let u(f) be the third derivative of -f**5/90 - 4*f**4/9 - 64*f**3/9 - 19*f**2. Factor u(g).
-2*(g + 8)**2/3
Let d(j) be the second derivative of 0*j**5 + 0*j**2 + 1/2*j**3 + 0 - 1/1620*j**6 + 0*j**4 + j. Let p(m) be the second derivative of d(m). Factor p(v).
-2*v**2/9
Let y(s) be the third derivative of -s**5/60 + s**4/8 - s**3/3 - 3*s**2. Factor y(b).
-(b - 2)*(b - 1)
Let w(s) be the third derivative of s**8/756 + 8*s**7/945 + s**6/54 + 2*s**5/135 - 11*s**2. Factor w(q).
4*q**2*(q + 1)**2*(q + 2)/9
Let p = 329 + -1329/5. Let z = p + -63. Solve 0*i + 0 - z*i**2 = 0 for i.
0
What is t in 0*t**2 - 3/7*t**3 + 0*t + 3/7*t**4 + 0 = 0?
0, 1
Factor 13*v**3 - 11*v**3 - 5*v**2 + 13*v**3 - 10*v**4.
-5*v**2*(v - 1)*(2*v - 1)
Suppose -8*f = -6*f - 6. Factor 8*r**2 + 2*r**3 + 2*r**3 + 24*r - 2*r**f - 16*r.
2*r*(r + 2)**2
Suppose -8 = 3*r - 20. Suppose 0*v**3 - v**3 + 3*v**4 - 4*v**r = 0. Calculate v.
-1, 0
Let j(t) be the second derivative of 1/2*t**6 + 0*t**2 - 1/7*t**7 - 2*t + 0 + 0*t**3 - 3/5*t**5 + 1/4*t**4. Let j(q) = 0. Calculate q.
0, 1/2, 1
Let l(d) = d**2 + 7*d + 6. Let z be l(-6). Suppose -3*i + 2 = -z*i - a, -10 = 5*a. Factor i*w - 1/3*w**4 + 0 + 0*w**2 + 1/3*w**3.
-w**3*(w - 1)/3
Let j(s) be the first derivative of -2*s**5/25 - 7*s**4/10 - 12*s**3/5 - 4*s**2 - 16*s/5 + 10. Factor j(g).
-2*(g + 1)*(g + 2)**3/5
Solve r - r - 97*r**2 + 94*r**2 - 3*r = 0 for r.
-1, 0
Suppose b - 4*b = -12. Let i be 4/b - (1 - 4). Let 2/7*m**2 - 2/7*m**i - 2/7*m + 0 + 2/7*m**3 = 0. What is m?
-1, 0, 1
Let j(b) be the second derivative of b**8/480 - 4*b**7/315 + b**6/90 - b**4/4 - 3*b. Let w(n) be the third derivative of j(n). Determine k so that w(k) = 0.
0, 2/7, 2
Let l(a) be the first derivative of -2*a**6/3 - 4*a**5/5 + a**4 + 4*a**3/3 - 13. Factor l(f).
-4*f**2*(f - 1)*(f + 1)**2
Let j(l) be the third derivative of -7/300*l**6 + 0 + 0*l**3 + 1/75*l**5 + 0*l**4 - 3*l**2 + 0*l - 4/525*l**7. Factor j(v).
-2*v**2*(v + 2)*(4*v - 1)/5
Factor -48*i**2 - 3*i**3 + 144*i + 0*i**3 + 7*i**3.
4*i*(i - 6)**2
Let z(g) be the second derivative of 0*g**2 + 1/6*g**3 + 0 - 1/6*g**4 + 1/20*g**5 - 4*g. Let z(n) = 0. What is n?
0, 1
Let 2/5*v**2 - 2/5 - 2/5*v**3 + 2/5*v = 0. Calculate v.
-1, 1
Suppose -2*u = 2 - 10. Let w be -1*((2 - 2) + -3). Determine b, given that u*b**2 - 5*b**2 - b**w + 10*b**4 - 8*b**4 = 0.
-1/2, 0, 1
Let r be 1 - -50*4/(-216). Let n(c) be the second derivative of -c + 1/90*c**5 - 1/54*c**4 + 0 + 0*c**2 - r*c**3. Factor n(w).
2*w*(w - 2)*(w + 1)/9
Factor -3*l**3 - 3/2*l**2 + 3/4*l**5 + 9/4*l + 3/2 + 0*l**4.
3*(l - 2)*(l - 1)*(l + 1)**3/4
Suppose -c - 5*o + 29 = 0, -3*c + 2*o - 6 = -2*c. Let k(z) be the first derivative of 20/21*z**3 - 3 + 3/14*z**c + 4/7*z + 9/7*z**2. Factor k(b).
2*(b + 1)*(b + 2)*(3*b + 1)/7
Let c(k) = -k**3 + 5*k**2 + 5*k + 14. Let y be c(6). Suppose y*a = 3*a. Determine p, given that -2/9*p**3 + 0*p + a + 0*p**2 = 0.
0
Let n(i) be the second derivative of -i**9/16632 - i**8/2310 - i**7/1155 + 7*i**3/6 - 3*i. Let h(b) be the second derivative of n(b). Factor h(o).
-2*o**3*(o + 2)**2/11
Let y be (-15)/(-9)*1*3. Let l(d) be the second derivative of 0*d**2 + 1/42*d**7 + 1/6*d**3 - 2*d - 2/15*d**6 + 3/10*d**y + 