*5 + 1/24*x**6. Factor h(v).
5*v*(v - 4)**2
Factor 1/12*y**2 - 11/12*y - 1.
(y - 12)*(y + 1)/12
Let c(r) be the third derivative of 0*r + 0*r**5 + 2*r**2 + 0*r**3 + 0 - 1/240*r**6 + 1/12*r**4. Factor c(x).
-x*(x - 2)*(x + 2)/2
Let n be (-14)/(-21) + (-28)/(-21). Let x(d) be the first derivative of -1/4*d**4 + 1/2*d**n - 2/3*d**3 + 1/10*d**5 + 3/2*d - 9. Let x(m) = 0. Calculate m.
-1, 1, 3
Suppose 0 = 4*u, 0*r + 5*r - 25 = 3*u. Let z be (-20)/(-15)*r/20. Find v such that 2/3*v**2 - 1/3*v - 2/3*v**4 + z*v**5 + 0*v**3 + 0 = 0.
-1, 0, 1
Let i(z) be the second derivative of -1/8*z**4 - 7*z + 0 + 3/4*z**2 + 0*z**3. Let i(f) = 0. What is f?
-1, 1
Factor 14 + 8/3*m - 2/3*m**2.
-2*(m - 7)*(m + 3)/3
Factor -24/13*y - 12/13*y**3 - 8/13 - 2/13*y**4 - 2*y**2.
-2*(y + 1)**2*(y + 2)**2/13
Let f = 67 + -62. What is z in 9*z**3 + 3 + 93*z**2 - 30*z - 37*z**3 - 96*z**4 + 67*z**f - 38*z**3 + 29*z**5 = 0?
-1, 1/4, 1/2, 1
Let p(b) be the second derivative of -2*b**7/21 + 52*b**6/15 - 253*b**5/5 + 364*b**4 - 1176*b**3 - 153*b. Find w such that p(w) = 0.
0, 6, 7
Factor -278*l**3 + 137*l**3 + 137*l**3 - 96*l**2.
-4*l**2*(l + 24)
Let j = -3365/7 - -30341/63. Let 4/9*q**2 - 4/3 - j*q = 0. What is q?
-1, 3
Let h(p) be the first derivative of 1/5*p**3 + 0*p**2 + 1/20*p**4 + 0*p + 9. Let h(f) = 0. Calculate f.
-3, 0
Let a(q) = q - 6. Let v be a(6). Suppose v*g + 3*g = 6. Factor 9*i - 69*i + 36 - i**3 + 28*i**g - 3*i**3.
-4*(i - 3)**2*(i - 1)
Let z(u) = 7*u**5 + 21*u**4 + 26*u**3 + 12*u**2 - 5*u + 10. Let k(a) = -a**5 - a**4 + a - 2. Let g(x) = 5*k(x) + z(x). Let g(r) = 0. Calculate r.
-6, -1, 0
Let l be -5*(4 + -5 + -2). Suppose -17 = -i - l. Factor 7*n - 6*n**2 + 21*n + 12*n - 100 + 2*n**i.
-4*(n - 5)**2
Let x be (11 + (-1 - -5))/3. Let t(l) be the third derivative of -x*l**2 + 1/840*l**7 + 0 - 1/240*l**6 + 0*l**5 + 1/48*l**4 - 1/24*l**3 + 0*l. Factor t(s).
(s - 1)**3*(s + 1)/4
Let f be 9 - 255/60 - (-1)/4. Let x(k) be the second derivative of 1/24*k**4 - f*k - 1/4*k**2 + 0*k**3 + 0. Factor x(j).
(j - 1)*(j + 1)/2
Suppose -5*v = 5*k, -2*k = -3*v + v - 8. Suppose -2*a = 2*g - 6, 4*g + k*a - 4 = 2. What is h in 1/3*h**3 - 1/3*h**2 - 2/3*h + g = 0?
-1, 0, 2
Let f(s) be the second derivative of -5*s**4/4 + 5*s**3/6 + 51*s. Solve f(q) = 0.
0, 1/3
Let a = 1084/3 + -361. Let c(i) be the third derivative of -1/12*i**4 + 0 + 0*i + i**2 - a*i**3 - 1/120*i**5. Factor c(n).
-(n + 2)**2/2
Let l be -1 - (6/(-56))/(63/(-7882)). Let p = 107/6 + l. Let p*v**3 - 6/7*v - 15/7*v**4 + 0 - 3/7*v**2 = 0. Calculate v.
-2/5, 0, 1
Let p = 4 - -1. Suppose 5 = 4*g + p. Suppose 1/7*x**2 + g + 1/7*x = 0. What is x?
-1, 0
Let g(q) be the first derivative of q**4/4 + q**3/3 - 8*q**2 + 20*q + 219. Determine b, given that g(b) = 0.
-5, 2
Suppose 0 = 8*n - 57 + 9. Let v be (-8)/n + 4 + -2. Find t such that v - 1/3*t - 1/3*t**2 = 0.
-2, 1
Let j = 0 - 0. Let k be 1/3 + (-2086)/(-447). Let -5/3*n**4 + j + 2/3*n - 1/2*n**k + 2*n**2 - 1/2*n**3 = 0. Calculate n.
-2, -1/3, 0, 1
Let x be 4 - (6/21 + (-28)/49). What is w in 25/7*w**2 - x*w + 9/7 = 0?
3/5
Let x(b) be the third derivative of b**5/60 - b**4/12 - 5*b**3/2 + 20*b**2 - 1. Determine t, given that x(t) = 0.
-3, 5
Let o(i) be the second derivative of -i**7/105 - i**6/60 + 11*i**2/2 - 13*i. Let w(v) be the first derivative of o(v). Factor w(l).
-2*l**3*(l + 1)
Let l(a) be the second derivative of a**7/5 + 4*a**6/5 + 18*a**5/25 + 3*a - 26. Solve l(k) = 0 for k.
-2, -6/7, 0
Suppose -13 = -3*r - 1. Factor 10*l + 4*l**2 - 16*l + 6*l - r.
4*(l - 1)*(l + 1)
Suppose -512*o + 4*o**2 + 9*o**2 - 2*o**3 - 45*o**2 - 32*o**2 = 0. What is o?
-16, 0
Determine q, given that 4*q**4 + 15*q**3 + 5*q + 1392*q**2 + 6*q**3 - 2*q - 13*q**4 - 1407*q**2 = 0.
0, 1/3, 1
Let d(l) = l**3 + 18*l**2 - 18*l + 24. Suppose 15 = -h - 4. Let i be d(h). Suppose 1/2*n**4 - n + 3/2*n**3 + 0 - 1/2*n**i - 1/2*n**2 = 0. Calculate n.
-1, 0, 1, 2
Let w(d) = 3*d + 6. Let x be w(-11). Let f be 15/x + (-3)/9*-3. Factor -f*g - 2/9*g**2 - 2/9.
-2*(g + 1)**2/9
Suppose 0 = i + 13 + 502. Let r = i + 3097/6. Let r*m**2 - 1/3 - 5/6*m = 0. What is m?
-2/7, 1
Factor 2*m + 15*m**2 + 773*m**3 - 2*m - 20 - 778*m**3.
-5*(m - 2)**2*(m + 1)
Determine w, given that -1/4*w**3 + 7/4*w**2 - 3 - w = 0.
-1, 2, 6
Let p(l) be the first derivative of -14*l**5/45 - 17*l**4/18 - 26*l**3/27 - l**2/3 + 103. Factor p(v).
-2*v*(v + 1)**2*(7*v + 3)/9
Let y(t) = 4*t**2 - 9*t + 2. Let m be y(0). Factor -14/5*s - 2/5*s**3 - m*s**2 - 6/5.
-2*(s + 1)**2*(s + 3)/5
Let u = -4 + 8. Factor -4*f**4 - 2*f**5 + 4*f**3 - f**4 + 40*f**2 + 6*f**5 - 11*f**u - 16*f - 32.
4*(f - 2)**3*(f + 1)**2
Let t = 130 - 130. Let l be t + 32/(-24)*(-6)/28. Factor 0 - 4/7*h**3 + 0*h - 2/7*h**4 - l*h**2.
-2*h**2*(h + 1)**2/7
Factor 0 + 0*g + 6/5*g**2 - 3/5*g**3.
-3*g**2*(g - 2)/5
Factor 2/11*m**3 + 6/11*m**2 - 8/11 + 0*m.
2*(m - 1)*(m + 2)**2/11
What is f in -6 - 57/2*f**2 - 39/2*f**3 + 69/2*f**4 + 30*f - 21/2*f**5 = 0?
-1, 2/7, 1, 2
Let v(f) be the second derivative of -f**4/12 - 139*f**3/6 + 70*f**2 + 436*f. Solve v(r) = 0 for r.
-140, 1
Let l(p) = 2*p**3 - 14*p**2 - 20*p + 2. Let g(t) = -3*t**3 + 27*t**2 + 40*t - 5. Let j(o) = -2*g(o) - 5*l(o). Suppose j(z) = 0. What is z?
-1, 0, 5
Let n = 249 - 244. Let r(x) be the third derivative of 1/18*x**3 - 1/180*x**n + 5*x**2 + 0*x - 1/360*x**6 + 0 + 1/72*x**4. Let r(y) = 0. Calculate y.
-1, 1
Factor -19*n**2 + 94*n + 14*n - 3*n**3 + n**2 - 120 + 0*n**3.
-3*(n - 2)**2*(n + 10)
Let v be (3 + (-20)/8)*2*3. Suppose -4*g = -9*g + 3*d + v, -5*g = -d - 1. Find w such that -2/3*w + g + 1/3*w**2 = 0.
0, 2
Suppose 4*p = b, -p + 1 = -b + 2*p. Let h = 8 + b. Factor -5*m**3 + 5*m**5 + h + 2 - 6.
5*m**3*(m - 1)*(m + 1)
Suppose -17/7*w**2 + 0 + 15/7*w**5 - 2/7*w + 17/7*w**4 - 13/7*w**3 = 0. What is w?
-1, -2/15, 0, 1
Find z such that 47/3*z**3 + 84*z**2 - 800/3 - 4/3*z**4 - 3140/3*z = 0.
-8, -1/4, 10
Let m(o) = -6*o**3 - 24*o**2 + 9. Let a(q) = q**3 - q**2 - 1. Let p(y) = 9*a(y) + m(y). Factor p(u).
3*u**2*(u - 11)
Suppose 2*i**2 - 18*i - 10*i + 12*i = 0. What is i?
0, 8
Let s(u) be the second derivative of 0*u**3 + 0 - 1/20*u**5 - 1/4*u**6 + 0*u**4 + 7*u + 0*u**2. What is n in s(n) = 0?
-2/15, 0
Suppose 3*j = -3, -2*w - 2*j - 17 = j. Let a(p) = p**2 + 6*p - 5. Let b be a(w). Factor -27*k**4 - 22*k**4 + 12*k**3 + 30*k**b + 13*k**4 - 27*k + 15*k**5 + 6.
3*(k - 1)**3*(k + 1)*(5*k - 2)
Let i(l) be the second derivative of 2/9*l**2 + 4*l + 0 + 1/9*l**3 + 1/54*l**4. Factor i(f).
2*(f + 1)*(f + 2)/9
Solve 0 - 39/8*l**2 - 9/8*l - 3/2*l**3 = 0.
-3, -1/4, 0
Let s(k) be the third derivative of k**5/120 - 43*k**4/24 + 1849*k**3/12 + 352*k**2. Factor s(b).
(b - 43)**2/2
Let p(t) = t**2 + 2*t. Let k(s) = 18*s**2 - 22*s + 10. Let u(f) = -k(f) + 2*p(f). Find g, given that u(g) = 0.
5/8, 1
Let p be 0 + 182/(-21) + 9. Let g(y) be the first derivative of 0*y + 1/6*y**4 - p*y**2 + 0*y**3 + 10. Let g(u) = 0. Calculate u.
-1, 0, 1
Let l be 12/(-3 - 0) - 441/(-119). Let u = 93/85 + l. Determine r so that -4/5*r + u*r**2 - 4/5*r**5 - 2/5 - 2/5*r**4 + 8/5*r**3 = 0.
-1, -1/2, 1
Let -92/15*d - 134/15*d**2 - 8/3*d**3 + 0 + 2/15*d**4 = 0. What is d?
-2, -1, 0, 23
Let v(y) be the third derivative of -y**5/570 - 11*y**4/114 - 121*y**3/57 - 3*y**2 - 20*y. Determine p, given that v(p) = 0.
-11
Let d(a) be the first derivative of -a**3 + 0*a**2 + 3/16*a**4 + 0*a + 26. Find q, given that d(q) = 0.
0, 4
Let n = 167 - 167. Let o(p) be the third derivative of -p**2 + 0 + 1/540*p**6 + 0*p + 0*p**4 - 1/270*p**5 + n*p**3. Factor o(t).
2*t**2*(t - 1)/9
Suppose 56*z - 258 = 13*z. Suppose -4/3 - z*d**2 + 22/3*d = 0. What is d?
2/9, 1
Suppose -3*x + 19 - 3 = 5*y, -4*x = 5*y - 18. Let p(c) be the first derivative of 1/15*c**3 - 8 + 1/5*c**y + 0*c. Suppose p(n) = 0. What is n?
-2, 0
Factor 29*z**2 - 25*z - 868*z**3 + 863*z**3 + z**2.
-5*z*(z - 5)*(z - 1)
Let r be (-8)/(-4) + 12/((-1800)/295). Let x(m) be the second derivative of 0*m**3 + 0 + 9/100*m**5 + 0*m**2 - r*m**4 - 10*m. Factor x(g).
g**2*(9*g - 2)/5
Let m(k) be the second derivative of -k**5/8 + 5*k**4/3 + 15*k**3/4 + 184*k. Find o such that m(o) = 0.
-1, 0, 9
Let c = 991/9 - 988/9. Let k = -41 + 125/3. Factor 5/3*m**3 + 8/3*m**2 + c*m - k.
(m + 1)**2*(5*m - 2)/3
Let x(z) be the second derivative of 7*z**6/120 + 13*z