(-24) + -9 - (-2)/(-16). Factor -1/2*t**3 - 1/2 + 1/2*t**2 + d*t.
-(t - 1)**2*(t + 1)/2
Let m(a) be the first derivative of 10*a**3/39 + 242*a**2/13 + 192*a/13 - 56. Find s, given that m(s) = 0.
-48, -2/5
Let k(u) = u**3 + 7*u**2 + 8*u + 12. Let f be k(-6). Suppose 2*q = -q - f*q. Factor -1/3*r**4 + 0 + q*r**3 + 0*r**2 + 0*r + 1/6*r**5.
r**4*(r - 2)/6
Let j(t) be the first derivative of -1/1020*t**5 + 0*t - 2/3*t**3 - 7 + 0*t**2 - 1/3060*t**6 + 0*t**4. Let w(s) be the third derivative of j(s). Factor w(q).
-2*q*(q + 1)/17
Let s(c) = 21*c**4 - 29*c**3 + 6*c**2 + 2*c - 2. Let l(i) = 21*i**4 - 30*i**3 + 6*i**2 + 3*i - 3. Let u(a) = 2*l(a) - 3*s(a). Let u(k) = 0. What is k?
0, 2/7, 1
Let l = 5611/6 - 934. Let a(s) be the second derivative of 0 - l*s**4 - 1/2*s**5 + 0*s**2 - 2/3*s**3 - 9*s. Factor a(o).
-2*o*(o + 1)*(5*o + 2)
Let z(u) be the third derivative of -u**7/105 + u**6/30 - u**4/6 + u**3/3 - 253*u**2. Suppose z(p) = 0. What is p?
-1, 1
Let m(h) be the second derivative of -h**7/630 + h**5/90 - h**3/18 + 3*h**2 - 3*h. Let d(b) be the first derivative of m(b). What is q in d(q) = 0?
-1, 1
Factor -1/3*z**2 - 19/6*z + 10/3 + 1/6*z**3.
(z - 5)*(z - 1)*(z + 4)/6
Let q(j) be the third derivative of -j**8/13440 + j**7/840 + 7*j**6/1440 - 41*j**4/24 - 10*j**2. Let u(n) be the second derivative of q(n). Factor u(y).
-y*(y - 7)*(y + 1)/2
Let o = 471 + -468. Let b(k) be the first derivative of -2/11*k**o + 1/22*k**4 + 2/11*k**2 + 0*k + 5. Let b(w) = 0. What is w?
0, 1, 2
Let h(c) be the second derivative of -c**7/189 + 13*c**6/135 - 31*c**5/45 + 64*c**4/27 - 32*c**3/9 - 148*c. Determine q so that h(q) = 0.
0, 2, 3, 4
Find x such that 40*x - 140*x**3 + 22*x**2 + 86*x**2 + 100*x**3 + 2*x**4 - 14*x**4 = 0.
-5, -1/3, 0, 2
Let m(i) be the second derivative of i**5/60 + i**4/24 - 3*i**2/2 - 7*i. Let n(j) be the first derivative of m(j). Factor n(p).
p*(p + 1)
Let v = -97714 - -780269/8. Let y = -180 - v. Factor -9/8*p**3 + 0 + 9/8*p**2 + y*p**4 - 3/8*p.
3*p*(p - 1)**3/8
Let i(a) be the first derivative of -a**4/12 + 11*a**3/9 - 13*a**2/2 + 15*a - 88. Suppose i(x) = 0. Calculate x.
3, 5
Let q(k) be the third derivative of k**6/300 + k**5/25 + 11*k**4/60 + 2*k**3/5 - k**2 + 7*k. Let q(t) = 0. Calculate t.
-3, -2, -1
Let z(v) = 9*v**2 - 79*v + 641. Let j(u) = 5*u**2 - 40*u + 320. Let c(t) = 7*j(t) - 4*z(t). Determine r, given that c(r) = 0.
18
Suppose -290*m - 33*m = 0. Suppose -2/9*q**4 + m*q + 2/9*q**2 + 8/9*q**5 + 0 - 8/9*q**3 = 0. Calculate q.
-1, 0, 1/4, 1
Factor -2/9*s**3 + 8192/9 - 2816/3*s + 86/3*s**2.
-2*(s - 64)**2*(s - 1)/9
Let n(m) = -m**3 - 1. Let q(s) = s**2 + s. Suppose 2*d = -u + 1, 3*u = d + d - 5. Suppose 5*w + 3 = 8. Let h(v) = d*q(v) + w*n(v). Factor h(a).
-(a - 1)**2*(a + 1)
Suppose 2*d - 21 = -5*q, -4 = -3*d + 2*q - 1. Let k be 20/4 + (-5 - -2). Factor f**d + 1 - 2*f - f**4 + k*f**3 - f**3.
-(f - 1)**3*(f + 1)
Let c be (20*8/60)/((-2)/(-3)). Suppose 11 + c = 5*d. Factor -2/3*y**d - 4/3 + 2*y + 0*y**2.
-2*(y - 1)**2*(y + 2)/3
Let i be -3 + ((-844)/(-308) - (-6)/(-21)). Let o = -32/99 - i. Factor -o*r**2 - 8/9*r - 2/3.
-2*(r + 1)*(r + 3)/9
Let i(w) be the third derivative of 0*w + 9*w**2 + 0*w**4 + 0 - 8/3*w**3 + 1/15*w**5. What is y in i(y) = 0?
-2, 2
Let a be (-64)/(-28) + (-4)/(-84)*-6. Factor 1/4*v + 0 - 1/2*v**a + 1/4*v**3.
v*(v - 1)**2/4
Suppose 4/5*n**2 - 176/5 - 28/5*n = 0. Calculate n.
-4, 11
Let z(m) be the first derivative of 4*m - 4*m + 6 - m**4. Let z(y) = 0. Calculate y.
0
Let y = 380 + -1892/5. Let t(r) be the first derivative of -3*r**4 + 441/10*r**6 - 462/25*r**5 + 3 + y*r**3 + 0*r**2 + 0*r. Let t(i) = 0. What is i?
-2/9, 0, 2/7
Factor 5*f**2 + 4*f**5 - 15*f**3 - 4*f + 15*f**3 + 3*f**2 + 57*f**4 - 65*f**4.
4*f*(f - 1)**3*(f + 1)
Let k(m) be the first derivative of 0*m**2 + 3/35*m**5 + 0*m - 1/42*m**6 - 11 + 0*m**3 - 1/14*m**4. Factor k(l).
-l**3*(l - 2)*(l - 1)/7
Let g = 2227 + -2225. Determine r so that 0*r**g - 1/5*r**5 + 0*r + 1/5*r**4 + 0 + 0*r**3 = 0.
0, 1
Let v(g) be the first derivative of -g**7/2520 + g**6/540 - 13*g**3 - 6. Let b(p) be the third derivative of v(p). Suppose b(o) = 0. What is o?
0, 2
Suppose -16*m + 37 + 27 = 0. Let 44/9*g**3 + 2/9*g**5 + 0 + 16/3*g**2 + 2*g + 16/9*g**m = 0. Calculate g.
-3, -1, 0
Suppose -4*w = 2*h - 24 + 2, 4*h = -5*w + 32. Let n be (-3)/60*-5*32/12. Factor r**2 + 0 + 1/3*r**h + n*r.
r*(r + 1)*(r + 2)/3
Let b be (-62 + 62)/((-32)/(-4)). What is l in 5/4 + 5/2*l**3 - 5/2*l + b*l**2 - 5/4*l**4 = 0?
-1, 1
Let t(s) be the third derivative of 2*s**3 + 1/40*s**6 + 3*s - 2*s**2 + 1/336*s**8 + 0 + 23/60*s**5 - 1/30*s**7 - 4/3*s**4. Determine d so that t(d) = 0.
-2, 1, 6
Let v(x) be the second derivative of 2*x**7/63 - 2*x**6/15 - 2*x**5/15 + 2*x**4/3 + 2*x**3/9 - 2*x**2 + x + 14. Determine y, given that v(y) = 0.
-1, 1, 3
Let s(l) be the second derivative of -l**7/5460 + l**6/1170 + l**5/195 + 11*l**4/12 + 10*l. Let t(v) be the third derivative of s(v). Factor t(b).
-2*(b - 2)*(3*b + 2)/13
Let p(q) be the second derivative of -7*q**5/300 - 19*q**4/120 + q**3/5 - 2*q**2 - 3*q. Let a(d) be the first derivative of p(d). Let a(n) = 0. What is n?
-3, 2/7
Let o be 1 - (-2 - (-1 + 3)). Suppose -2*n - 1 = -o. Factor -28*m**n + 3*m - 2*m + 4*m + 3*m.
-4*m*(7*m - 2)
Suppose 3*n - 4*n + s = -55, -2*n = -5*s - 119. Suppose y + 3*y = n. What is b in -2*b**4 + 6*b**3 - y*b**3 + 3*b**3 - b**2 - b**2 = 0?
-1, 0
What is n in -6/17*n**2 - 4 - 206/17*n = 0?
-34, -1/3
Suppose -3*p = -5*y + 10, -5*p + 4*p = -5. Suppose 4*l = y*v - 17, 4*l + 4*v - 45 = -17. Factor -3 + 5 + 10*j**4 - 14*j**l - 6*j**3 + 2 + 6*j.
2*(j - 1)**2*(j + 1)*(5*j + 2)
Factor -64*m**4 + 62*m**4 + 0*m - 6*m**3 + 8*m.
-2*m*(m - 1)*(m + 2)**2
Factor 36/7*c + 0 - 32/7*c**2 - 4/7*c**3.
-4*c*(c - 1)*(c + 9)/7
Let y(w) be the second derivative of 5*w + 3/2*w**2 - 1/36*w**4 - 1/360*w**5 - 1/9*w**3 + 0. Let s(l) be the first derivative of y(l). Factor s(b).
-(b + 2)**2/6
Let d(f) = f**3 + f**2 + f - 4. Let o(w) = -8*w**3 + 20*w**2 - 27*w + 12. Let s(x) = -6*d(x) - 2*o(x). Factor s(l).
2*l*(l - 3)*(5*l - 8)
Let w(o) be the third derivative of 11*o**2 + 0*o - 2/105*o**5 + 0*o**3 + 1/735*o**7 + 1/420*o**6 + 0 - 1/21*o**4. Find p, given that w(p) = 0.
-2, -1, 0, 2
Let x(v) be the second derivative of 7*v**7/6 - 35*v**6/6 + 39*v**5/20 + 163*v**4/12 - 44*v**3/3 + 6*v**2 + 7*v + 6. Determine t so that x(t) = 0.
-1, 2/7, 1, 3
Let g be (-1 - -3) + 2 - 3. Suppose g = -3*x + 13. Let -6*j + 0*j**3 + 3*j**3 + 3*j**3 + 3*j**x - 3 = 0. What is j?
-1, 1
Let n(r) be the second derivative of 28*r - 2/51*r**3 - 1/102*r**4 + 1/170*r**5 + 0 + 0*r**2. Factor n(t).
2*t*(t - 2)*(t + 1)/17
Suppose -3*v + 6*v + 15 = 0, 3*z - 152 = v. Suppose -z = -19*n - 11. Let -2/3*t + 8/15*t**n + 4/15 - 2/15*t**3 = 0. What is t?
1, 2
Let b(x) be the third derivative of -9*x**2 + 1/210*x**5 + 0*x + 0*x**3 - 1/84*x**4 + 0. What is u in b(u) = 0?
0, 1
Let t(y) = -55*y - 4342. Let x be t(-79). Solve -2/7*r**x + 6/7*r + 0*r**2 - 4/7 = 0.
-2, 1
Let l(x) be the first derivative of -x**5/330 + x**4/44 - 2*x**3/33 - 10*x**2 - 16. Let p(d) be the second derivative of l(d). Solve p(h) = 0 for h.
1, 2
Let t be (-1728)/108*(5/(-4) - -1). Solve 0*p**2 + 4/15*p**3 - 4/15*p - 2/15*p**t + 2/15 = 0 for p.
-1, 1
Let t = 267 + -265. Let r(y) be the second derivative of 2/3*y**3 - 1/6*y**4 + 0 - y**t + y. Let r(p) = 0. What is p?
1
Suppose 49*m = 14*m. Factor 2/13*h - 2/13*h**3 + m*h**2 + 0.
-2*h*(h - 1)*(h + 1)/13
Let b(z) = 2*z**2 - 13*z + 3. Let f(l) = -2*l**2 + 14*l - 2. Let m be 2*((-6)/(-4) - -1). Let s(n) = m*f(n) + 6*b(n). Determine x, given that s(x) = 0.
2
Let c(w) be the first derivative of -w**3 + 3*w**2/2 + 18*w - 318. Solve c(h) = 0 for h.
-2, 3
Suppose 0 = -6*r - 39 + 159. Let z be (-16)/r*(-4 + -1 + 1). Suppose z + 1/5*y**2 + 8/5*y = 0. What is y?
-4
Factor 2/17*g**2 + 10/17*g + 8/17.
2*(g + 1)*(g + 4)/17
Suppose -3*j = -0*j - 5*g + 3, -5*j - 5*g + 35 = 0. Suppose 0*m = -j*m + 36. Factor 12*c**4 + m*c**3 - 25*c**3 + 118*c**2 - 114*c**2.
4*c**2*(c - 1)*(3*c - 1)
Let -18/5 + 2/5*z**2 + 0*z = 0. What is z?
-3, 3
Suppose 1 = 11*g - 12*g, -4*g = -3*l + 10. Let -1/2 - 11/4*q - 9/4*q**l = 0. Calculate q.
-1, -2/9
Let c(g) be the first derivative of -8 + 3/10*g**2 + 1/15*g**3 + 0*g. Factor c(f).