1/2 + 7/4*a + l*a**2.
(a + 2)*(3*a + 1)/4
Let s(w) be the second derivative of w**4/3 - 60*w**3 + 4050*w**2 - 24*w. Find d, given that s(d) = 0.
45
Let o(z) be the first derivative of -z**5/10 + 5*z**4/8 + z**3/2 - 17*z**2/4 + 5*z - 12. What is l in o(l) = 0?
-2, 1, 5
Let r = -140 - -132. Let v be ((-45)/(-20))/((-12)/r). Determine w, given that -3*w + v*w**2 + 0 = 0.
0, 2
Suppose -4*o + 35 - 6 = -h, -4*h = -3*o + 38. Suppose -11*q = -o*q. Factor q + 0*t**2 + 0*t - 4/13*t**4 + 2/13*t**3 + 2/13*t**5.
2*t**3*(t - 1)**2/13
Let x be 100/(-225) + 1420/360. Determine v so that -93/2*v + 13 + x*v**2 = 0.
2/7, 13
Factor -3/7*h**2 - 18*h + 129/7.
-3*(h - 1)*(h + 43)/7
Let k(t) = 164*t - 1474. Let h be k(9). Let 1/2*d**h - 1/4*d**3 + 0*d + 0 = 0. Calculate d.
0, 2
Let g(h) be the third derivative of -1/60*h**4 + 0 + 0*h + 11*h**2 - 1/15*h**3 - 1/100*h**6 + 1/30*h**5. Factor g(k).
-2*(k - 1)**2*(3*k + 1)/5
Let r be (-123)/(-9) + 2/6. Let d(n) = n**3 - 9*n**2 + 8*n. Let g be d(8). Let -8*o**3 - 8*o + g + 13*o**2 + 13*o**2 + 4 - r*o = 0. Calculate o.
1/4, 1, 2
Let v(r) be the third derivative of 5*r**8/3024 - r**7/270 - 13*r**6/1080 + 31*r**5/540 - 5*r**4/54 + 2*r**3/27 + 3*r**2 + 6. Determine c so that v(c) = 0.
-2, 2/5, 1
Let y be ((-39)/(-78))/((-2)/(-1)). Factor 1/2*c - 1/4 - y*c**2.
-(c - 1)**2/4
Let a(h) be the first derivative of h**5 - 7*h**4/4 - 38*h**3/3 + 38*h**2 - 24*h - 266. Determine x so that a(x) = 0.
-3, 2/5, 2
Suppose -2*h = -5*y + 50 - 12, -y - 2*h - 2 = 0. Let p(i) be the first derivative of 5 - y*i - 5*i**2 - 2/3*i**3 + 1/2*i**4. Factor p(w).
2*(w - 3)*(w + 1)**2
What is s in -20/3*s - 20/9*s**3 + 2/9*s**4 + 0 + 62/9*s**2 = 0?
0, 2, 3, 5
Let 4/3*o**5 - 608/3*o + 164/3*o**4 + 0 - 16/3*o**2 + 152*o**3 = 0. What is o?
-38, -2, 0, 1
Let y(c) be the first derivative of -c**3 + 6*c**2 + 15*c + 38. Suppose y(k) = 0. What is k?
-1, 5
Suppose 0 = 3*b - 4*t - 79, -b - 2*t + 6 = -7. Find h such that b*h**2 - 4 - 46*h**2 - 8*h + 20*h**2 - h**3 = 0.
-2, -1
Let g(u) be the first derivative of -5*u**6/6 + 13*u**5 - 275*u**4/4 + 355*u**3/3 + 100*u**2 - 500*u + 167. Solve g(p) = 0 for p.
-1, 2, 5
Suppose 2*q - 2*q**4 + 2803*q**2 - q**5 - 2795*q**2 + 2*q + 3*q**3 = 0. Calculate q.
-2, -1, 0, 2
Suppose 5*h + 23 = 4*t - 0*t, -t + 2 = -5*h. Factor -t + 7 - 2*v**3.
-2*v**3
Let n(a) = -10*a**2 - 4*a + 7. Let y(h) = 95*h**2 + h + 2 - 92*h**2 - 4. Let v be -1*(2 + 0) - -8. Let z(x) = v*n(x) + 21*y(x). Factor z(r).
3*r*(r - 1)
Let l be (-3 + 4)/((-1)/(-7)). Suppose 10 = 4*x + 2*k, 0 = x + 4*k - l*k - 13. Let -4 - x*m**2 + 7 - 3 = 0. What is m?
0
Let y = 12339 - 12336. Suppose 2/9*p**y - 8/9*p**2 + 4/3 + 2/9*p = 0. What is p?
-1, 2, 3
Let t(j) be the second derivative of -2*j**6/15 + 54*j**5/35 + 16*j**4/21 - 212*j. Determine r so that t(r) = 0.
-2/7, 0, 8
Suppose -3*z = t - z, -3*z - 3 = 0. Factor 0*u - 2*u**t - 6*u - u + 3*u.
-2*u*(u + 2)
Suppose -y + 2*g = -1 + 6, -2*g = y - 11. Let v be 48/5 + (-6)/(-15). Find k such that -16*k**2 - 26*k**y - 8*k**3 - 2*k**5 - 12*k**4 + v*k**3 = 0.
-2, 0
Let i be ((-798)/(-28))/19*30/9. Suppose -9/2*w**3 - w + 0 + 5/2*w**4 + 7/2*w**2 - 1/2*w**i = 0. What is w?
0, 1, 2
Let t(s) = 55*s**4 + 45*s**3 + 120*s**2 - 65*s - 65. Let u(n) = 6*n + 5 + 3 - 4*n**3 - 2 + 0*n**2 - 11*n**2 - 5*n**4. Let r(d) = -6*t(d) - 65*u(d). Factor r(y).
-5*y**2*(y + 1)**2
Let c be (0 + 1)/(-102*(-7)/84). Let h = 21/34 - c. Determine f, given that -h*f**2 - 1/2 + f = 0.
1
Let v(x) be the first derivative of -x**4/8 + x**3/2 + 6*x**2 + 14*x + 288. Factor v(a).
-(a - 7)*(a + 2)**2/2
Let y(o) be the first derivative of o**5/10 - o**4/3 + o**3/3 + 29*o - 28. Let x(h) be the first derivative of y(h). Suppose x(f) = 0. What is f?
0, 1
Let m(o) = 4*o**2 - 6*o - 4. Let l be m(-2). Factor -149*w - 7*w**3 + 53*w + l*w**2 + 5*w**3 + 128.
-2*(w - 4)**3
Let i(f) be the third derivative of f**5/90 + f**4/9 - 4*f**3/3 - 2*f**2 - 2*f. Let i(j) = 0. What is j?
-6, 2
Let m be 30 - (-2541)/(-84) - 1*-1. Factor 0 - 3/4*r**3 + 3/4*r**5 - 3/4*r**4 + m*r**2 + 0*r.
3*r**2*(r - 1)**2*(r + 1)/4
Let t(k) = 2*k**4 - k**2. Let a(c) = 13*c**4 - 135*c**3 + 124*c**2 + 135*c - 132. Let m(l) = -a(l) + 5*t(l). Solve m(g) = 0 for g.
-1, 1, 44
Suppose -152 = -3*q - 4*u, -58 = -q + 2*u - 7*u. Let g be q/9 - 2/6. Find a, given that -3*a + 8*a**4 - 7*a**4 - 5*a**2 + g*a**3 - 2*a + 4*a**4 = 0.
-1, 0, 1
Suppose -2*q = b - 9, -4*q - b + 0*b = -13. Factor -1 + 8*i**2 - i**2 + 3*i - 6*i**q - 3.
(i - 1)*(i + 4)
Let x(n) = -2*n**2 - n - 2. Let w(u) = -13*u**2 - 5*u - 10. Let j(k) = -5*w(k) + 30*x(k). Suppose j(v) = 0. Calculate v.
-1, 2
Let q(j) be the second derivative of j**3/6 - 8*j**2 - 35*j. Let t be q(16). Factor -2/9*x**2 - 2/9*x**4 + 0*x + 4/9*x**3 + t.
-2*x**2*(x - 1)**2/9
Determine i, given that -100*i - 40 + 30*i**2 + 0*i + 105*i**3 + 2*i**4 - 40*i**2 + 43*i**4 = 0.
-2, -2/3, 1
Let y be 80/12*2/5. Factor 16/3*f**2 + 0 - 4*f**3 + 16/3*f - y*f**4 + 4/3*f**5.
4*f*(f - 2)**2*(f + 1)**2/3
Find x such that 1/6*x**2 - 59/2 - 88/3*x = 0.
-1, 177
Let m be (-62)/(-4) - 27/(-18). Suppose -4*x - 5 = -m. Solve x*u**2 - 3/2*u**5 - 4*u**4 + 1 - 2*u**3 + 7/2*u = 0.
-1, -2/3, 1
Let d = -74228/9 - -8248. Suppose -4/9 + 0*r**3 + 0*r - d*r**4 + 8/9*r**2 = 0. What is r?
-1, 1
Let l(c) be the third derivative of 10*c**2 - 1/540*c**5 - 1/54*c**4 + 5/3*c**3 + 0*c + 1/1620*c**6 + 0. Let m(j) be the first derivative of l(j). Factor m(o).
2*(o - 2)*(o + 1)/9
Let m(i) = -6*i + 14*i - 9*i + 10. Let t be m(10). Factor t*r**3 + 2/3*r**2 + 0 + 0*r - 2/3*r**4.
-2*r**2*(r - 1)*(r + 1)/3
Let q(u) = -2*u**3 + 69*u**2 + 110*u - 70. Let a be q(36). Determine w so that -6/5 + 4/5*w + 2/5*w**a = 0.
-3, 1
Let c(h) = 3*h**2 - 58*h + 21. Let y be c(19). Suppose -2*w = -1 - 5. Suppose -y*k**5 - 2*k**w - 3*k + 8*k**3 - k**5 = 0. Calculate k.
-1, 0, 1
Let o(d) be the third derivative of 0*d + 0 + 20*d**2 + 7/12*d**5 + 10/3*d**3 + 10/3*d**4. Factor o(z).
5*(z + 2)*(7*z + 2)
Let j(c) be the second derivative of -c**10/30240 + c**8/2240 + c**7/1260 + 5*c**4/3 + 14*c. Let a(d) be the third derivative of j(d). Factor a(t).
-t**2*(t - 2)*(t + 1)**2
Suppose 6 = 4*b - 2*r + 4, 2*r = -3*b + 12. Let n(y) be the first derivative of y**4 - 2 + 12*y - 10*y**b + 4/3*y**3. Suppose n(t) = 0. Calculate t.
-3, 1
Let -12006/5*r - 14/5*r**3 - 3364/5 - 816/5*r**2 = 0. What is r?
-29, -2/7
Let b(z) = -z**3 + 5*z**2 + 5*z + 6. Let g be b(6). Suppose g = -u - 3*v + 6, v - 6 = -u - v. Suppose -2*o**2 + 4*o**2 - 6*o + u*o = 0. Calculate o.
0
Let l(p) = -16*p**3 - 3*p**2 + p. Let f be l(2). Let j = -962/7 - f. Factor -8/7*h + 4/7 + j*h**2.
4*(h - 1)**2/7
Suppose 0 = 2*z + 2*d - 6, -z - 2*d + 6 - 3 = 0. Suppose 6*v + z = 3. Solve -3/4*p**3 + 0*p + 1/2*p**2 + v + 1/4*p**4 = 0 for p.
0, 1, 2
Let u(x) be the first derivative of -5*x**9/3024 - x**8/84 - x**7/28 - x**6/18 - x**5/24 + 4*x**3/3 + 10. Let t(d) be the third derivative of u(d). Factor t(q).
-5*q*(q + 1)**4
Determine t, given that 968*t**2 + 1/2 - 44*t = 0.
1/44
What is h in -5/2*h + 15/2*h**2 + 0 = 0?
0, 1/3
Suppose -1/4*m**2 - 35/2*m - 1225/4 = 0. What is m?
-35
Let a = -76268/5 - -15260. Solve 16/5*b**5 + 0*b + 4*b**3 + 0 - 4/5*b**2 - a*b**4 = 0.
0, 1/2, 1
Factor -8/3*m + 1/3*m**2 + 7/3.
(m - 7)*(m - 1)/3
Let i(h) be the second derivative of -2*h**7/105 - h**6/30 + h**5/15 + h**4/6 - 23*h**2/2 + 21*h. Let t(s) be the first derivative of i(s). Factor t(n).
-4*n*(n - 1)*(n + 1)**2
Let g(a) = 23*a - a**2 - 10*a + 5*a**4 - 1 - 2*a**5 - 4*a**3 - 7*a. Let q(p) = p**5 - p**4 - p**2 - p - 1. Let o(s) = -4*g(s) - 4*q(s). Factor o(b).
4*(b - 2)*(b - 1)**3*(b + 1)
Suppose 66 + 18 = 6*n. Let a = 16 - n. Suppose 1/2*m**5 + 1/2*m - m**3 - m**a + 1/2 + 1/2*m**4 = 0. Calculate m.
-1, 1
Let y be (42/(-8))/(1089/(-484)). Solve -7/3*z**5 - 2/3*z**4 - 2/3 + 4/3*z**2 + 14/3*z**3 - y*z = 0.
-1, -2/7, 1
Let a(z) = -4*z**2 - 29*z - 12. Let h(l) = -l**2 - 7*l - 3. Let r(b) = 2*a(b) - 9*h(b). Let g be r(-5). Determine f so that 1 + 5*f**2 - 1 - 2 - g*f**2 = 0.
-1, 1
Let g(p) be the third derivative of 0*p + 1/24*p**3 - 1/240*p**5 + 0 - 1/480*p**6 + 12*p**2 + 1/96*p**4. Factor g(u).
-(u - 1)*(u + 1)**2/4
Let n(c) be the third derivative of c**7/1890 - c**6/54 + 5*c**5/18 - 17*c**4/24 + 18*c**2. Let o(b) be the second deriva