 -78/7 - 9/7*u**2 - 123/7*u = 0. Calculate u.
-13, -2/3
Factor -6*o**2 - 6*o - 8*o + 32*o - 10*o**3 - 10 + 8*o**3.
-2*(o - 1)**2*(o + 5)
Let 1/5*y**4 + 0*y + 0 + 2/5*y**2 + 3/5*y**3 = 0. What is y?
-2, -1, 0
Let v = 204 - 145. Suppose 16*q + v*q**2 - 13*q**5 - 208*q**3 - 124*q**4 + 16 - 11*q**5 - 167*q**2 = 0. Calculate q.
-2, -1, -1/2, 1/3
Let c(n) be the first derivative of 2*n**3/15 - 6*n**2/5 + 2*n + 135. Factor c(z).
2*(z - 5)*(z - 1)/5
Solve 7*h + 51*h**2 - 2*h - 61*h**2 + 10*h**4 - 5*h**5 = 0.
-1, 0, 1
Let i = -2447 - -2451. Let z(n) be the third derivative of 0*n + 13*n**2 - 1/160*n**6 + 1/32*n**i + 1/8*n**3 - 1/80*n**5 + 0. Determine h, given that z(h) = 0.
-1, 1
Let x(l) be the second derivative of l**4/21 - 52*l**3/3 + 2366*l**2 + 700*l. Factor x(q).
4*(q - 91)**2/7
Let h(b) be the first derivative of -b**4/12 - b**3/3 - b**2/3 - 18. Factor h(l).
-l*(l + 1)*(l + 2)/3
Factor -3720 - 342*v**2 - 1438*v + 216*v**2 - 146*v - 3*v**3 + 144*v + 1320.
-3*(v + 2)*(v + 20)**2
Let i = 5493 + -5491. Determine g so that 1/3*g + 2/3 - 1/3*g**3 + 1/3*g**4 - g**i = 0.
-1, 1, 2
Let a(g) = -35*g + 249. Let v be a(7). Factor v + 4/9*x**2 + 8/3*x.
4*(x + 3)**2/9
Suppose -161*j + 187*j - 63 = -11. Factor 0*g - 2/5*g**j + 2/5.
-2*(g - 1)*(g + 1)/5
Suppose 0 = -4*x - p - 1, -x - 7 + 6 = p. Factor 4/9*f**3 - 4/9*f + 0 + x*f**2.
4*f*(f - 1)*(f + 1)/9
Let w(v) = -v**3 + 15*v**2 + 36*v - 19. Let a be w(17). Let d be 60/25 - 6/a. Factor -1/4*c**3 + 0*c**d + 0 + 1/4*c.
-c*(c - 1)*(c + 1)/4
Let b(m) be the third derivative of m**5/60 - 7*m**4/96 - m**3/12 + 12*m**2. Factor b(a).
(a - 2)*(4*a + 1)/4
Let v(m) be the second derivative of m**4/12 + m**3/6 + m**2/2 + 30*m. Let j(y) = -5*y**2 + 2*y - 12. Let b(d) = -j(d) - 4*v(d). Let b(z) = 0. What is z?
2, 4
Let b(w) be the third derivative of 0*w**3 + 0*w + 1/15*w**4 + 0 - 1/150*w**5 + w**2. Factor b(t).
-2*t*(t - 4)/5
Factor -2/3 - 7/2*i - 7/2*i**2 - 2/3*i**3.
-(i + 1)*(i + 4)*(4*i + 1)/6
Let c be (-28)/238 + 344/34. Suppose 5*n - c = -o, 4*n - 37 = o + 4*o. Factor 2/15*p**4 - 2/15*p**2 - 2/15*p**n + 0 + 2/15*p.
2*p*(p - 1)**2*(p + 1)/15
Let b(j) = -6*j**4 + 66*j**3 + 10*j**2 - 2112*j - 4348. Let a(y) = 19*y**4 - 199*y**3 - 31*y**2 + 6336*y + 13040. Let u(x) = -2*a(x) - 7*b(x). Factor u(i).
4*(i - 11)**2*(i + 3)**2
Suppose -16*o = 85*o + 3 - 3. Factor 3*w**4 + 12*w**3 + 0*w + o + 16*w**2 + 1/4*w**5.
w**2*(w + 4)**3/4
Let c(y) be the first derivative of -y**3 - 5*y**2/2 - 2*y - 87. Let c(x) = 0. What is x?
-1, -2/3
Let q = 636 - 1907/3. Let n(c) be the second derivative of -c + q*c**3 + 0 + 0*c**2 + 1/6*c**4. Suppose n(j) = 0. Calculate j.
-1, 0
Let c(v) be the third derivative of 0 - 1/24*v**5 + 0*v**3 + 1/96*v**6 + 7*v**2 + 0*v + 5/96*v**4. Determine y, given that c(y) = 0.
0, 1
Suppose 4/7*l**5 + 104/7*l**4 - 320/7*l**2 - 1352/7 + 664/7*l**3 - 2236/7*l = 0. Calculate l.
-13, -1, 2
Let n(h) be the third derivative of 0*h + 1/380*h**6 + 0 + 1/570*h**5 - 40*h**2 - 2/57*h**4 + 4/57*h**3. Solve n(a) = 0.
-2, 2/3, 1
Let l(g) be the first derivative of 2/45*g**5 - 2/9*g**3 + 2/9*g + 1/18*g**2 + 1/36*g**4 + 11. Solve l(b) = 0 for b.
-2, -1/2, 1
Let w(h) be the third derivative of 1/6*h**4 - 4*h**2 + h**3 + 0 + 0*h - 1/30*h**5. Find f such that w(f) = 0.
-1, 3
Let b = -57695/21976 + 1/2747. Let u = b + 121/40. Factor -u*t - 2/5*t**4 + 2/5*t**2 + 2/5*t**3 + 0.
-2*t*(t - 1)**2*(t + 1)/5
Let l(m) be the second derivative of -m**6/255 - 13*m**5/170 - m + 95. Suppose l(f) = 0. What is f?
-13, 0
Let i(y) be the second derivative of -y**7/21 - y**6/5 - y**5/10 + y**4/2 + 2*y**3/3 + 104*y. What is j in i(j) = 0?
-2, -1, 0, 1
Let n(u) be the first derivative of 3*u**4/4 + 41*u**3 + 60*u**2 - 569. Factor n(c).
3*c*(c + 1)*(c + 40)
Let w be (1 + (-46)/50)/(3894/295). Let l(n) be the second derivative of -4/33*n**3 + w*n**6 + 4/33*n**4 + 5*n + 0*n**2 + 0 - 1/22*n**5. Solve l(x) = 0 for x.
0, 1, 2
Let a = 3 + 2. Suppose 768 = a*o - o. Suppose 192*v**3 + 2*v - 3*v**2 + v**4 - o*v**3 = 0. What is v?
-2, 0, 1
Let o(w) be the first derivative of w**4/48 - w**3/8 + 12*w + 9. Let l(p) be the first derivative of o(p). Factor l(q).
q*(q - 3)/4
Let a(p) be the first derivative of p**4/28 - 2*p**3/7 + 6*p**2/7 - 10*p + 15. Let u(s) be the first derivative of a(s). Determine q, given that u(q) = 0.
2
Suppose 30/11*b**2 + 8/11 + 64/11*b = 0. Calculate b.
-2, -2/15
Let o(r) = 8*r**3 - 28*r**2 - 28*r + 12. Let y(f) = -f**3 - f - 3. Let l(z) = o(z) + 4*y(z). Solve l(d) = 0 for d.
-1, 0, 8
Let z(u) be the first derivative of -u**4/4 - 11*u**3/3 + 11*u**2/2 - 10*u + 6. Let w be z(-12). What is g in 4*g + 13*g**w - 4*g**2 - 10*g**2 + 4 - g = 0?
-1, 4
Let v(w) be the third derivative of w**6/660 - 7*w**5/330 + 7*w**4/132 + 5*w**3/11 - 166*w**2. Determine y, given that v(y) = 0.
-1, 3, 5
Let a(z) = -6*z**2 + 5*z - 3. Let o(b) = b**2 - b. Suppose -2*u = -u + 14. Let h(k) = u*o(k) - 2*a(k). Factor h(f).
-2*(f - 3)*(f + 1)
Let m be (-6)/(-21) - (-1072)/(-28). Let k = 42 + m. What is r in 8*r - 14*r**2 - 6*r**k - 2*r**2 - 14*r**3 + 0*r - 8*r**3 = 0?
-2, 0, 1/3
Let q be ((-1)/(-10))/(5/(-8260)). Let t = -164 - q. Let t*l - 4/5 - 2/5*l**2 = 0. Calculate l.
1, 2
Let j(l) be the first derivative of 0*l + 4/3*l**3 - 12*l**2 + 9. Factor j(s).
4*s*(s - 6)
Let x(w) be the second derivative of -1/5*w**5 + 0*w**2 + 0 + 0*w**4 + 0*w**3 - 2/21*w**7 + 4/15*w**6 - w. Factor x(f).
-4*f**3*(f - 1)**2
Let o(j) be the second derivative of -j**5/60 + j**4/4 - 4*j**3/3 - 2*j**2 - 3*j + 13. Let r(i) be the first derivative of o(i). Factor r(n).
-(n - 4)*(n - 2)
Find o, given that -8/3*o + 0 + 6*o**2 - 4/3*o**3 = 0.
0, 1/2, 4
Let y(j) = 10*j**3 + 2*j**2 + 3*j + 3. Let k(h) = 10*h**3 + h**2 + 2*h + 2. Let w(z) = 6*k(z) - 4*y(z). Factor w(d).
2*d**2*(10*d - 1)
Let q = -129014/5 + 25804. Determine o so that -4/15*o - 2/3*o**3 + 14/15*o**5 + q*o**2 - 6/5*o**4 + 0 = 0.
-1, 0, 2/7, 1
Let c(s) = -20*s**2 + 1445*s + 100820. Let z(d) = -d**2 + d. Let m(i) = -c(i) + 25*z(i). Determine u, given that m(u) = 0.
-142
Let 15*k**3 + 5*k**4 - 6*k - 2*k - 6*k - 6*k = 0. Calculate k.
-2, 0, 1
Suppose -2*q + 26 = k - 7*q, 4*q = 2*k - 22. Let d be 5/(-10)*k*(-4)/6. Let d*p**4 + p**3 + 0 + p**2 + 1/3*p = 0. What is p?
-1, 0
Let a be ((-832)/6)/(35/21). Let k = a - -84. Let 2/5*u**2 + 0*u + 2/5*u**4 + 0 - k*u**3 = 0. What is u?
0, 1
Suppose m = -3*v + 32, 5*v - 3*m - 15 - 57 = 0. Suppose -b - 3 = -8. Factor -16*t**3 + 2*t + 5*t**b - 3*t**5 + v*t**3.
2*t*(t - 1)**2*(t + 1)**2
Let j(d) be the second derivative of d**5/45 - 5*d**4/9 + 50*d**3/9 - 250*d**2/9 + 81*d. Determine a so that j(a) = 0.
5
Let c(d) be the third derivative of 0 + 1/15*d**5 + 1/12*d**4 + 0*d**3 + 0*d + 9*d**2 + 1/60*d**6. Solve c(t) = 0 for t.
-1, 0
Let h(w) be the first derivative of 3/20*w**4 + 0*w**3 - 11 + 0*w + 0*w**2. Factor h(p).
3*p**3/5
Let u be 0/(-1) + 2*-2. Let t(z) = -z**2 - z - 11. Let m(a) = -29 + 9 + 14 + 4. Let p(i) = u*t(i) + 22*m(i). Factor p(k).
4*k*(k + 1)
Let i(b) be the first derivative of 2*b**3/3 + 84*b**2 + 3528*b + 95. Factor i(u).
2*(u + 42)**2
Let y(i) = -i**3 + 8*i**2 - 5*i + 3. Let d be y(6). Factor -8*q**2 - 8*q**2 - 5*q**3 - 14*q**2 - d*q.
-5*q*(q + 3)**2
Let k(x) be the third derivative of 0*x + 3/2*x**4 + 2/5*x**5 + 0 + 0*x**3 + 4*x**2 + 1/30*x**6. Factor k(h).
4*h*(h + 3)**2
Let g = 9430 + -66008/7. Determine z, given that 0 + 8/7*z + g*z**2 = 0.
-4, 0
Let v(y) be the second derivative of 0 + 0*y**3 + 1/20*y**5 + 6*y - 1/12*y**4 + 0*y**2. Find r such that v(r) = 0.
0, 1
Let w(p) = 12*p**2 + 122*p + 281. Let g(l) = -2*l**2 - 20*l - 47. Let z(m) = 34*g(m) + 6*w(m). Factor z(o).
4*(o + 2)*(o + 11)
Suppose -718 + 706 = -6*o. Let 1/4*v**4 + 0 - v**3 - 1/2*v + 5/4*v**o = 0. What is v?
0, 1, 2
Determine s so that 6*s**2 + 3/5*s**3 + 69/5*s + 42/5 = 0.
-7, -2, -1
Let q(t) be the first derivative of t**5/70 - t**4/21 + 31*t + 20. Let c(w) be the first derivative of q(w). Determine f, given that c(f) = 0.
0, 2
Let j(x) be the second derivative of 5*x**4/12 + 5*x**3/3 - 4*x + 3. Let j(h) = 0. What is h?
-2, 0
Let d(l) be the first derivative of -l**4/22 - 26*l**3/33 - 39*l**2/11 - 54*l/11 - 216. Factor d(v).
-2*(v + 1)*(v + 3)*(v + 9)/11
Let p(u) = 0 + 1 - 3 - u - 6. Let c be p(-10). Factor -4*t**c + 6*t