5
Let v(b) = -2*b**4 + 185*b**3 + 676*b**2 + 504*b - 5. Let j(f) = -3*f**4 + 186*f**3 + 675*f**2 + 504*f - 6. Let u(r) = -5*j(r) + 6*v(r). Solve u(o) = 0 for o.
-56, -3, -1, 0
Factor 167*w - 97*w**2 - 117*w - 28*w**2 - 5.
-5*(5*w - 1)**2
Let x(b) be the first derivative of 3/4*b**4 - 1/6*b**3 + 14 - 1/2*b**5 + 0*b**2 + 0*b. Factor x(q).
-q**2*(q - 1)*(5*q - 1)/2
Suppose -79*b - 5*h = -78*b + 6, 0 = 7*b - 3*h - 34. Factor 0 - 2/3*d**3 - 1/3*d**2 + 0*d - 1/3*d**b.
-d**2*(d + 1)**2/3
Let u = 4671 - 4668. Determine z so that 0*z**u + 0 + 1/2*z**4 - z - 3/2*z**2 = 0.
-1, 0, 2
Let q(n) be the second derivative of n**4/12 - n**3/2 - 3*n**2 - n. Let h be q(6). Factor 9 + h*o + 12*o**2 - 29*o - 22*o.
3*(o - 3)*(4*o - 1)
Let f = -33 - -35. Solve 12*q**2 - f*q**2 - 4*q**3 - 6*q**2 = 0 for q.
0, 1
Let h(s) = 2*s**3 - 50*s**2 + 94*s - 44. Let n be h(23). Factor -2/13*f**n - 8/13*f + 0 + 2/13*f**4 + 8/13*f**3.
2*f*(f - 1)*(f + 1)*(f + 4)/13
Suppose -56*f**4 - 897*f**3 - 468*f**2 - 868*f**2 + 3*f**5 - 784*f - 4*f**5 - 2*f**4 - 288*f**2 = 0. What is f?
-28, -1, 0
Factor -18/7*r**2 + 24/7*r + 3/7*r**3 + 0.
3*r*(r - 4)*(r - 2)/7
Determine l so that 20*l + 167 + 4489*l**2 - 4494*l**2 + 58 = 0.
-5, 9
Let q(u) be the second derivative of -u**7/126 - u**6/90 + 11*u**5/60 - 7*u**4/36 - 5*u**3/9 + 4*u**2/3 + 12*u - 9. Solve q(f) = 0 for f.
-4, -1, 1, 2
Let z = -8 - -11. Suppose 3*f + 5*y = 110 + 21, -4*y = z*f - 136. Solve d + 14*d**4 + 16*d**2 - 9*d - 14*d**3 + f*d**3 = 0.
-2, -1, 0, 2/7
Suppose -7*a + 551 - 537 = 0. Factor 2/21 - 2/21*w**a + 0*w.
-2*(w - 1)*(w + 1)/21
Let v be (2 - -1)*1/2 - (-308)/616. Find f, given that 4/11 + 2/11*f**3 - 2/11*f - 4/11*f**v = 0.
-1, 1, 2
Let f = 786/205 + -108/41. Factor -f*w - 2/5*w**2 - 4/5.
-2*(w + 1)*(w + 2)/5
Factor 0 + 2/21*m**2 - 10/21*m.
2*m*(m - 5)/21
Let m(q) = -9*q**2 - 22*q - 36. Let v(h) = 16*h**2 - 6*h**2 - 2*h - 1 - 9*h**2 + 0. Let f(l) = m(l) + 4*v(l). Factor f(a).
-5*(a + 2)*(a + 4)
Let 50/3*x**2 + 224/3*x - 392 + 2/3*x**3 = 0. Calculate x.
-14, 3
Solve -25/3*s**5 - 265/6*s**4 + 18 + 213/2*s**2 + 90*s - 94/3*s**3 = 0.
-3, -2/5, 3/2
Let f be (-3)/(-8) + (-63)/(-24). Factor -4*c**3 - 635*c - 12 - 26*c**f + 3*c**5 - 60*c**2 + 590*c.
3*(c - 4)*(c + 1)**4
Factor 61666*z**4 - z**5 - 7*z - 17*z**2 - 24*z**3 - 61676*z**4 - 5*z**2.
-z*(z + 1)**3*(z + 7)
Suppose -8*m**2 + 3*m**2 + 445*m + 28343 + 8*m**2 - 2951 + 107*m = 0. What is m?
-92
Let p(c) be the third derivative of 3*c**6/28 - 33*c**5/70 + 4*c**4/21 + 4*c**3/21 + 79*c**2 + 2*c. Solve p(i) = 0 for i.
-2/15, 1/3, 2
Let z(y) be the third derivative of y**6/300 - 11*y**5/50 + 24*y**4/5 - 256*y**3/15 - 58*y**2. Determine h, given that z(h) = 0.
1, 16
Let y(m) be the third derivative of m**6/720 + m**5/48 - m**4/8 + 11*m**3/6 - 39*m**2. Let w(n) be the first derivative of y(n). Let w(s) = 0. Calculate s.
-6, 1
Let i be 5282/114 + 2/(-6). Determine j, given that -14*j - 150*j - i*j - 1259*j**2 - 946*j**2 - 5 = 0.
-1/21
Let s(q) = q**3 + 2*q**2 - 4*q - 5. Let l be s(-3). Let i be l*2/6 - 112/(-42). Factor 0 - 3/4*t + 3/4*t**i.
3*t*(t - 1)/4
Let r(w) be the third derivative of -2*w**7/75 - w**6/15 - w**5/25 + 3*w**2 - 7*w. Factor r(o).
-4*o**2*(o + 1)*(7*o + 3)/5
Let p = -186 + 193. Let d(l) be the third derivative of -6*l**2 + 1/224*l**8 + 0 - 1/40*l**5 + 0*l**3 - 1/24*l**4 + 0*l + 1/80*l**6 + 1/60*l**p. Factor d(b).
b*(b + 1)**3*(3*b - 2)/2
Suppose 0*j**2 - 4*j**4 - j + 3*j**4 - 2 + 12*j**3 + 3*j**2 - 11*j**3 + 0*j = 0. Calculate j.
-1, 1, 2
Suppose 0 = k - 3*z + 3, 3*z = 4*k - z - 4. Suppose 220*t = 198*t. Determine d, given that t*d**2 - 3/7*d**k + 3/7*d + 0 = 0.
-1, 0, 1
Let q = 24754/33 + -750. Let f(h) be the first derivative of -3/11*h**2 + 1/11*h**4 + 2/11*h + q*h**3 - 6/55*h**5 + 1/33*h**6 + 3. Factor f(w).
2*(w - 1)**4*(w + 1)/11
Let f(v) = 4*v**2 + 3*v + 2. Suppose 0*w - 2*w = 2. Let s be f(w). Factor -m - 2 + 5*m**s + 11*m**2 + 5*m**3 + 0*m.
(m + 1)*(2*m + 1)*(5*m - 2)
What is w in 1408*w**3 - 544*w - 148*w**2 + 186 - 714 - 1412*w**3 = 0?
-33, -2
Suppose -16 = -5*f + a, 0 = f - 194*a + 195*a - 8. Suppose 0*v**f + 1/2*v**3 + 0 - 1/4*v - 1/4*v**5 + 0*v**2 = 0. What is v?
-1, 0, 1
Let a(z) be the third derivative of z**5/210 - z**4/42 + z**3/21 + 6*z**2 - 6*z. Find j such that a(j) = 0.
1
Let z(n) be the second derivative of -3/110*n**5 + 0*n**2 - 6*n + 0*n**3 + 1/33*n**4 + 1/165*n**6 + 0. Let z(l) = 0. What is l?
0, 1, 2
Let r(t) = t**2 - 15*t + 40. Let u be r(10). Let j be ((-14)/63)/(5/u). Factor 0 + 2/9*g**4 - 8/9*g**3 + 10/9*g**2 - j*g.
2*g*(g - 2)*(g - 1)**2/9
Suppose 10*j - 7*j + 3*n = 3, 3*j - 3*n - 15 = 0. Suppose 64/3 + 352/3*b**2 - 380/3*b**4 + 256/3*b**j + 100/3*b**5 - 320/3*b = 0. What is b?
-1, 2/5, 2
Solve 4 - 7 + 5*f**4 + 3 + 7*f**2 - 20*f**3 + 8*f**2 = 0.
0, 1, 3
Suppose 2*z = -121 + 131. Let l(u) be the first derivative of -2/15*u**3 + 0*u + 0*u**2 - 2/25*u**z - 1/5*u**4 + 10. Determine k so that l(k) = 0.
-1, 0
Let m = 22112 - 22109. Factor 2/21*y**m + 2/7*y - 2/7*y**2 - 2/21.
2*(y - 1)**3/21
Let l(f) be the second derivative of -f**9/11340 + f**8/3360 - f**6/1080 - 7*f**4/12 + 5*f. Let i(z) be the third derivative of l(z). Factor i(j).
-2*j*(j - 1)**2*(2*j + 1)/3
Let b(z) be the first derivative of -20 - 3/2*z - 49/8*z**2 - z**4 - 26/3*z**3. Factor b(d).
-(d + 6)*(4*d + 1)**2/4
Let -2/7*w**3 - 2/7*w**5 + 8/7*w**4 + 16/7 - 20/7*w**2 + 8/7*w = 0. What is w?
-1, 2
Factor 20*c**3 - 11*c**5 + 20*c**5 - 28*c + 4*c**3 - 20*c**4 + 8*c**2 - 5*c**5 + 12.
4*(c - 3)*(c - 1)**3*(c + 1)
Factor 10/3*o**3 + 0*o + 2/3*o**4 + 0 + 0*o**2.
2*o**3*(o + 5)/3
Let u(o) be the second derivative of -o**7/420 + o**6/90 + 19*o**3/6 + 26*o. Let j(i) be the second derivative of u(i). Suppose j(q) = 0. What is q?
0, 2
Solve 55/6 + 19/2*t**2 + 37/2*t + 1/6*t**3 = 0 for t.
-55, -1
Let k be ((-12)/42)/((-72)/42). Solve -5/6*c + 1/3 + 2/3*c**3 + k*c**5 - 2/3*c**4 + 1/3*c**2 = 0 for c.
-1, 1, 2
Let q be (10/(-4))/((-18)/9). Factor 5/4 - 5/4*n**2 + q*n**3 - 5/4*n.
5*(n - 1)**2*(n + 1)/4
Suppose 384*g + 54*g**3 + 206*g**4 - 110*g**2 - 415*g**4 - 178*g**2 + 206*g**4 = 0. What is g?
0, 2, 8
Let n be 14/(-4) + 35/(-14) + 3. Let m be (-44)/52 - n - 2. Factor 2/13*u**3 - 2/13*u + 0 + 2/13*u**2 - m*u**4.
-2*u*(u - 1)**2*(u + 1)/13
Let b(w) be the first derivative of -5*w**3/3 - 15*w**2 + 35*w - 22. Factor b(v).
-5*(v - 1)*(v + 7)
Let u be 27/(-18) + (-18)/(-4). Let q(i) = -i - 2. Let n be q(-5). Factor -20*h - u - 3*h**3 - 21*h**2 - 6*h**n + 5*h.
-3*(h + 1)**2*(3*h + 1)
Factor -35 - 40*a**2 - 5/2*a**3 - 145/2*a.
-5*(a + 1)**2*(a + 14)/2
Let h(y) be the third derivative of -8/105*y**7 - 9*y**2 + 0 + 5/6*y**4 - 1/84*y**8 + 2/15*y**5 + 0*y + 4/3*y**3 - 2/15*y**6. Let h(u) = 0. What is u?
-2, -1, 1
Find s, given that -3*s**2 + 352 - 7*s**2 + 9*s**2 - 168*s - 3*s**2 = 0.
-44, 2
Let i(o) = -2*o**4 + 9*o**2 - 13*o + 6. Let w = -15 + 9. Let q(u) = -2*u**4 + 10*u**2 - 14*u + 6. Let p = 23 + -19. Let g(f) = p*i(f) + w*q(f). Factor g(v).
4*(v - 1)**3*(v + 3)
Let y(j) be the second derivative of -j**4/4 - j**3/2 - 13*j. Let r(z) = -2*z**2 - 2*z. Let s(i) = -4*r(i) + 3*y(i). Factor s(l).
-l*(l + 1)
Suppose 3*g + 1 = 7. Determine q so that 3*q**3 + 3*q**g + q**3 - 7*q**3 = 0.
0, 1
Let d = -318392 + 70364780/221. Let a = 14/17 - d. Factor -6/13*q**2 + a*q**3 + 4/13*q + 0.
2*q*(q - 2)*(q - 1)/13
Suppose 4 = 5*t - 4*t. Suppose -10 = -t*i - 2. Factor 0*o**4 - 3*o**3 + i*o**3 - 2*o**2 + o**4 + 2*o**3.
o**2*(o - 1)*(o + 2)
Factor -9/4 - 3*h - 3/4*h**2.
-3*(h + 1)*(h + 3)/4
Let h(o) = 3*o**2 + 45*o + 27. Let m(s) = s**2 + 23*s + 13. Let u be 2*-3*5/(-10). Let q(p) = u*h(p) - 5*m(p). What is j in q(j) = 0?
-4, -1
Let m(t) be the second derivative of t**6/15 - t**5/5 - t**4/2 + 8*t**3/3 - 4*t**2 + 4*t + 23. Factor m(c).
2*(c - 2)*(c - 1)**2*(c + 2)
Determine b, given that -6*b + 49*b - 22*b + 0*b**2 + 3*b**2 + 18 = 0.
-6, -1
Let z(u) be the third derivative of u**10/6048 - u**8/1344 - 13*u**4/24 - 4*u**2. Let p(d) be the second derivative of z(d). Determine q, given that p(q) = 0.
-1, 0, 1
Let h be 2/(-40) - 2*3/(-24). Let l(r) be the second derivative of 1/3*r**3 + 1/9*r**4 - 1/3*r**2 + 0 + 3*r - 1/45*r**6 - h*r**5 + 1/21*r**7. Solve l(q) = 0.
-1, 1/3, 1
Find u, given that -148*u**2 - 222 + 304*u**2 - 15