- 2/5*r**3 - l*r - 9/5*r**2 - 1/30*r**4. Factor h(w).
-2*(w + 3)**2/5
Suppose j = -4*j + 60. Suppose j*x = 16*x. Factor 9/5*a**5 + 0 + 6/5*a**2 + 21/5*a**3 + 24/5*a**4 + x*a.
3*a**2*(a + 1)**2*(3*a + 2)/5
Factor 76/7*j**2 - 46/7*j**3 + 440/7*j + 400/7 + 2/7*j**5 - 8/7*j**4.
2*(j - 5)**2*(j + 2)**3/7
Let a be -7*(-7 - -8) - (-15)/2. What is u in u + a*u**2 - u**3 - 1/2*u**4 + 0 = 0?
-2, -1, 0, 1
Let d(q) be the first derivative of -q**3/12 + 3*q**2/4 - 9*q/4 + 31. Let d(a) = 0. Calculate a.
3
Let b(r) = 12*r - 19. Let w be b(8). Factor s**4 - 77 + w + 4*s**4.
5*s**4
Let i(r) be the third derivative of -r**6/120 + r**5/240 + 3*r**4/8 - 3*r**3/8 + 3*r**2 - 28*r. Solve i(p) = 0.
-3, 1/4, 3
Let p(b) = -16*b**3 + 8*b**2 + 80*b - 72. Let g(w) = w**4 - w**3 - w**2 + w. Let a(y) = 4*g(y) + p(y). Factor a(h).
4*(h - 3)**2*(h - 1)*(h + 2)
Let q = -942 + 944. Factor -2/5 + 8/5*k + 4/5*k**3 - 2*k**q.
2*(k - 1)**2*(2*k - 1)/5
Suppose -271 + 271 = -113*i. Factor 1/4*h**2 + h + i.
h*(h + 4)/4
Let s(g) be the third derivative of -841*g**7/10 - 5829*g**6/20 - 39589*g**5/140 + 201*g**4/14 - 2*g**3/7 - 351*g**2. Factor s(n).
-3*(n + 1)**2*(203*n - 2)**2/7
Suppose -h + 24 = -0. Let l = h - 18. Suppose w**2 - l + w + 6 = 0. What is w?
-1, 0
Suppose 11 + 1 = -5*x + 4*z, -3*z + 9 = x. Let t(r) be the second derivative of 8*r - 1/130*r**5 + 1/39*r**3 - 1/78*r**4 + 1/13*r**2 + x. Solve t(m) = 0.
-1, 1
Let u(d) be the second derivative of d**7/3780 - d**6/360 + d**5/90 - 5*d**4/4 - 17*d. Let x(m) be the third derivative of u(m). Factor x(q).
2*(q - 2)*(q - 1)/3
Suppose 2*w + 25 = 3*j + 2*j, 25 = w + 5*j. Factor s + 5*s - 11*s**3 + w*s**3 - 3*s**2 + 8*s**3.
-3*s*(s - 1)*(s + 2)
Let p = 5 + -5. Suppose p = a + 10*a - 22. Find n such that -1/2*n**3 - 6*n - 3*n**a - 4 = 0.
-2
Let z = 66 - 67. Let q(s) = -6*s**2 - 6*s. Let b(g) = g**2 - g. Let p(j) = z*q(j) - 2*b(j). What is n in p(n) = 0?
-2, 0
Let b(o) be the first derivative of -1/28*o**4 - 11/14*o**2 - 6/7*o - 39 - 2/7*o**3. Suppose b(a) = 0. Calculate a.
-3, -2, -1
Let m be 2*(-6)/(-189)*9. Let d(y) be the first derivative of 16/7*y**3 - m*y**4 + 2/35*y**5 + 32/7*y - 7 - 32/7*y**2. Factor d(w).
2*(w - 2)**4/7
Let s be (-124)/(-372) - (0/1 - 7/33). Suppose -10/11*p + 2/11 + 4/11*p**3 + s*p**5 - 14/11*p**4 + 12/11*p**2 = 0. Calculate p.
-1, 1/3, 1
Let j(m) be the third derivative of -m**8/336 - m**7/30 - 17*m**6/120 - 17*m**5/60 - m**4/4 - 105*m**2. Factor j(g).
-g*(g + 1)**2*(g + 2)*(g + 3)
Let k(d) be the third derivative of d**5/630 - 11*d**4/126 + d**3/3 + 4*d**2 - 4. Factor k(n).
2*(n - 21)*(n - 1)/21
Let z(j) be the first derivative of 6 - 4*j**3 + 8*j**2 - 2*j**4 + 16*j + 4/5*j**5. Factor z(m).
4*(m - 2)**2*(m + 1)**2
Let d(a) = 2*a**2 + 16*a + 5. Let m be d(-11). Suppose -m*q**2 + 3 - 69*q**2 + 122*q**2 + 15*q = 0. What is q?
-1/6, 1
Let q be (-1 - 4/(-2))/(17/68). Suppose 34*g**3 + 2*g**5 + 2*g - 43*g**3 + 4*g**2 - g + 3*g - g**q = 0. What is g?
-2, -1/2, 0, 1, 2
Let b(m) be the second derivative of -m**4/54 + 10*m**3/27 - 7*m**2/3 - 9*m. Let b(a) = 0. Calculate a.
3, 7
Let y be -24*19/(-152)*(-4)/(-6). Suppose -2*q + 3 + 1/3*q**y = 0. What is q?
3
Let q = 55 + -52. Let q*b**3 - b + 8 - 10*b**2 - 4*b + 9*b = 0. Calculate b.
-2/3, 2
Let k(o) be the third derivative of o**7/42 - o**6/3 + 2*o**5 - 20*o**4/3 + 40*o**3/3 - 132*o**2. Factor k(r).
5*(r - 2)**4
Let k(r) be the second derivative of r**4/28 - r**3/7 - 9*r**2/14 + 51*r - 3. Factor k(v).
3*(v - 3)*(v + 1)/7
Let h(r) be the first derivative of -6*r**5/5 - 15*r**4/4 - 4*r**3 - 3*r**2/2 + 96. Factor h(s).
-3*s*(s + 1)**2*(2*s + 1)
Suppose -23*j = -90 - 25. Solve 2/5*t**3 - 4/15*t**2 + 0*t + 0*t**4 - 2/15*t**j + 0 = 0 for t.
-2, 0, 1
Let c(b) = -4*b**3 - 2 - 8*b**5 + 6 - 8*b**4 - 6*b**3 - 6*b**3. Let j(s) = -7*s**5 - 9*s**4 - 15*s**3 - s**2 + 3. Let t(a) = 3*c(a) - 4*j(a). Factor t(d).
4*d**2*(d + 1)**3
Suppose 3*z - 28 = k, -3*k = 11018*z - 11021*z + 24. Determine m so that 16/7*m**k - 2/7*m**3 - 32/7*m + 0 = 0.
0, 4
Factor 14*s**2 + 4*s + 13*s**3 + 6*s**2 + 6*s**4 + 3*s**2 + s**5 - 11*s**2.
s*(s + 1)**2*(s + 2)**2
Let d(z) be the third derivative of z**7/1155 - 14*z**6/165 + 52*z**5/55 - 152*z**4/33 + 400*z**3/33 + 64*z**2 - 3*z. Suppose d(w) = 0. What is w?
2, 50
Suppose -110*h = 85*h - 49*h - 292. Factor 4*u - 8/5*u**h - 16/5 + 1/5*u**3.
(u - 4)*(u - 2)**2/5
Let q(j) be the second derivative of -j**7/12600 - j**6/3600 + j**5/300 + 5*j**4/3 + 22*j. Let l(p) be the third derivative of q(p). Factor l(t).
-(t - 1)*(t + 2)/5
Let b = -92/3 - -3767/120. Let t = -1/8 + b. Factor 3/5 + 9/5*w + 9/5*w**2 + t*w**3.
3*(w + 1)**3/5
Let y be 12/(-24) + 5/2. Let z be (12/(-2))/((-3)/y). Find c, given that -c + z*c**2 - 3*c - c**2 - 2*c = 0.
0, 2
Let k(p) be the third derivative of -3*p**2 + 0*p + 4/11*p**3 + 0*p**4 + 0 - 1/110*p**5. Factor k(f).
-6*(f - 2)*(f + 2)/11
Let g(r) = 4*r**4 - 7*r**3 + 3*r**2. Let b(y) = -124 + 124 - 2*y**3 - y**4 + 3*y**3. Let d(u) = 5*b(u) + g(u). Solve d(w) = 0.
-3, 0, 1
Let m(y) be the second derivative of y**7/70 + y**6/20 + y**5/20 + 7*y**2 + 14*y. Let t(z) be the first derivative of m(z). Factor t(f).
3*f**2*(f + 1)**2
Let d(o) = 8 + 12*o**2 + 457*o + 5 - 5 + 6*o**3 - 447*o. Let s(r) = r**3 + r**2 + 1. Let p(n) = -d(n) + 4*s(n). Determine j, given that p(j) = 0.
-2, -1
Let o(h) = -4*h**4 + h**3 + h**2 + 15*h**4 - 10*h**4. Let u(i) = 8*i**4 + 6*i**3 + 6*i**2. Let r(f) = -6*o(f) + u(f). Determine p so that r(p) = 0.
0
Factor 3*i**5 - 6797*i**3 + 3425*i**3 - 33*i**4 + 3402*i**3.
3*i**3*(i - 10)*(i - 1)
Determine w so that -13/12*w**2 - 1/3 + 17/12*w**4 - 1/3*w**5 + 5/3*w - 4/3*w**3 = 0.
-1, 1/4, 1, 2
Let m(g) be the second derivative of -22/3*g**4 - 34/15*g**6 + 16/3*g**3 + 0 - 5*g + 28/5*g**5 - 2*g**2 + 8/21*g**7. Let m(k) = 0. Calculate k.
1/4, 1
Let s be (-6)/(-9) - (28/(-3))/4. Factor -2*v + 2*v - 4*v - 2*v**5 + 2*v - 2 + 4*v**s + 4*v**2 - 2*v**4.
-2*(v - 1)**2*(v + 1)**3
Let m(f) be the first derivative of 1/3*f**3 + 9 - 1/12*f**4 + 5/3*f + 3/2*f**2. Suppose m(g) = 0. What is g?
-1, 5
Let l(k) be the second derivative of -k**5/4 - 10*k**4 - 115*k**3/6 + 407*k. Determine t, given that l(t) = 0.
-23, -1, 0
Let h(a) be the first derivative of a**3/6 - 27*a**2/4 + 25*a + 751. What is p in h(p) = 0?
2, 25
Let x(j) be the first derivative of -5*j**3/3 - 775*j**2 - 120125*j - 517. Solve x(y) = 0 for y.
-155
Suppose 6 = 4*z - 6. Find c such that -z*c**3 + 7*c - 11*c - 4*c**2 - 11*c + 16*c**2 + 6 = 0.
1, 2
Let b(k) be the first derivative of 1/20*k**5 - 6 + k**3 - 3/8*k**4 + 3/4*k - 5/4*k**2. Let b(a) = 0. Calculate a.
1, 3
Let r(q) be the first derivative of q**5/15 + 5*q**4/3 + 50*q**3/3 - 13*q**2/2 + 1. Let a(x) be the second derivative of r(x). Factor a(y).
4*(y + 5)**2
Let t(x) be the second derivative of -x**8/252 + 2*x**7/315 - 26*x**2 - 33*x. Let z(d) be the first derivative of t(d). Solve z(u) = 0 for u.
0, 1
Let m(h) = -3*h**3 + 18*h**2 + 4. Let u be m(6). Let 9*x**3 + x**3 - 4*x**u - 3*x**3 + 8*x - 4*x**5 + 5*x**3 + 20*x**2 = 0. What is x?
-1, 0, 2
Let s(z) be the first derivative of -4*z - 3/2*z**2 + 18 + 1/3*z**3. Factor s(b).
(b - 4)*(b + 1)
Let x(c) be the first derivative of -14 - 2/3*c**6 - 4/5*c**5 + 2*c**4 + 0*c**2 + 0*c + 0*c**3. Find u, given that x(u) = 0.
-2, 0, 1
Let t(g) = -15*g**2 + 225*g. Let h(x) be the first derivative of 2*x**3/3 - 16*x**2 + 48. Let d(y) = 20*h(y) + 3*t(y). Factor d(n).
-5*n*(n - 7)
Suppose 132*f = 2*h + 133*f - 2, 2 = -2*h + f. Factor 4/17*z**2 + 0*z**3 - 2/17 - 2/17*z**4 + h*z.
-2*(z - 1)**2*(z + 1)**2/17
Suppose -4*t + 18 - 154 = 0. Let m = -18 - t. Factor m*v**2 - 8*v + 16*v**2 - 4*v**2.
4*v*(7*v - 2)
Suppose -16 = -9*l + 11. Let k(a) be the first derivative of -12*a**2 - a**l + 12*a - 3 + 6*a**4 - 9/5*a**5. What is q in k(q) = 0?
-1, 2/3, 1, 2
Suppose 19*t = 14*t + 10. Let 4*w**t - 62 + 13 - 16*w + 1 = 0. Calculate w.
-2, 6
Suppose 0 = 3*b + b - 5*c + 9, -1 = -c. Let d be b*6*(-8)/24. Find z such that 4*z**2 + d*z - 3*z**2 - 6*z + 7*z**2 = 0.
0, 1/2
Let c be (10 - 4)*2/4. Let t be 16/c*9/6. Factor 17 - 9 + 4*h**5 - t.
4*h**5
Let m(p) = 5*p**4 + 1066*p**3 - 23196*p**2 + 43344*p - 21151. Let t(h) = h**4 + 178*h**3 - 3866*h**2 + 7224*h - 3525. Let d(a) = -6*m(a) + 34*t(a). Factor d(f).
4*(f - 4