2*f**4 + 2*f**3 + 2*f**2 - 3. Let v(d) = 3*r(d) + 7*z(d). Factor v(j).
-j**2*(j - 1)*(j + 2)
Factor 0 + 2/7*p**4 - 2/7*p - 2/7*p**2 + 2/7*p**3.
2*p*(p - 1)*(p + 1)**2/7
Let s(z) be the third derivative of -1/24*z**4 - 1/60*z**5 + 0*z**3 + 0*z + 0 + 2*z**2. Factor s(i).
-i*(i + 1)
Let x(h) be the third derivative of h**7/315 - 4*h**6/315 - h**5/210 + 4*h**4/63 - 4*h**3/63 - 2*h**2. Let x(m) = 0. Calculate m.
-1, 2/7, 1, 2
Let p(l) = 10*l - 6. Suppose -4*r = -v - 18, -5*r + 16 = 3*v - v. Let u = r + 1. Let n(j) = j**2 + 21*j - 11. Let q(d) = u*p(d) - 2*n(d). Solve q(f) = 0.
2
Let n(y) be the third derivative of -y**6/180 - y**5/30 - y**4/12 - y**3/3 + 2*y**2. Let h(g) be the first derivative of n(g). Factor h(i).
-2*(i + 1)**2
Let w(z) be the third derivative of -1/30*z**5 + 0 - 1/2*z**4 + z**2 - 3*z**3 + 0*z. Factor w(q).
-2*(q + 3)**2
Let b = 88 - 439/5. Find w, given that -4/5*w - b*w**2 - 4/5 = 0.
-2
Let q(w) be the third derivative of -w**6/600 - w**5/150 + 6*w**2. Factor q(z).
-z**2*(z + 2)/5
Suppose 0 = -4*y + 5*g + 6, -y - 5*g - 7 = 4. Let q be 6/1 - (-3)/y. Solve 0*n - 1/4*n**q + 0 + 1/4*n**2 = 0 for n.
0, 1
Let n(f) be the second derivative of 3*f**7/70 - f**6/40 - f**5/10 - 2*f**2 + 6*f. Let p(g) be the first derivative of n(g). Factor p(c).
3*c**2*(c - 1)*(3*c + 2)
Let s(z) = z**3 + 18*z**2 - 21*z - 38. Let b be s(-19). Factor -2/11 + b*d + 2/11*d**2.
2*(d - 1)*(d + 1)/11
Suppose 13*x - 21*x = 0. Factor -2/3*k**3 + 0*k + 0*k**2 + 0*k**4 + 2/3*k**5 + x.
2*k**3*(k - 1)*(k + 1)/3
Let f(o) be the second derivative of 3/20*o**5 + 1/2*o**3 + 0 + 9*o - 1/2*o**4 + 0*o**2. Factor f(q).
3*q*(q - 1)**2
Let w = -51 + 205/4. Suppose -r - 3*t + 11 = 3, t = r. Determine p, given that -1/2 - 3/4*p - w*p**r = 0.
-2, -1
Find c such that 25*c**2 - 5*c**4 - 18*c**3 - 3*c**5 - 3*c - 13*c**2 + 17*c**4 = 0.
0, 1
Let w(r) be the third derivative of r**8/1344 - r**7/105 + r**6/20 - 2*r**5/15 + r**4/6 - 9*r**2. Factor w(d).
d*(d - 2)**4/4
Let k = 5 - 0. Suppose 8*a = k*a. Find x, given that a + 1/4*x**2 + 0*x + 1/4*x**3 = 0.
-1, 0
Let n = -117 + 1055/9. Factor 0*v + 0 - 4/9*v**3 + 2/9*v**2 + n*v**4.
2*v**2*(v - 1)**2/9
Suppose 3*f - 6 = 6*f. Let w be (-8)/10*5/f. Let w*r**3 + r**3 - r**3 = 0. Calculate r.
0
Let o(c) = c**3 + c**2 + c. Let s(b) = b - 1. Let x be s(6). Let r(i) = -6*i**3 - 6*i**2 - 5*i. Let w(g) = x*o(g) + r(g). Let w(y) = 0. Calculate y.
-1, 0
Suppose -14*w + 125 - 83 = 0. Solve -8/9 + 0*m + 2/3*m**2 + 2/9*m**w = 0 for m.
-2, 1
Suppose -12*h + 35/2*h**4 + 12*h**3 - 31/2*h**2 - 2 = 0. What is h?
-1, -2/5, -2/7, 1
Suppose -2*y - 14 = -g, -2*g + y + 18 = -y. Suppose -g = 2*t - 4*t. Let 8/3*m**4 + 2*m - 10/3*m**t + 2/3 - 2*m**3 = 0. What is m?
-1, -1/4, 1
Let x(u) be the second derivative of u**6/10 - 9*u**5/20 + u**4/4 + 3*u**3/2 - 3*u**2 + 9*u. Factor x(w).
3*(w - 2)*(w - 1)**2*(w + 1)
Let i = -44 - -120. Let b = -530/7 + i. Let 0 - 2/7*m**2 + 2/7*m**4 - b*m + 2/7*m**3 = 0. Calculate m.
-1, 0, 1
Let o(z) be the third derivative of -z**6/360 - z**5/36 + z**4/72 + 5*z**3/18 - 28*z**2. Factor o(q).
-(q - 1)*(q + 1)*(q + 5)/3
Suppose 2*f = -9 + 9. Let o(v) be the third derivative of -2/15*v**4 + 0 - 4/15*v**3 - 1/300*v**6 - 1/30*v**5 + 2*v**2 + f*v. Let o(j) = 0. What is j?
-2, -1
Factor 0*f**2 + 21/4*f**5 + 0*f + 0*f**3 + 0 + 3/2*f**4.
3*f**4*(7*f + 2)/4
Let d(v) be the second derivative of 0*v**4 + 0*v**6 + 3*v - 3/10*v**5 + 1/14*v**7 + 0*v**2 + 0 + 1/2*v**3. Factor d(g).
3*g*(g - 1)**2*(g + 1)**2
Solve -1500/7*d - 1875/7 - 450/7*d**2 - 60/7*d**3 - 3/7*d**4 = 0.
-5
Let o(z) be the first derivative of 2*z**6/9 + 2*z**5/5 - z**4/6 - 2*z**3/3 - z**2/3 - 11. Suppose o(y) = 0. Calculate y.
-1, -1/2, 0, 1
Suppose 0 = -5*f - 5, -2*w - 2 + 4 = 4*f. Find u, given that -2/7 - 2/7*u**4 - 8/7*u**w - 12/7*u**2 - 8/7*u = 0.
-1
Let i be 1/5 + 34/5. Suppose -9*o + 3 = -8*o. Suppose i*b**o + b**4 - 2*b**3 - b**2 - 5*b**4 = 0. Calculate b.
0, 1/4, 1
Suppose 7 = 5*p - 3. Let k(t) be the first derivative of -2/27*t**3 + 0*t**p - 1 + 2/9*t. Factor k(f).
-2*(f - 1)*(f + 1)/9
Let z(x) = 2*x - 21. Let h be z(11). Let w be (-8)/(h + -4 - 4). What is y in -w*y**3 + 2/7*y + 6/7*y**5 - 4/7*y**4 + 4/7*y**2 + 0 = 0?
-1, -1/3, 0, 1
Let a(f) be the second derivative of 0 + 2/5*f**2 + 0*f**4 + 2*f - 1/5*f**3 + 1/50*f**5. Factor a(n).
2*(n - 1)**2*(n + 2)/5
Let p = -4759/35 + 136. Let l(y) be the second derivative of -p*y**6 + 0*y**2 + 0*y**3 + 1/98*y**7 - 2*y + 0 + 3/140*y**5 + 0*y**4. Find a such that l(a) = 0.
0, 1
Let n(u) = -u**5 - 7*u**4 + 6*u**3 + 17*u**2. Let v(j) = j**5 + 4*j**4 - 3*j**3 - 8*j**2. Let d(z) = 2*n(z) + 5*v(z). Factor d(o).
3*o**2*(o - 1)*(o + 1)*(o + 2)
What is q in -2/7*q**2 - 8/7*q - 6/7 = 0?
-3, -1
Let x = 11 - 6. Suppose -5*o + 10 = -x*n, 5*n - o - 4 = n. Factor -2*d**2 + 0*d**2 - 6*d + 4 - n*d**4 + 7*d**3 + d**3 - 2*d**3.
-2*(d - 2)*(d - 1)**2*(d + 1)
Let h(j) be the first derivative of 4*j**5 - 3*j**4 - 8*j**3/3 + 3. Factor h(m).
4*m**2*(m - 1)*(5*m + 2)
Let w be -9*((-10)/6)/5. Factor 31*o + 20*o**3 - w*o - 8 - 36*o**2 + 0*o**4 - 4*o**4.
-4*(o - 2)*(o - 1)**3
Let o be 68/(-170) + ((-64)/30)/(-2). Factor -o*r**3 + 1/3 + 2/3*r - 1/3*r**2.
-(r - 1)*(r + 1)*(2*r + 1)/3
Factor -4 + 11*j**2 - 20*j**2 + 13*j**2.
4*(j - 1)*(j + 1)
Let c(p) = 2*p - 3. Let b be c(3). Factor 5 - b*d**4 + 3*d**4 - 4 + d**4 - 2*d**2.
(d - 1)**2*(d + 1)**2
Factor -5/4*c - 1/4*c**2 - 1.
-(c + 1)*(c + 4)/4
Let h be 0 - (1 - (-17)/(-7)). Suppose -8*l + 40 = 8. Find w such that -10/7*w**l + 4/7*w + h*w**2 + 0 + 2*w**5 - 18/7*w**3 = 0.
-1, -2/7, 0, 1
Let s(q) be the first derivative of 1/12*q**3 + 2 + 0*q + q**2 - 1/120*q**5 + 0*q**4. Let g(d) be the second derivative of s(d). Factor g(k).
-(k - 1)*(k + 1)/2
Let v be (-4)/(-28) - 3/21. Suppose v = -5*q + 3 + 12. Factor 2/9 + 0*x - 2/3*x**4 + 16/9*x**q - 4/3*x**2.
-2*(x - 1)**3*(3*x + 1)/9
Let k(j) be the first derivative of j**7/980 + j**6/315 + j**5/420 + j**3 - 1. Let y(f) be the third derivative of k(f). Factor y(m).
2*m*(m + 1)*(3*m + 1)/7
Let o(s) be the first derivative of -s**4/14 + 8*s**3/21 + s**2/7 - 8*s/7 + 22. Factor o(y).
-2*(y - 4)*(y - 1)*(y + 1)/7
Let t = -10 + 14. Suppose -c + 6 = 1. Suppose -t*w**4 + 3*w**2 - 3*w**2 + 2*w**c - 2*w**3 - 4*w**5 = 0. What is w?
-1, 0
Suppose -4*j + 3*m + 8 = 0, 3*m + 0 = 2*j + 2. Let y = 7 - j. Let -4/5*h**y + 0 + 2/5*h + 2/5*h**3 = 0. Calculate h.
0, 1
Suppose 12*x - 340 + 292 = 0. Suppose -3/2*v**3 - 5/2*v + 1/4*v**x + 3/4 + 3*v**2 = 0. What is v?
1, 3
Let g(w) = 2*w**3 - 4*w**2 + 3*w - 2. Let o be g(2). Factor -12*b**3 + 4*b**5 - 8*b + 17*b**2 - 7*b**4 + 3*b**2 + 3*b**o.
4*b*(b - 1)**3*(b + 2)
Let t = -204959/168 + 1220. Let u(x) be the third derivative of 0*x + t*x**7 - 1/12*x**3 - 1/80*x**5 + 0 + x**2 + 7/96*x**4 - 7/480*x**6. Solve u(v) = 0.
-1, 2/5, 1
Suppose 106*f - 107*f + 5 = 0. Let m(o) be the first derivative of 5/12*o**4 - 1 - 1/15*o**f + 0*o - 8/9*o**3 + 2/3*o**2. Solve m(b) = 0.
0, 1, 2
Let p(g) be the third derivative of -g**7/840 + g**6/120 - g**5/40 + g**4/24 - g**3/24 + 2*g**2. Solve p(q) = 0 for q.
1
Suppose 3 - 1 = 2*x. Let z(p) be the first derivative of 0*p - p**2 - 3/2*p**4 - 2*p**3 - x - 2/5*p**5. Factor z(q).
-2*q*(q + 1)**3
Let g(m) be the first derivative of 0*m - 2/5*m**5 - 1/2*m**4 - 3 + 0*m**2 + 1/3*m**6 + 2/3*m**3. Factor g(v).
2*v**2*(v - 1)**2*(v + 1)
Find l such that 20 + 4*l**3 + 5*l**5 - 25*l**4 + 382*l**2 - 40*l + 31*l**3 - 377*l**2 = 0.
-1, 1, 2
Let f(j) be the third derivative of 3*j**2 + 0*j + 1/9*j**4 + 7/45*j**7 + 16/45*j**5 + 0 + 0*j**3 + 77/180*j**6. What is l in f(l) = 0?
-1, -2/7, 0
Let w(c) be the third derivative of 0 - 2/75*c**5 + 5*c**2 + 0*c - 1/15*c**3 - 1/12*c**4. Factor w(d).
-2*(d + 1)*(4*d + 1)/5
Let a(v) be the second derivative of -v**4/32 - 3*v**3/16 + 3*v**2/4 - 3*v. Suppose a(s) = 0. Calculate s.
-4, 1
Determine w so that 16*w**2 - 6*w + 8*w**3 - 2*w**5 - 4*w**4 + 4*w + 2*w = 0.
-2, 0, 2
Factor -5*d**4 - 2*d**2 + 10*d**3 + 5*d**2 - 11*d**2 + 3*d**2.
-5*d**2*(d - 1)**2
Find o such that 1/8*o**2 + 0 + 0*o = 0.
0
Let b(r) be the second derivative of r**7/4620 - r**6/660 + r**5/220 - r**4/132 - r**3/2 - r. Let p(g) be the second derivative of b(g). Solve p(f) = 0.
1
Let t(d) be the first derivative of -3*d**5/40 + d**4/8 + d*