(j).
2*(j - 2)*(j + 1)
Let x(y) be the first derivative of 0*y**3 + y + 1 + 1/24*y**4 + 0*y**2 - 1/40*y**5. Let n(k) be the first derivative of x(k). Solve n(j) = 0 for j.
0, 1
Factor -7*u**3 - 21*u - 4 - 24*u**2 - 9*u**3 + 2*u - 4*u**4 + 3*u.
-4*(u + 1)**4
Let p = 44 + -131/3. Let z(x) be the first derivative of -5/6*x**4 + 4/9*x**6 + 2/5*x**5 + 0*x + p*x**2 - 2/3*x**3 - 1. Find w such that z(w) = 0.
-1, 0, 1/4, 1
Let y(q) = q + 3. Let s be y(-3). Solve -3*r + 2*r**2 + 1 - r + 1 + s = 0.
1
Let z(g) = -g**2. Let s(n) = n**4 + 4*n**3 - 12*n + 9. Let u(h) = -s(h) - 2*z(h). Factor u(b).
-(b - 1)**2*(b + 3)**2
Let s = 2101/6 + -349. Let p(f) be the first derivative of -1/2*f**2 + s*f**3 - 7/10*f**5 - 2 + 5/12*f**6 - 3/8*f**4 + 0*f. Find j, given that p(j) = 0.
-1, 0, 2/5, 1
Suppose 2*w = 2 + 4. Suppose 2*t - 10 = -3*t. Determine o so that 4*o**5 - o**2 + 2 - 3*o**t - 4*o**2 + 6*o**4 - 4*o**w = 0.
-1, 1/2, 1
Let f(u) = u**3 + 3*u**2 - u - 4. Let b be f(-2). Factor 5*a - b + 0 + 0*a**2 - 4*a + a**2.
(a - 1)*(a + 2)
Let n(s) be the first derivative of -1/2*s**6 - 25*s**3 - 12*s - 57/4*s**4 - 24*s**2 + 4 - 21/5*s**5. Factor n(b).
-3*(b + 1)**3*(b + 2)**2
Factor -5/2*y**2 + 25/2*y + 0.
-5*y*(y - 5)/2
Let v(w) be the first derivative of w**4/12 + 2*w**3/9 + 4. Factor v(z).
z**2*(z + 2)/3
Suppose 4*j + 2*x + 5 = x, 2*x - 1 = 3*j. Let g(p) = 2*p**2. Let o be g(j). Factor -2/7 - 4/7*i - 2/7*i**o.
-2*(i + 1)**2/7
Suppose 0 = 4*a - x - 19, -3*a - 3*x = -0*x - 3. Suppose 9*v**4 - 4*v**3 + 4*v + 6*v**4 + 0*v**2 - 19*v**a + 4*v**2 = 0. What is v?
-1, 0, 1
Let p(k) be the first derivative of -k**5/20 - k**4/16 + 8. Factor p(n).
-n**3*(n + 1)/4
Suppose 3*q = 4*q - 2*q. Let r(y) be the second derivative of 1/12*y**3 + q - 1/8*y**2 + 2*y - 1/48*y**4. Factor r(f).
-(f - 1)**2/4
Suppose 2*a - 21 = 17. Let l**2 + l**2 + 6*l**3 + 19 - a + 6*l**4 + 2*l**5 = 0. Calculate l.
-1, 0
Let d be (-3)/5 + 69/15. Solve -15*j**2 + 2 + d*j**4 - 8*j + 3*j**2 - 2 = 0 for j.
-1, 0, 2
Let x be (-2)/(-9) - (-7)/9. Let z = -13 + 15. Factor 4*f - x + f**2 - 2*f - z*f**2.
-(f - 1)**2
Factor 73*b**5 - 33*b**5 - 35*b**5 + 5*b**4.
5*b**4*(b + 1)
Let s be (-21)/14*1/(-3). Solve 3/2*a**3 + s*a + 3/2*a**2 + 0 + 1/2*a**4 = 0.
-1, 0
Let j be (-13)/78*(-1 + -3). Suppose 2*n - j*n**3 + 0*n**2 + 4/3 = 0. What is n?
-1, 2
Factor -12/7 - 10/7*p - 2/7*p**2.
-2*(p + 2)*(p + 3)/7
Let s(x) = -6*x**2 - 8*x - 6. Let i(p) = 7*p**2 + 9*p + 7. Let b(a) = 4*i(a) + 5*s(a). Factor b(d).
-2*(d + 1)**2
Let b(j) = j**5 + j**4 + j**3 + 1. Let f(n) = -4*n**5 + 11*n**4 + 36*n**3 + 20*n**2 + 1. Let u(d) = b(d) - f(d). Factor u(z).
5*z**2*(z - 4)*(z + 1)**2
Let f(n) be the third derivative of -n**6/150 - 2*n**5/75 + 2*n**4/15 + 16*n**3/15 + n**2 - 8. Factor f(m).
-4*(m - 2)*(m + 2)**2/5
Suppose d + d = 6. Find h, given that 0*h - d*h**2 + 2 - 2*h**3 - 4*h**2 + 5*h**2 + 2*h = 0.
-1, 1
Suppose o = u - 5, -u - 5 = -4*o - 19. Let i = u + 0. Factor -2*s + 1 - i*s**2 - 2*s**4 + 12*s**3 + 11*s**4 - 2*s.
(s + 1)**2*(3*s - 1)**2
Suppose 0 = 2*j - 20 + 2. Let x be ((-3)/4)/(j/(-6)). Suppose -x + 1/4*i**2 - 1/4*i = 0. What is i?
-1, 2
Let x(v) = v**2 - 8*v + 4. Let a(h) = -h**2. Let u(l) = 6*l**2 - 23*l + 12. Let r(g) = 3*a(g) + u(g). Let i(b) = -4*r(b) + 11*x(b). Factor i(t).
-(t - 2)**2
Let o(q) = q**3 - 14*q**2 - 17*q + 30. Let k be o(15). Let s be (-7)/(-2) + (-1)/2. Factor -2/5*b**4 + 4/5*b**s - 2/5*b**2 + k*b + 0.
-2*b**2*(b - 1)**2/5
Factor 8/3*b + 10/3 - 2/3*b**2.
-2*(b - 5)*(b + 1)/3
Let c(x) be the third derivative of -x**8/1344 + x**7/140 - x**6/480 - x**5/10 - x**4/6 + 21*x**2. Solve c(r) = 0.
-1, 0, 4
Let y(c) = -12*c**2 - 3*c - 4. Suppose -4*q - 2 + 18 = 0. Let f(a) = 84*a**2 + 21*a + 27. Let x(t) = q*f(t) + 27*y(t). Factor x(p).
3*p*(4*p + 1)
Suppose 3*n - 2*z - 17 = -0*n, 10 = -2*n - 4*z. Suppose -22/9*f**n - 8/9*f**4 - 2/9*f + 2/9 - 2*f**2 = 0. What is f?
-1, 1/4
Let o(c) = -4*c - 5. Let s be o(-4). Let r = s - 5. Determine x, given that -2*x**5 - x**3 + 6*x + 0*x**5 - 5*x**3 - r*x**4 + 2 + 2*x**3 + 4*x**2 = 0.
-1, 1
Suppose -r + 26 = -4*o, 3*r + 10*o = 7*o + 3. Find w, given that 9/2*w**4 - 3*w**3 + 3*w - r*w**2 + 3/2 = 0.
-1, -1/3, 1
Suppose -9*q + 12*q = 9. Let 16/9*m - 686/9*m**5 + 140/3*m**q + 152/9*m**2 + 0 + 98/9*m**4 = 0. What is m?
-2/7, 0, 1
Suppose 0*b + 9 = b. Let l = b - 7. Factor -1/2*c**2 + 2*c - l.
-(c - 2)**2/2
Let d(x) be the first derivative of 8*x**5/75 - x**4/6 + 2*x**3/45 - 4. Factor d(i).
2*i**2*(i - 1)*(4*i - 1)/15
Let t(u) be the second derivative of -3*u**5/160 - 3*u**4/16 - 3*u**3/4 - 3*u**2/2 + 8*u - 2. Suppose t(r) = 0. What is r?
-2
Let h(o) = -o**3 - 17*o**2 - 35*o - 75. Let d be h(-15). Factor -2/7*x**2 - 1/7*x**3 + d - 1/7*x.
-x*(x + 1)**2/7
Factor -4/5*w + 0 - 1/5*w**4 + 1/5*w**3 + 4/5*w**2.
-w*(w - 2)*(w - 1)*(w + 2)/5
Let k be 4/(-14) - 104/(-70). Factor -6/5*r**3 + k*r - 4/5 + 4/5*r**2.
-2*(r - 1)*(r + 1)*(3*r - 2)/5
Let c(h) be the first derivative of -h**6/36 - h**5/30 + h**4/24 + h**3/18 + 3. Let c(b) = 0. What is b?
-1, 0, 1
Let n = 39 + -33. Let u(t) be the third derivative of 1/70*t**7 - 7/120*t**n + 0*t**3 + 1/12*t**5 + t**2 + 0*t + 0 - 1/24*t**4. Factor u(y).
y*(y - 1)**2*(3*y - 1)
Let t(q) be the third derivative of -1/280*q**7 - 5*q**2 + 1/32*q**4 + 1/12*q**3 + 0*q + 0 - 1/80*q**5 - 7/480*q**6. Suppose t(x) = 0. What is x?
-1, 2/3
Let c(o) be the first derivative of 2*o**3/3 - o**2 - 4*o - 6. Factor c(r).
2*(r - 2)*(r + 1)
Let d(k) = k**2 + 5 - 2 - k - 2*k**2. Let i(w) = 1. Let c(a) = d(a) - 3*i(a). Factor c(o).
-o*(o + 1)
Let m(t) be the second derivative of -t**6/1440 - t**5/240 - t**4/96 - 2*t**3/3 + 3*t. Let i(j) be the second derivative of m(j). Solve i(f) = 0.
-1
Let a(l) be the third derivative of -l**7/1050 - l**6/300 - l**5/300 + 2*l**2. Solve a(x) = 0 for x.
-1, 0
Let q be 0 + ((-12)/(-3) - 2). Suppose 2 + q = 2*h. Factor 4*g**h + 4*g + g**2 - 2*g - 7*g**3.
-g*(g - 1)*(7*g + 2)
Suppose j - 76 = -3*j. Solve 9*x**4 + 9*x**4 + j*x**5 - 5*x**5 + 4*x**3 = 0 for x.
-1, -2/7, 0
Let q(o) = 7*o**2 - o + 4. Let h(n) = 11*n**2 - n + 6. Let v(d) = -5*h(d) + 8*q(d). Let k be v(3). Suppose -44*l - 50*l**k + 3 - 11 + 4*l = 0. What is l?
-2/5
Let s be (-22 - -23) + (-3)/2 - -1. Suppose 5*f = -0*m - 2*m, 0 = f - 3*m - 17. Suppose -s - 7/2*l - 11/2*l**f + 7/2*l**3 + 6*l**4 = 0. What is l?
-1, -1/3, -1/4, 1
Let g(n) = -50*n**5 - 16*n**4 + 48*n**3 + 24*n**2 + 6*n. Let c(i) = -i**4 - i**2 - i. Let r(f) = 4*c(f) + g(f). Suppose r(d) = 0. What is d?
-1, -1/5, 0, 1
Let o be 2/12 + (-46)/(-12). Suppose s - 3*f - 9 = 0, s - o*s + 9 = -3*f. Factor -2/5*g**4 + s*g**3 - 2/5 + 4/5*g**2 + 0*g.
-2*(g - 1)**2*(g + 1)**2/5
Let f = 348 - 345. Factor 0 + 3/4*o**f + 3/4*o**2 + 0*o.
3*o**2*(o + 1)/4
Let s(m) = -m - 1. Let h be s(-5). Factor 3*k**3 + 3*k**h + 3*k**5 - 6*k**4 - 6*k**5 + 3*k**2.
-3*k**2*(k - 1)*(k + 1)**2
Let s be (-6 - -1)/(-4 + 0 + 3). Let t(r) be the third derivative of -1/42*r**4 - 1/84*r**6 + 0 + 0*r**3 - 2*r**2 + 0*r + 1/30*r**s. Factor t(x).
-2*x*(x - 1)*(5*x - 2)/7
Let m(p) be the second derivative of -1/15*p**6 + 1/3*p**4 + 1/3*p**3 - 1/5*p**5 - p - p**2 + 0 + 1/21*p**7. Factor m(r).
2*(r - 1)**3*(r + 1)**2
Suppose 2*d - 1 = 3. Factor -13*t**4 - 3*t**3 - d*t**2 + 16*t**4 - 4*t**2.
3*t**2*(t - 2)*(t + 1)
Suppose 0 = 6*d - 9 - 3. Let z(w) be the second derivative of 0 + 0*w**2 + 1/6*w**5 - 1/30*w**6 + d*w + 1/9*w**3 - 1/4*w**4. Factor z(g).
-g*(g - 2)*(g - 1)*(3*g - 1)/3
Factor -4*m**4 + 2*m**4 - 4*m**3 + 11*m**4 - 7*m**4 + 2*m**2.
2*m**2*(m - 1)**2
Let g(c) be the first derivative of 1/18*c**3 + 1/6*c - 1/6*c**2 + 9. Find t such that g(t) = 0.
1
Let j(p) = 6*p**3 + 15*p**2 - 48*p - 27. Let x(b) = b**3 + 2*b**2 - 7*b - 4. Let y(q) = 2*j(q) - 15*x(q). Factor y(t).
-3*(t - 2)*(t + 1)**2
Factor 15/7*p - 12/7*p**2 + 3/7*p**3 - 6/7.
3*(p - 2)*(p - 1)**2/7
Let a(b) be the first derivative of b**6/360 - b**5/180 - b**4/72 + b**3/18 + b**2 + 4. Let t(r) be the second derivative of a(r). Factor t(y).
(y - 1)**2*(y + 1)/3
Let m(u) be the second derivative of -u**4/12 - 2*u**3/3 - 3*u**2/2 - 14*u. Suppose m(v) = 0. Calculate v.
-3, -1
Let q(b) be the second derivative of b**7/4200 + b**6/400 + b**4/3 + 2*b. Let d(w) be the third derivative of q(w). Factor d(m).
3*m*(m + 3)/5
Let u(r