0
Let n(j) be the first derivative of -j**3/24 + j**2/16 + 5. Solve n(y) = 0 for y.
0, 1
Factor 18*p**2 - 14*p**2 + 793 - 96*p - 217.
4*(p - 12)**2
Let c(b) be the first derivative of 0*b - b**2 - 2/5*b**5 + 1/2*b**4 + 3 + 2/3*b**3. Factor c(l).
-2*l*(l - 1)**2*(l + 1)
Let p(a) be the first derivative of 0*a**4 - 2 - 3*a + 0*a**2 - 3/5*a**5 + 2*a**3. Let p(w) = 0. What is w?
-1, 1
Let j be (3 - 5 - -3)*-2. Let p be 1/((j + 0)/(-4)). Solve n**p + 2*n + 4*n**2 - n**2 = 0.
-1/2, 0
Let g(q) be the second derivative of -q**7/420 + q**6/45 - q**5/12 + q**4/6 + q**3 + 4*q. Let a(z) be the second derivative of g(z). Factor a(j).
-2*(j - 2)*(j - 1)**2
Let n(c) be the third derivative of 5*c**8/336 + c**7/14 + c**6/8 + c**5/12 - 19*c**2. Factor n(q).
5*q**2*(q + 1)**3
Factor -11*d + 6*d**2 - 12 + 9*d**4 + 47*d - 30*d**3 + 3*d**2.
3*(d - 2)**2*(d + 1)*(3*d - 1)
Let r(s) be the third derivative of s**9/241920 - s**7/20160 + s**5/12 + s**2. Let f(b) be the third derivative of r(b). Factor f(j).
j*(j - 1)*(j + 1)/4
Let h(l) = -l**2 - 5*l - 7*l + 4*l. Let v be h(-8). Find r such that v + 1/3*r**2 + 0*r = 0.
0
Let p(m) be the second derivative of 0 + 4*m + 8/27*m**3 + 26/27*m**4 + 0*m**2 - 49/135*m**6 + 7/9*m**5. Find z, given that p(z) = 0.
-2/7, 0, 2
Let u(j) be the first derivative of j**5/10 - j**3 - 2*j**2 - 3*j/2 - 19. Factor u(h).
(h - 3)*(h + 1)**3/2
Let c(q) be the first derivative of -147*q**5/10 + 63*q**4/8 + 12*q**3 + 3*q**2 - 7. Factor c(u).
-3*u*(u - 1)*(7*u + 2)**2/2
Let y be 12/18 - 4/(-21). Determine p, given that y*p**2 - 2/7*p**3 - 6/7*p + 2/7 = 0.
1
Let c = 1/874 - -1303/6992. Let r = 23/48 + c. Let r*o**2 - 4/3 - 2/3*o = 0. What is o?
-1, 2
Let p be 1 - (-2)/(0 - 2). Suppose -3 = -w - p*w. Factor 4*k + w*k**2 + 1 - 3*k + k**3 + 0*k + 2*k.
(k + 1)**3
Find y such that -1/2 + 15/8*y + 1/2*y**2 = 0.
-4, 1/4
Let i(j) be the second derivative of j**7/231 + 4*j**6/165 + 3*j**5/55 + 2*j**4/33 + j**3/33 + 4*j. Factor i(v).
2*v*(v + 1)**4/11
Let v be 2*(-3 + 234/60). Factor 3/5 - v*h - 3/5*h**3 + 9/5*h**2.
-3*(h - 1)**3/5
Let n be ((72/(-6))/3)/((-9)/6). Suppose -n*a**2 - 2/3*a**3 - 10/3*a - 4/3 = 0. What is a?
-2, -1
What is c in -2*c**2 - 5*c**4 + 0*c**4 - 3*c**3 + 3*c**4 + c**4 = 0?
-2, -1, 0
Let q(j) be the first derivative of -1/12*j**3 + 0*j + 1/240*j**5 + 1/2*j**2 - 1 - 1/96*j**4. Let h(p) be the second derivative of q(p). Factor h(o).
(o - 2)*(o + 1)/4
Let q be (-18)/(-10) - 1/(-5). Suppose -7*k + q*k = 0. Factor 2/3*j**4 - 2/3*j**2 + 1/3*j - 1/3*j**5 + k*j**3 + 0.
-j*(j - 1)**3*(j + 1)/3
Let r(d) = 100*d**4 - 14*d**3 - 84*d**2 + 30*d. Let j(m) = -100*m**4 + 15*m**3 + 84*m**2 - 31*m. Let u(q) = -6*j(q) - 5*r(q). Determine k, given that u(k) = 0.
-1, 0, 3/5
Let g(l) be the second derivative of l**4/36 + 5*l**3/9 + 25*l**2/6 - 8*l. Find z, given that g(z) = 0.
-5
Let q(c) be the first derivative of -c**7/42 + c**6/15 + c**5/15 - c**2 + 3. Let x(p) be the second derivative of q(p). Factor x(l).
-l**2*(l - 2)*(5*l + 2)
Let y = 5 - 2. Solve 0*d**y + d**3 + d**3 - 2*d**4 = 0 for d.
0, 1
Let f(h) = 1 + h + h - 3*h. Let k be f(-3). Find t such that -t**3 - 1/2*t**k + t + 0*t**2 + 1/2 = 0.
-1, 1
Let m(c) be the third derivative of -1/36*c**4 + 1/180*c**5 + 0*c + 0 + c**2 + 1/18*c**3. Find b such that m(b) = 0.
1
Suppose a - 3*a = -10. Let r = a + -3. Suppose 4 + 2*u**r + 6*u - 2*u + 2*u = 0. What is u?
-2, -1
Let 6/5*c**2 + 0 + 0*c + 27/5*c**3 - 6/5*c**4 - 27/5*c**5 = 0. Calculate c.
-1, -2/9, 0, 1
Let c(y) be the third derivative of y**6/10 + 9*y**5/5 - 39*y**4/8 + 5*y**3 - 13*y**2. Suppose c(k) = 0. Calculate k.
-10, 1/2
Let z(x) be the first derivative of -x**4/4 + 2*x**3/3 + 3*x**2/2 + 1. Factor z(l).
-l*(l - 3)*(l + 1)
Let i(v) = -2 - 3*v**2 - 3*v**3 + 4 - 2. Let m(s) = 3*s**3 + 3*s**2. Let f(b) = 3*i(b) + 4*m(b). Find t, given that f(t) = 0.
-1, 0
Let k(w) be the third derivative of 0*w + 0*w**3 + 1/840*w**8 + 0*w**5 + 0*w**4 - 1/525*w**7 + 0 + 0*w**6 - w**2. Factor k(p).
2*p**4*(p - 1)/5
Let d be (3/(-36))/((-6)/12). Let h(u) be the second derivative of 0 + 0*u**2 + 2*u + d*u**4 - 2/3*u**3. Factor h(b).
2*b*(b - 2)
Determine f so that -2/5*f - 1/5*f**4 + 2/5*f**3 + 1/5 + 0*f**2 = 0.
-1, 1
Let x(v) be the first derivative of -v**5/5 + v**4/3 + 2*v**3/3 - 2*v**2 + 4*v - 2. Let l(f) be the first derivative of x(f). Solve l(t) = 0.
-1, 1
Let l(s) = 12*s**5 - 8*s**4 - 2*s**3 - 2*s**2 + 10*s - 10. Let q(o) = -o**5 + o**4 - o + 1. Let d(c) = l(c) + 10*q(c). Factor d(x).
2*x**2*(x - 1)*(x + 1)**2
Let k = 16 + -11. Factor 0*d + 0*d**3 + 0 + 0*d**4 + 1/2*d**k + 0*d**2.
d**5/2
Let r(n) = 2*n**5 - 4*n**4 - n**3 + 8*n**2 + 3*n. Let u(q) = 2*q**5 - 4*q**4 - 2*q**3 + 8*q**2 + 4*q. Let o(l) = 4*r(l) - 5*u(l). Factor o(t).
-2*t*(t - 2)**2*(t + 1)**2
Suppose 0 = 2*z - z. Let f = -136 + 682/5. Let z + 0*p**4 + 0*p**2 - f*p**5 - 2/5*p + 4/5*p**3 = 0. What is p?
-1, 0, 1
Let u(p) = 32*p**4 - 76*p**3 + 60*p**2 - 8*p - 4. Let b(t) = 31*t**4 - 76*t**3 + 60*t**2 - 7*t - 5. Let m(c) = -4*b(c) + 3*u(c). Factor m(l).
-4*(l - 1)**3*(7*l + 2)
Factor 2*y**2 + 4/3*y + 0 + 2/3*y**3.
2*y*(y + 1)*(y + 2)/3
Let c(m) = -m + 5. Let t(h) = -h**3 - h**2 - 1. Let l be t(-2). Let z be c(l). Factor -1/2*g + 1/4*g**z + 1/4.
(g - 1)**2/4
Let s(l) be the third derivative of -l**7/8820 + l**6/840 - l**4/12 + 5*l**2. Let u(v) be the second derivative of s(v). Suppose u(a) = 0. Calculate a.
0, 3
Let s(t) = -2*t**2 + 14*t + 3. Let i(w) be the first derivative of -w**3 + 13*w**2/2 + 2*w + 4. Let l(z) = 5*i(z) - 4*s(z). Factor l(d).
-(d - 1)*(7*d - 2)
Let b be 2/(-8)*5/(-15). Let n(a) be the second derivative of 1/30*a**6 + 0*a**2 + 2*a + 1/6*a**3 - 1/20*a**5 - b*a**4 + 0. Factor n(f).
f*(f - 1)**2*(f + 1)
Let h(n) = -n - 2. Let i = 0 - 2. Let g be h(i). Determine w so that 1/3*w**3 + 0 - 1/3*w**4 + 0*w + g*w**2 = 0.
0, 1
Suppose 1/3*a**2 - 4/3 - a = 0. Calculate a.
-1, 4
Factor -1 + 7/3*w - 5/3*w**2 + 1/3*w**3.
(w - 3)*(w - 1)**2/3
Suppose -5*u = 2*g + 9, 4*g - u - 4*u = -63. Let k = 12 + g. Find b, given that k + 1/2*b + 1/2*b**2 = 0.
-1, 0
Let m(t) be the first derivative of t**6/21 + 30. Let m(y) = 0. What is y?
0
Suppose 2/3*a**4 + 4*a + 16/3*a**2 - 6 - 4*a**3 = 0. Calculate a.
-1, 1, 3
Let h(i) be the first derivative of -i**5/210 + i**3/21 + 3*i**2/2 - 3. Let q(z) be the second derivative of h(z). Determine g, given that q(g) = 0.
-1, 1
Suppose -3*b + 4*n - 5 = 5, -n = 2*b - 8. Let v = -12 + 37/3. Factor 1/3*o**4 + v*o**5 + 0*o + 0 - 1/3*o**b - 1/3*o**3.
o**2*(o - 1)*(o + 1)**2/3
Let z(q) be the first derivative of q**8/1008 - q**6/180 + q**4/72 + 3*q**2/2 - 2. Let n(v) be the second derivative of z(v). Solve n(m) = 0.
-1, 0, 1
Let l(f) be the second derivative of f**6/225 + f**5/150 - f**4/18 + f**3/15 - 4*f. Let l(p) = 0. What is p?
-3, 0, 1
Let x(u) = 5*u**5 + 2*u**4 - 27*u**3 - 28*u**2 - 8*u + 4. Let b(i) = -6*i**5 - 2*i**4 + 27*i**3 + 27*i**2 + 7*i - 3. Let r(g) = -4*b(g) - 3*x(g). Factor r(f).
f*(f - 2)*(f + 1)**2*(9*f + 2)
Factor -6 + 2 + 0 - 16*r + 44*r**2 - 7*r**3 - 17*r**3.
-4*(r - 1)**2*(6*r + 1)
Factor 4*j**3 + 5*j**5 - 133 + 133 + 4*j**2 + 7*j**5 - 20*j**4.
4*j**2*(j - 1)**2*(3*j + 1)
Let p(i) be the second derivative of -3*i**5/2 + 13*i**4/3 + 4*i**3 - 8*i**2 - 18*i. Factor p(v).
-2*(v - 2)*(3*v + 2)*(5*v - 2)
Let v(z) = -z**4 - 6*z**3 - 4*z**2 - 7. Let y(s) = -2*s**4 - 11*s**3 - 7*s**2 - 13. Suppose -3*w = -2*w + 6. Let l(n) = w*y(n) + 11*v(n). Factor l(h).
(h - 1)**2*(h + 1)**2
Let o(f) be the second derivative of f**6/30 + 11*f. Find m, given that o(m) = 0.
0
Suppose -n - 3 = -3*i, -4*n + i - 5*i = -36. Suppose 0 = 5*h - 16 + n. Suppose 9/4*f**4 - 1/4 - 2*f**h - f**5 - 1/2*f**3 + 3/2*f = 0. Calculate f.
-1, 1/4, 1
Let u(a) be the second derivative of a**7/56 + 7*a**6/60 + 13*a**5/40 + a**4/2 + 11*a**3/24 + a**2/4 - 35*a. What is r in u(r) = 0?
-1, -2/3
Let h be 231/88*8/30. Let t(q) be the second derivative of 0*q**2 + 0 + 2/3*q**3 + q - h*q**5 - 5/6*q**4. Find i such that t(i) = 0.
-1, 0, 2/7
Let q be (4/(-8))/(273/(-132) + 2). Determine w, given that 0 - 8/9*w - 40/9*w**2 - q*w**3 - 44/9*w**4 - 10/9*w**5 = 0.
-2, -1, -2/5, 0
Let f be 3/5 - 7319/(-52260). Let u = 2/201 + f. Factor -u*j**2 - 1/4 - j.
-(j + 1)*(3*j + 1)/4
Solve 2/11*p + 2/11*p**5 - 4/11*p**3 + 0*p**