e the first derivative of -1/7*w**5 + 6/7*w - 2 - 1/21*w**3 - 17/28*w**4 + 17/14*w**2. Suppose i(r) = 0. What is r?
-3, -1, -2/5, 1
Suppose -j = 4*j. Let y = j - -2. Suppose -15 + 15 - 2*w**y - 2*w = 0. What is w?
-1, 0
Factor r**5 + r**4 - 5*r**3 + 2*r - r**3 - 4*r**3 - r**2 + 7*r**3.
r*(r - 1)**2*(r + 1)*(r + 2)
Factor -5*b**3 - 3 - 5 + 7 + 3*b**3 + 3*b**2.
-(b - 1)**2*(2*b + 1)
Let w = -152 - -461/3. Find h, given that -w*h - 1/3*h**3 - 4/3*h**2 - 2/3 = 0.
-2, -1
Let k(o) be the second derivative of -o**4/24 + o**3/4 - o**2/2 + 20*o. Factor k(g).
-(g - 2)*(g - 1)/2
Let n(m) = m**2 + 7*m. Let p(a) = -3*a**2 - 15*a. Let t(s) = 7*n(s) + 3*p(s). Determine x so that t(x) = 0.
0, 2
Factor -8*r - 38 + 38 - 8*r**2 - 2*r**3.
-2*r*(r + 2)**2
Find l such that -4/9 + 2/9*l**2 + 2/9*l = 0.
-2, 1
Let d(y) be the second derivative of y**8/840 - y**7/140 + y**6/60 - y**5/60 - 3*y**3/2 + 7*y. Let k(n) be the second derivative of d(n). Factor k(g).
2*g*(g - 1)**3
Let f(t) be the first derivative of t**6/16 - 3*t**5/40 - 9*t**4/16 - 55. Factor f(q).
3*q**3*(q - 3)*(q + 2)/8
Let t = -12 + 7. Let h(u) = u**3 - u**2 + u - 1. Let z(l) = 31*l**3 - 19*l**2 - 16*l + 4. Let y(g) = t*h(g) - z(g). Solve y(m) = 0 for m.
-1/6, 1
Suppose 2*i = 7*i - 100. Suppose 5*z - z - i = 0. Factor 0*v**2 + 0*v**4 + 0 - 2/7*v - 2/7*v**z + 4/7*v**3.
-2*v*(v - 1)**2*(v + 1)**2/7
Let z be (-2)/(-4) + (-11)/22. Let w(n) be the second derivative of 0 + 0*n**4 + 0*n**2 + z*n**3 + n + 0*n**5 - 1/45*n**6. Factor w(c).
-2*c**4/3
Factor -1/5 - 2/5*b**3 + 3/5*b**2 + 0*b.
-(b - 1)**2*(2*b + 1)/5
Let s(j) be the third derivative of 1/480*j**6 - j**2 + 0*j**3 + 0 + 0*j**4 + 0*j - 1/120*j**5. Factor s(d).
d**2*(d - 2)/4
Factor 0*q - 3/4*q**3 + 3/4*q**2 + 0 + 3/4*q**5 - 3/4*q**4.
3*q**2*(q - 1)**2*(q + 1)/4
Let q(a) = 3*a**2 - 7*a - 4. Let f(x) = -3 + 5*x**2 + 0*x**2 - 6*x - 2*x**2. Let y(w) = 4*f(w) - 3*q(w). Let y(v) = 0. Calculate v.
0, 1
Let c(f) be the first derivative of -f - 2 - 1/4*f**2 + 1/2*f**3. Factor c(i).
(i - 1)*(3*i + 2)/2
Let p(z) be the second derivative of -z**7/231 + z**6/165 + z**5/55 - z**4/33 - z**3/33 + z**2/11 + 16*z. Factor p(m).
-2*(m - 1)**3*(m + 1)**2/11
Let k = 103/84 + -10/21. Suppose 0 + 0*n - k*n**2 = 0. Calculate n.
0
Let o(b) be the second derivative of 0*b**4 - 1/35*b**5 + 0*b**3 + 0*b**2 - 4*b - 1/105*b**6 + 0. Suppose o(f) = 0. What is f?
-2, 0
Let y(d) be the third derivative of 0*d**3 - 1/105*d**7 - 1/30*d**5 + 0*d + 0*d**4 - 2*d**2 + 0 - 1/30*d**6. Find q, given that y(q) = 0.
-1, 0
Let v(x) = x**3 + 5*x**2 + 4*x + 1. Let w = -7 - -4. Let k be v(w). Factor -8*h**3 + k*h**3 + 2*h**2 - h**2.
-h**2*(h - 1)
Let o be 5 - 0/2*(-17 + 16). Factor -1/2*p**2 + 3/4*p**4 + 1/4*p**o - 3/4*p - 1/4 + 1/2*p**3.
(p - 1)*(p + 1)**4/4
Factor -2*b + 13/8*b**2 + 5/8 - 1/4*b**3.
-(b - 5)*(b - 1)*(2*b - 1)/8
Let u(c) be the first derivative of 3/5*c - 4 + 3/5*c**2 + 1/5*c**3. Solve u(y) = 0.
-1
Factor 6 + 3*j**3 - j**4 + 7*j**4 - 123*j**2 + 114*j**2 - 3*j**4 - 3*j.
3*(j - 1)**2*(j + 1)*(j + 2)
Let g(f) be the third derivative of f**7/945 + f**6/180 + f**5/270 - f**4/36 - 2*f**3/27 - 3*f**2. Factor g(k).
2*(k - 1)*(k + 1)**2*(k + 2)/9
Let b(q) be the first derivative of -q**4/10 - 4*q**3/5 - 12*q**2/5 - 16*q/5 + 9. Let b(y) = 0. Calculate y.
-2
Let c(h) be the second derivative of -h**8/3360 - h**7/420 + h**5/15 - 5*h**4/12 + 6*h. Let d(n) be the third derivative of c(n). Factor d(p).
-2*(p - 1)*(p + 2)**2
Let j be (0 - -4) + (-5 - -6). Suppose t**5 + 3*t**4 + t**2 - 4*t**4 - t**3 + 0*t**4 + 0*t**j = 0. What is t?
-1, 0, 1
Let a(j) = -11*j**2 - 8*j + 2. Let y(u) be the first derivative of -4*u**3 - 9*u**2/2 + 3*u - 1. Let o(b) = 3*a(b) - 2*y(b). Suppose o(p) = 0. Calculate p.
-2/3, 0
Suppose -52 + 49 = -x. Let i(a) be the second derivative of -7/12*a**4 + 0 - 1/3*a**x + 3*a + 0*a**2. Let i(p) = 0. Calculate p.
-2/7, 0
Let 55*r**3 + 2*r - 7*r**3 + 24*r**2 + r = 0. What is r?
-1/4, 0
Let q(o) be the third derivative of 9/10*o**5 + 0*o - 2*o**2 + 1/105*o**7 - 3/20*o**6 + 0*o**3 - 9/4*o**4 + 0. Factor q(s).
2*s*(s - 3)**3
Let h = -8 + 10. Factor -3*t**3 + 5*t**4 + t - 2*t**4 + 1 + 1 + h*t**3 - 5*t**2.
(t - 1)**2*(t + 1)*(3*t + 2)
Let v be 2/((-6)/27 + 168/27). Let g(n) be the first derivative of -1/2*n**2 + 1/4*n**4 - v*n**3 - 3 + n. Determine f, given that g(f) = 0.
-1, 1
Let y = 2/109 + 103/327. Let 1/3*s**2 + y*s + 0 = 0. Calculate s.
-1, 0
Let g = 529/121380 + -4/2023. Let o(h) be the third derivative of 0*h**4 + 0*h**3 + 0*h + 0 - g*h**6 + 0*h**5 - 2*h**2. Find n, given that o(n) = 0.
0
Factor 3*n**4 + 2 - 4*n + 3*n**4 - 8*n**2 + 4*n**3 - 5*n**4 + 5*n**4.
2*(n - 1)*(n + 1)**2*(3*n - 1)
Let m = -51 + 33. Let f = -16 - m. Factor -o + 0 - 3*o**f - 13/4*o**3 - 3/2*o**4 - 1/4*o**5.
-o*(o + 1)**2*(o + 2)**2/4
Let h(n) be the third derivative of n**5/240 + n**4/24 + n**3/6 + n**2. Factor h(d).
(d + 2)**2/4
Let m(r) be the first derivative of -r**7/14 + 6*r + 1. Let a(u) be the first derivative of m(u). Determine n so that a(n) = 0.
0
Suppose -6 = -3*g, -g + 22 = 4*h + 2*g. Suppose -2*j**h - j**4 - j**3 - 2*j**3 = 0. What is j?
-1, 0
Suppose 4*k = 16 - 0. Factor 0*w**3 + 2/5*w**5 - 2/5*w + 0 - 4/5*w**2 + 4/5*w**k.
2*w*(w - 1)*(w + 1)**3/5
Let g = -719/9 + 241/3. Suppose -2/9*p**4 + 0 - 2/9*p**2 + g*p**3 + 0*p = 0. Calculate p.
0, 1
Let z(k) = -k**3 - 6*k**2 + 14*k - 14. Let y be z(-8). Let i(d) = d**3 - 5*d**2 + 2. Let m be i(5). Determine g, given that 0 + 2/3*g + 4/3*g**3 - m*g**y = 0.
0, 1/2, 1
Suppose x = 0, 0*z - z = -x. Factor z*u - 6/7*u**4 + 8/7*u**3 + 0 - 2/7*u**2.
-2*u**2*(u - 1)*(3*u - 1)/7
Let k be 0 - -1 - ((-180)/42 + 4). Factor 2/7*u**5 - 1/7 + 6/7*u + 16/7*u**3 - k*u**4 - 2*u**2.
(u - 1)**4*(2*u - 1)/7
Let c(f) be the third derivative of 0*f**3 + 0 - 1/2*f**4 + 0*f - 6*f**2 + 1/20*f**5. Factor c(w).
3*w*(w - 4)
Let o(s) be the second derivative of -3*s**5/40 - 3*s**4/2 - 9*s**3 + 46*s. Suppose o(j) = 0. Calculate j.
-6, 0
Let h(l) = 4*l**2 + l - 3. Suppose -4*i - 17 - 3 = 0. Let b(m) = 7*m**2 + 2*m - 5. Let n(f) = i*h(f) + 3*b(f). Solve n(d) = 0 for d.
-1, 0
Suppose 4*m - 6 = m. Factor 6*l - 3*l**m - 4*l + l + 0*l.
-3*l*(l - 1)
Suppose -5*s + 3 = -2. Let o(b) = -6*b**2 - 2*b - 8. Let v(c) be the third derivative of c**4/24 - c**3/6 + 3*c**2. Let q(n) = s*o(n) - 6*v(n). Factor q(y).
-2*(y + 1)*(3*y + 1)
Let z(m) = m**4 + 17*m**3 + 29*m**2 + 13*m - 3. Let o(c) = 8*c**4 + 152*c**3 + 260*c**2 + 116*c - 28. Let i(y) = 3*o(y) - 28*z(y). Factor i(w).
-4*w*(w + 1)*(w + 2)**2
Suppose 3*c = 8 + 10. Let k be (-20)/(-8)*-1*(-8)/5. Factor -17*y**2 - 3*y**2 - c*y**2 - 11*y - 12*y**3 - 13*y - 2*y**k - 8.
-2*(y + 1)**2*(y + 2)**2
Solve 27/4*u**2 - 3/2 + 21/4*u = 0 for u.
-1, 2/9
Let p = -127 + 637/5. Let -4/5 + 6/5*u - p*u**2 = 0. What is u?
1, 2
Let l(d) be the second derivative of -d**6/6 + 7*d**5/4 - 25*d**4/4 + 15*d**3/2 + 45*d. Factor l(z).
-5*z*(z - 3)**2*(z - 1)
Factor -1/2*v**3 + 0*v**2 + 0 + 1/2*v.
-v*(v - 1)*(v + 1)/2
Let i(n) be the second derivative of 0*n**2 + 0 + 1/15*n**4 + 1/50*n**5 + 1/15*n**3 + n. Determine k so that i(k) = 0.
-1, 0
Let h(q) be the first derivative of -7*q**8/480 - q**7/80 + q**6/30 - q**5/60 + 2*q**3/3 - 4. Let r(n) be the third derivative of h(n). Factor r(o).
-o*(o + 1)*(7*o - 2)**2/2
Factor -64/7 - 80/7*g + 25/7*g**3 - 10/7*g**4 + 1/7*g**5 + 20/7*g**2.
(g - 4)**3*(g + 1)**2/7
Let l be 2 - 2/6*0. Suppose y + 6 = -l*d, -3*y + 32 = d - 5*d. Determine t, given that 1/4*t - 3/2*t**2 - t**3 + 3/4*t**5 + t**y + 1/2 = 0.
-1, 2/3, 1
Let j(p) = -4*p**3 + 6*p**2 + 2*p + 2. Let q(t) = t**3 + t**2 - t - 1. Let i(f) = -2*j(f) - 4*q(f). Factor i(m).
4*m**2*(m - 4)
Let l = 6 - 4. Find u such that 1 - 3*u**2 - u**3 + 4*u**2 + l - 4 + u = 0.
-1, 1
Suppose -4*g - g + 545 = 0. Let h = g - 543/5. Factor 0*y + 0 + 4/5*y**3 - h*y**4 - 2/5*y**2.
-2*y**2*(y - 1)**2/5
Let c(o) = -6*o**3 - 2*o - 2. Let u be c(-1). Suppose -z + 5*m - 3 = -12, z - 6 = 2*m. Factor -f**4 - 2*f**4 - 2*f**2 - u*f**z + 14*f**2 - 3*f**5.
-3*f**2*(f - 1)*(f + 2)**2
Let h(p) be the first derivative of 6/5*p**5 - 3 + 2/3*p**3 + 3/2*p**4 + 1/3*p**6 + 0*p**2 + 0*p. Suppose h(b) = 0. What is b?
-1, 0
Let t(n) = -n**3 - n**2 - n. Let i(b) = 8*b**3 - 22*b**2 + 86*b - 81. Let m(r) = -i(r) - 5*t(r). Factor m