te x.
-8, 2
Let v = 434 - 431. Let t(p) be the first derivative of -v - 8/7*p + 0*p**2 + 2/21*p**3. Determine d, given that t(d) = 0.
-2, 2
Let k = -8/9 - -109/72. Let w(t) be the second derivative of -k*t**3 - 35/48*t**4 + 5/2*t**2 + 10*t + 0. Factor w(h).
-5*(h + 1)*(7*h - 4)/4
Let l = 118621/270 + -1318/3. Let d(c) be the third derivative of 1/945*c**7 + 0*c + 1/270*c**5 - 3*c**2 + 0*c**4 + 0 + 0*c**3 - l*c**6. Factor d(z).
2*z**2*(z - 1)**2/9
Let r(o) be the third derivative of -o**9/5040 - o**8/2240 + o**7/840 + o**6/240 + 5*o**4/4 + 19*o**2. Let v(a) be the second derivative of r(a). Factor v(q).
-3*q*(q - 1)*(q + 1)**2
Suppose -11/3*a - 1/3*a**2 - 10/3 = 0. What is a?
-10, -1
Let j(a) be the third derivative of a**6/660 - a**5/110 + a**4/66 - 11*a**2. What is w in j(w) = 0?
0, 1, 2
Let g be (308/(-847))/(1 + -3). Determine a so that -g*a**5 - 38/11*a**3 + 50/11*a**2 + 8/11 + 14/11*a**4 - 32/11*a = 0.
1, 2
Let z(y) be the first derivative of y**7/14 - 7*y**6/24 + 5*y**5/12 - 5*y**4/24 + 10*y**2 + 22. Let k(i) be the second derivative of z(i). Factor k(n).
5*n*(n - 1)**2*(3*n - 1)
Let h(m) = -6*m**2 - 162*m + 328. Let o(r) = 2*r**2 + 54*r - 110. Let q(b) = 6*h(b) + 20*o(b). Factor q(l).
4*(l - 2)*(l + 29)
Let m be (18/3)/(-6)*(1 - 1). Let p be (0 - -2) + 1 + m. Solve 2/9*k**p + 2/9*k**4 + 0 - 2/9*k**2 - 2/9*k**5 + 0*k = 0.
-1, 0, 1
Let z be 9/(-6)*1 - (-4 - -1). Let m = 69/38 - 6/19. What is y in -3*y**3 + 3*y + z*y**4 + 0 - m*y**2 = 0?
-1, 0, 1, 2
Let c = -9232/7 + 1320. Let 24/7*g**2 - c*g**4 + 4/7*g**3 + 4/7*g - 8/7 = 0. Calculate g.
-1, 1/2, 2
Let v(t) = -6*t**3 - 8*t**2 - 7*t + 5. Let a(x) = 5*x**3 - x**2 + 8*x**2 + 4*x + 0*x - 4 + 2*x. Let b(z) = -5*a(z) - 4*v(z). Factor b(f).
-f*(f + 1)*(f + 2)
Let l be 322/70 - 4/(-10). Factor 25/3*x**2 + 10/3*x + l*x**3 - 5/3*x**4 + 0 - 5/3*x**5.
-5*x*(x - 2)*(x + 1)**3/3
Factor -4833*v**4 + v**5 + 4835*v**4 - 8*v**2 + 4*v**3 - 2*v**5.
-v**2*(v - 2)**2*(v + 2)
Let f = 220/7 + -653/21. Let i(p) be the first derivative of 1/6*p**4 - f*p**2 + 0*p - 8 + 0*p**3. Factor i(v).
2*v*(v - 1)*(v + 1)/3
Let r(t) = 11*t**4 + 66*t**3 + 180*t**2. Let b(v) = -65*v**4 - 395*v**3 - 1080*v**2. Let w(i) = 6*b(i) + 35*r(i). Suppose w(o) = 0. Calculate o.
-6, 0
Factor 25 + 549*w**2 - 553*w**2 - 44*w + 23.
-4*(w - 1)*(w + 12)
Let a(t) be the first derivative of 1/108*t**4 + 0*t**3 + 1/270*t**5 - 3*t**2 + 0*t - 1/270*t**6 + 1. Let z(h) be the second derivative of a(h). Factor z(w).
-2*w*(w - 1)*(2*w + 1)/9
Factor 498*v**3 + 72*v**2 - 503*v**3 + 228*v**2 + 8410 - 4785*v.
-5*(v - 29)**2*(v - 2)
Factor 9*a - 12*a - 6*a - 24*a**2 + 27*a**2 - 54.
3*(a - 6)*(a + 3)
Let g(t) = -2*t**2 + 32*t - 8. Let o(r) = r**2 - 21*r + 5. Let n(h) = 5*g(h) + 8*o(h). Factor n(d).
-2*d*(d + 4)
Let o(h) be the third derivative of 32/27*h**3 + 11/270*h**6 + 0 - 2/15*h**5 - 10/27*h**4 - 53*h**2 + 1/504*h**8 + 19/945*h**7 + 0*h. Solve o(q) = 0 for q.
-4, -2, 2/3, 1
What is x in -4/9*x**4 + 0*x**2 + 0 + 0*x + 0*x**3 + 4/9*x**5 = 0?
0, 1
Let z(k) be the first derivative of -k**9/2016 - 3*k**8/1120 - k**7/280 + 11*k**3/3 + 10. Let v(t) be the third derivative of z(t). Factor v(d).
-3*d**3*(d + 1)*(d + 2)/2
Let x = 119 + -119. Let z(r) be the first derivative of -2/3*r**3 - 1/2*r**4 + x*r + 2/5*r**5 + r**2 + 1. Factor z(w).
2*w*(w - 1)**2*(w + 1)
Suppose -34/7 + 32/7*z + 2/7*z**2 = 0. What is z?
-17, 1
Let k be 7/14 - (-1950)/4. Suppose -3*h - h = -k. Let 0*y - y**2 + y**4 + 121*y**3 - h*y**3 + y = 0. Calculate y.
-1, 0, 1
Let q be -5*((-6 - 3/((-30)/124)) + -7). Let 5/3*b**2 - 80/3*b + 115/3*b**q + 20/3 - 25/3*b**4 - 35/3*b**5 = 0. What is b?
-2, -1, 2/7, 1
Let y(v) be the third derivative of v**8/1680 - v**7/210 + v**6/600 + 13*v**5/300 - v**4/60 - 4*v**3/15 + 2*v**2 + 27*v. Determine w so that y(w) = 0.
-1, 1, 2, 4
Let q(h) be the second derivative of h**5/40 + h**4/12 - 13*h**3/4 + 18*h**2 + 205*h. Let q(o) = 0. What is o?
-8, 3
Let o(s) be the third derivative of 41*s**2 + 0 + 0*s + 5/6*s**4 - 1/48*s**5 - 40/3*s**3. Factor o(i).
-5*(i - 8)**2/4
Solve -11*t**3 - 42*t**2 - 65*t**3 + 30 + 5*t**5 + 12*t**4 + 83*t + 33*t - 45*t = 0 for t.
-5, -1, -2/5, 1, 3
Let t = 203 - 200. Factor 0 + 2/5*d**t - 2/5*d + d**4 - d**2.
d*(d - 1)*(d + 1)*(5*d + 2)/5
Suppose 6/5*j**2 + 4/5*j**3 - 64/5*j + 6 = 0. Calculate j.
-5, 1/2, 3
Let p(k) = 2*k**3 - 34*k**2 + 14*k - 9. Let v(y) = -5*y**3 + 92*y**2 - 41*y + 26. Let h(t) = -8*p(t) - 3*v(t). Factor h(j).
-(j - 1)**2*(j + 6)
Solve -800 - 40*z - 1/2*z**2 = 0.
-40
Suppose -4 = -5*h + 6*h. Let p be (3/h)/((126/16)/(-3)). Factor p*n**2 - 8/7*n + 2/7*n**3 - 8/7.
2*(n - 2)*(n + 1)*(n + 2)/7
Let t(s) be the second derivative of s**7/13860 - s**6/1320 + 7*s**4/12 + 3*s. Let p(z) be the third derivative of t(z). Factor p(h).
2*h*(h - 3)/11
Let t be (1*(-10)/25)/((-27)/9). Suppose 2/15*f**4 - t*f**2 + 2/15*f**3 + 0 - 2/15*f = 0. What is f?
-1, 0, 1
Let j(x) be the first derivative of -2*x**2 - 3 + 4*x + 1/4*x**4 - 1/3*x**3. What is z in j(z) = 0?
-2, 1, 2
Find g such that 4/3 + 1/6*g**3 + 2*g + g**2 = 0.
-2
Let d(u) = -28*u**3 - 660*u**2 - 1356*u - 700. Let a(w) = -6*w**3 - 132*w**2 - 271*w - 140. Let r(c) = -24*a(c) + 5*d(c). What is f in r(f) = 0?
-1, 35
Let d = 27 + -24. Suppose -p = 2*y - 17, 6*p - d*p = 2*y - 5. Find t such that 26*t + y*t**2 - t**4 - 24*t - 2*t**2 - 2*t**2 = 0.
-1, 0, 2
Suppose -2909*o**3 + 2879*o**3 + 10*o**2 + 15 + 0*o - 5*o**5 + 14*o + 6*o - 25*o**4 + 15*o = 0. What is o?
-3, -1, 1
Let h be 9/((-1134)/36) - (-8)/14. Factor 0 - 2/7*k**4 + h*k**2 + 0*k + 2/7*k**3 - 2/7*k**5.
-2*k**2*(k - 1)*(k + 1)**2/7
Solve 38*t**2 - 1 + 12*t + 48*t**2 - 122*t**2 = 0 for t.
1/6
Let d(t) be the second derivative of t**4/20 + 3*t**3/5 + 55*t. What is k in d(k) = 0?
-6, 0
Let v be (-1 + 80/75)*5. Let d(x) be the first derivative of 0*x**2 + 0*x - 1/4*x**4 + 6 - v*x**3. Let d(z) = 0. What is z?
-1, 0
Let b(w) be the second derivative of w**7/294 + w**6/105 - w**5/28 - 5*w**4/42 + 2*w**3/21 + 4*w**2/7 - 48*w - 1. What is m in b(m) = 0?
-2, -1, 1, 2
Let o be 8/(-12) - (-160)/90. Let x(r) be the second derivative of 11/30*r**5 + o*r**3 + 11/12*r**4 + 1/18*r**6 + 2*r + 0 + 2/3*r**2. Factor x(i).
(i + 1)**2*(i + 2)*(5*i + 2)/3
Let h be (-130)/20*(-28)/42. Factor 4/3 - 7/6*v**2 - h*v.
-(v + 4)*(7*v - 2)/6
Let m = 171 + -171. Let o(f) be the third derivative of m + 1/120*f**6 + 1/90*f**5 + 0*f**4 + 0*f**3 + 1/630*f**7 - 2*f**2 + 0*f. Factor o(y).
y**2*(y + 1)*(y + 2)/3
Let v(r) = -9*r**2 - 8*r**2 - 9*r**3 + 17 - 8*r**3 + r + 16*r**3. Let y be v(-17). Suppose 0*x + 0 + y*x**3 - 1/7*x**2 + 1/7*x**4 = 0. What is x?
-1, 0, 1
Let x(w) = 3*w**2 + 4*w + 7. Let l be x(8). Let u be (2/((-16)/6))/(l/(-616)). Factor 5/3*j**u - 1 - 2/3*j.
(j - 1)*(5*j + 3)/3
Find c, given that -3/2*c**3 + 1/2*c**5 + 0 + 0*c - c**2 + 0*c**4 = 0.
-1, 0, 2
Suppose 3*h - 4 = -2*n - 0*n, -3*h - 5*n = -1. Let a = h - 9/5. Factor -1/5*z**2 + 0*z + a.
-(z - 1)*(z + 1)/5
Suppose -32*d - 127*d**2 - 27 + 131*d**2 - 22 + 13 = 0. What is d?
-1, 9
Let s be -2*(7 + 51/(-6)). Let i(k) be the first derivative of 3/4*k**2 + 0*k + 7 - 1/2*k**s. Solve i(z) = 0 for z.
0, 1
Factor 20*d**2 - 6*d**4 + 0 + 2*d**4 - 4 - 12*d**2.
-4*(d - 1)**2*(d + 1)**2
Let d(c) be the first derivative of 2*c - 1/4*c**5 + 1/6*c**4 + 1/6*c**3 + 0*c**2 - 4 - 1/5*c**6. Let r(h) be the first derivative of d(h). Factor r(w).
-w*(w + 1)*(2*w - 1)*(3*w + 1)
Let h(k) be the third derivative of 1/30*k**6 - 1/5*k**5 + 17*k**2 + 2/105*k**7 + 0 + 0*k - 5/6*k**4 - 4/3*k**3. Solve h(a) = 0 for a.
-1, 2
Factor 2*h**2 - 5*h**2 + 34 - 36*h - 94.
-3*(h + 2)*(h + 10)
Let l(h) be the third derivative of h**6/540 + 5*h**5/18 + 481*h**4/36 + 1369*h**3/27 - 34*h**2. Factor l(p).
2*(p + 1)*(p + 37)**2/9
Let i(m) be the third derivative of -m**5/270 + 2*m**4/27 - 5*m**3/9 + 4*m**2 + 5. Determine s so that i(s) = 0.
3, 5
Suppose -2*h - h + 5*k + 21 = 0, -5*h + 13 = -k. Determine n so that 3*n**2 - 50 - 7*n**2 + 2*n**h - 20*n = 0.
-5
Let c(x) = -x**2 - 3*x. Let f be c(-2). Suppose z = f*z - 3. Suppose 6*w**5 + 2*w**3 + 18*w**2 + 3*w**5 + 8*w**3 - 3 - z*w + 32*w**3 + 33*w**4 = 0. Calculate w.
-1, 1/3
Factor -48 - 3/5*v**2 - 63/5*v.
-3*(v + 5)*(v + 16)/5
Solve -342*h**4 - 30364 + 30460 - 162*h**4 - 740*h**3 + 1704*h**2 + 196