 be the first derivative of -2 - 12/5*t**5 + 3/2*t**2 + 3/2*t**4 + 4*t**3 - 3/2*t**6 + 0*t. What is m in i(m) = 0?
-1, -1/3, 0, 1
Let n(o) be the first derivative of -o**6/21 - 16*o**5/35 - 11*o**4/7 - 16*o**3/7 - 9*o**2/7 + 53. Factor n(a).
-2*a*(a + 1)**2*(a + 3)**2/7
Factor 164/9*d - 2/9*d**2 - 3362/9.
-2*(d - 41)**2/9
Let o(q) be the first derivative of -2/7*q - 1/7*q**4 + 2/35*q**5 + 0*q**3 - 4 + 2/7*q**2. Factor o(v).
2*(v - 1)**3*(v + 1)/7
Let c be (-2 - (-49)/14)*4/3. Let w(k) be the first derivative of -k**c + 1 - 1/3*k**3 - k. What is s in w(s) = 0?
-1
Let n(s) be the third derivative of s**7/210 + 3*s**6/20 + 11*s**5/20 + 2*s**4/3 - 562*s**2. What is f in n(f) = 0?
-16, -1, 0
Let y(v) be the second derivative of v**7/98 - 17*v**6/70 + 123*v**5/70 - 13*v**4/14 - 53*v**3/2 - 105*v**2/2 + 291*v. Suppose y(a) = 0. Calculate a.
-1, 5, 7
Solve 113*k**2 - 103*k**3 - 2*k**4 + 56*k - 199*k**2 - 34*k**3 + 7*k**4 = 0.
-1, 0, 2/5, 28
Let t be (21/4)/(6/40). Let g(h) = -5*h**2 - 7*h + 15. Let j(l) = 60*l**2 + 85*l - 180. Let y(a) = t*g(a) + 3*j(a). Factor y(b).
5*(b - 1)*(b + 3)
Let r(i) be the first derivative of -i**5/30 - 5*i**4/12 - 4*i**3/3 - 11*i**2/6 - 7*i/6 - 100. Suppose r(y) = 0. Calculate y.
-7, -1
Factor -3*r - 11*r**2 + 24 + 2*r + 4*r**3 + 5*r - 5*r**2.
4*(r - 3)*(r - 2)*(r + 1)
Let j(p) be the second derivative of 1/3*p**4 + 0*p**2 + 0*p**6 + 0 + 0*p**3 + 3/10*p**5 - 1/21*p**7 - 25*p. Factor j(v).
-2*v**2*(v - 2)*(v + 1)**2
Let r(k) be the first derivative of -1 + 6*k**2 + 22*k + k**4 + 13*k - 4*k**3 - 39*k. Suppose r(a) = 0. Calculate a.
1
Let v = 3491/770 + -13/385. Let v + 3/4*c - 3/4*c**2 = 0. What is c?
-2, 3
Let s(w) be the second derivative of -6*w**7/49 - 74*w**6/35 - 352*w**5/35 - 8*w**4/21 + 32*w**3 + 288*w**2/7 + 96*w. Suppose s(k) = 0. What is k?
-6, -2/3, 1
Let s(a) be the second derivative of -a**7/1008 - a**6/480 + a**5/120 + 5*a**4/12 + 5*a. Let m(o) be the third derivative of s(o). Factor m(i).
-(i + 1)*(5*i - 2)/2
Suppose 4 = -2*p + 4*x, 23*p - 27*p + 2*x = 2. Factor -1/2*h**2 + p + 0*h**3 + 0*h + 1/2*h**4.
h**2*(h - 1)*(h + 1)/2
Let l(a) be the third derivative of -2*a**7/105 - 53*a**6/30 - 155*a**5/3 - 625*a**4/2 + 6*a**2 - 46. Factor l(r).
-4*r*(r + 3)*(r + 25)**2
Let k(f) be the third derivative of -8*f**2 + 0*f - 1/10*f**5 - 7/6*f**4 + 5/3*f**3 + 0. What is q in k(q) = 0?
-5, 1/3
Suppose -621/2*c - 441/2*c**2 - 111/2*c**3 - 9/2*c**4 - 81 = 0. What is c?
-6, -3, -1/3
Let r(n) be the second derivative of 5*n**4/72 - 13*n**3/36 + n**2/2 + 4*n - 3. Let r(s) = 0. Calculate s.
3/5, 2
Let r = 103 + -39. Determine g, given that 17*g**4 - r*g**5 + 16*g**3 - 16*g**2 + 4*g**5 + 99*g**4 = 0.
-2/5, 0, 1/3, 2
Let m(d) be the first derivative of d**8/112 + d**7/70 - d**6/40 - d**5/20 - 9*d**2/2 - 3. Let y(s) be the second derivative of m(s). Factor y(z).
3*z**2*(z - 1)*(z + 1)**2
Let f be (17/4 + -3)*4. Let -30 + 63 - 23 + f*d**2 + 15*d = 0. What is d?
-2, -1
Let z(j) = 88*j - 528. Let q be z(6). Let c(m) be the second derivative of 8*m - 1/30*m**5 + 2/45*m**6 - 1/63*m**7 + 0*m**3 + 0 + q*m**2 + 0*m**4. Factor c(i).
-2*i**3*(i - 1)**2/3
Let f = -6/3857 + 7732/11571. Determine g, given that -1/3*g**2 + 2/3*g**3 - 1/6*g**4 + 1/2 - f*g = 0.
-1, 1, 3
Let t be (2/(-3))/((-14)/63). Suppose 4*c = t*i + i - 4, 7 = -c + 3*i. Solve -7*r**2 - 1 - 7*r - 1 + 0 + 4*r**3 + 3*r**c = 0.
-1/2, 2
Let o be (18/4)/((-27)/(-18)). Let k(z) be the first derivative of 0*z - z**2 + 5 + 0*z**o + 1/2*z**4. Let k(b) = 0. Calculate b.
-1, 0, 1
Let w(k) be the first derivative of -k**4 + 12*k**3 + 11. Factor w(s).
-4*s**2*(s - 9)
Let d = 4647 + -9269/2. Determine k, given that 2 + 5/4*k**4 + 27/4*k**3 + d*k**2 + 9*k = 0.
-2, -1, -2/5
Let l = -33 - -45. Find n such that 4*n**3 + l*n**2 - 58 - n + 58 + 9*n = 0.
-2, -1, 0
Let z = 212 - 211. Let x be (-3)/(-7) + (-3)/(-42)*z. Determine c so that -1/2*c + 1 - x*c**2 = 0.
-2, 1
Let u(a) be the second derivative of -a**7/10080 + a**5/120 + 5*a**4/4 + 14*a. Let c(v) be the third derivative of u(v). Find i such that c(i) = 0.
-2, 2
Factor 305 - 65*k + 1295 - 4*k**2 + 5*k**2 - 15*k.
(k - 40)**2
Let n(b) be the second derivative of b**7/5040 - b**6/2880 + 47*b**4/12 - b - 39. Let u(y) be the third derivative of n(y). Solve u(c) = 0.
0, 1/2
Factor 0 - 2/17*k**5 + 0*k - 24/17*k**2 + 46/17*k**3 - 20/17*k**4.
-2*k**2*(k - 1)**2*(k + 12)/17
Solve -2*h**3 - 9 + 0*h**3 - h**3 + 0*h**3 - 15*h**2 - 21*h = 0.
-3, -1
Let h(y) be the third derivative of -1/75*y**7 + 0 - 4/75*y**6 + 0*y**3 + 0*y + 14*y**2 - 11/150*y**5 - 1/30*y**4. Suppose h(z) = 0. Calculate z.
-1, -2/7, 0
Let d(y) be the second derivative of -y**5/170 + y**4/17 + 12*y**3/17 - 216*y**2/17 - 149*y. Factor d(o).
-2*(o - 6)**2*(o + 6)/17
Factor -16 - 4*a**3 + 6*a**3 - 60*a**2 + 12*a**3 + 72*a.
2*(a - 2)**2*(7*a - 2)
Let b(g) be the third derivative of -g**6/30 - g**5/5 + 2*g**4/3 - 41*g**2. Factor b(x).
-4*x*(x - 1)*(x + 4)
Solve -12 + 377*d**2 + 28*d - 20 - 373*d**2 = 0.
-8, 1
Let s be 151/14 - (((-357)/14)/17)/(-3). Let 34/7*t**2 + s*t + 0*t**3 - 2/7*t**4 + 40/7 = 0. Calculate t.
-2, -1, 5
Let w be -5 - 4/((-12)/(-9)). Let s(t) = 32*t**2 - 28*t - 16. Let u(a) = 21*a**2 - 19*a - 11. Let n(m) = w*u(m) + 5*s(m). Factor n(f).
-4*(f - 2)*(2*f + 1)
Let z(m) be the first derivative of -16 + 5/3*m**3 - 15/2*m**2 + 10*m. Factor z(h).
5*(h - 2)*(h - 1)
Suppose 16 = 5*r - 9. Let u(d) be the first derivative of 0*d**2 + 0*d**3 + 0*d + 0*d**4 - 3 + 1/6*d**6 - 1/5*d**r. Factor u(j).
j**4*(j - 1)
Let k be (1100/105)/5 - (-28)/(-294). Let z(y) be the second derivative of 0*y**2 + 0 - y**4 + 3/20*y**5 - k*y + 2*y**3. Factor z(j).
3*j*(j - 2)**2
Let t be (-14)/(-24) - 2/(-8)*-2. Let h(y) be the second derivative of 0 - 7*y - 1/20*y**5 + 5/6*y**3 + t*y**4 + 3/2*y**2. Find k, given that h(k) = 0.
-1, 3
Let q(t) be the second derivative of -16/33*t**3 + 1/165*t**6 + 7/110*t**5 - 7*t + 0 + 0*t**2 + 4/33*t**4. Find h such that q(h) = 0.
-4, 0, 1
Let i = 448/195 - 29/13. Let p(m) be the second derivative of i*m**4 + 4*m - 3/25*m**5 + 0 - 4/5*m**2 + 2/5*m**3 + 2/75*m**6. Factor p(x).
4*(x - 2)*(x - 1)**2*(x + 1)/5
Let l = -554/27 - -6148/297. Let -l*z**2 - 8/11 - 16/11*z + 2/11*z**4 - 2/11*z**5 + 10/11*z**3 = 0. Calculate z.
-1, 2
Let f(i) be the third derivative of i**7/1260 - 13*i**6/72 + 473*i**5/30 - 42527*i**4/72 + 79507*i**3/36 - 50*i**2. Factor f(a).
(a - 43)**3*(a - 1)/6
Let l(c) be the first derivative of -c**6/36 - 2*c**5/15 + 7*c**3/9 + 17*c**2/12 + c + 18. Find y such that l(y) = 0.
-3, -1, 2
Let r be -705 + 698 - (1 + -10). Factor -20/7 - 2/7*a**r - 22/7*a.
-2*(a + 1)*(a + 10)/7
Let o(a) be the first derivative of -16 + 0*a + 3/5*a**5 + 3/4*a**4 - a**3 - 3/2*a**2. Factor o(z).
3*z*(z - 1)*(z + 1)**2
Let t be (-1 - (-30)/5)/(1 + 0). What is g in 8*g - t*g**3 + 2*g**2 + 9*g**2 + 4*g**2 + 12*g = 0?
-1, 0, 4
Let i(v) be the second derivative of -6144*v**2 + 0 - 12*v**4 - 384*v**3 - 3/20*v**5 - 2*v. Find f, given that i(f) = 0.
-16
Suppose -2938/7*d - 676/7 - 18/7*d**3 + 464/7*d**2 = 0. Calculate d.
-2/9, 13
Let n(h) be the third derivative of h**7/420 - h**6/60 - h**5/120 + h**4/12 - 152*h**2. Determine u so that n(u) = 0.
-1, 0, 1, 4
Let z(o) be the first derivative of -o**5/30 + o**4/3 - o**3 + 13*o**2/2 - 3. Let k(i) be the second derivative of z(i). Solve k(t) = 0.
1, 3
Let c(k) = -3*k**5 - 6*k**4 + 3*k**3 + 27*k**2 - 18*k + 3. Let p(h) = -8*h**5 - 12*h**4 + 9*h**3 + 55*h**2 - 35*h + 5. Let d(v) = -7*c(v) + 3*p(v). Factor d(q).
-3*(q - 1)**4*(q + 2)
Let m(f) = f**3 - 6*f**2 + 5*f + 2. Let l be m(5). Suppose 4 + 23*h + 114*h**4 + 29*h**2 + 19*h**l + 40*h**3 + h - 102*h**4 = 0. Calculate h.
-1, -1/3
Suppose 121*s + 141*s = 297 + 489. Factor 24/5 + 48*z**2 - 36/5*z**s - 148/5*z.
-4*(z - 6)*(3*z - 1)**2/5
Suppose 0 = -5*u - 5*q + 85, 0 = q - 0 - 5. Factor u - 74*l**2 + 78*l**2 + 9*l + 7*l.
4*(l + 1)*(l + 3)
Let p(m) be the second derivative of -1/66*m**4 - m**2 - 4/11*m**3 - 48*m + 0. Factor p(k).
-2*(k + 1)*(k + 11)/11
Let s = -3413/23845 + 28/251. Let f = 389/285 + s. Factor 2/3 - f*p + 2/3*p**2.
2*(p - 1)**2/3
Let n(d) be the third derivative of d**8/168 + 22*d**7/105 + 14*d**6/5 + 49*d**5/3 + 343*d**4/12 - 2*d**2 - 5. Factor n(z).
2*z*(z + 1)*(z + 7)**3
Let z(r) = -r*