derivative of -l**8/24 - 2*l**7/105 + 7*l**6/30 + 2*l**5/15 - 7*l**4/12 - 2*l**3/3 + l**2 - 32*l. Determine t so that g(t) = 0.
-1, -2/7, 1
Let v be (-5 + 6 + 2)*3/18. Let n(d) be the first derivative of -1/2*d - 1/8*d**4 - 12 - 3/4*d**2 - v*d**3. Suppose n(j) = 0. What is j?
-1
Let p(a) = a**2 - 11*a - 30. Let c be p(14). Find m such that -4*m**2 - 19 - 15 + c*m + 26 = 0.
1, 2
Let h = -127/7 + 649/35. Factor -6/5*y**2 - 4/5*y + h.
-2*(y + 1)*(3*y - 1)/5
Suppose -101 = -7*k + 158. Find w, given that 6*w**2 + k*w - 35*w - 3 - 1 = 0.
-1, 2/3
Let g(y) = -y**2 + 139*y - 924. Let x be g(7). Let -6/7*n**3 - 2/7*n**4 + 0*n**2 + x + 0*n = 0. Calculate n.
-3, 0
Suppose 0 = 8*t - 7*t - 3. Let m = 2317/2 + -1157. What is z in 3*z**2 + 0*z + 3/2*z**t + 0 - m*z**4 = 0?
-1, 0, 2
Let i = 16249/11 - 1477. Factor -2/11*a**2 + i*a + 0.
-2*a*(a - 1)/11
Factor -13/5*c**3 + 4/5*c + 0 + 24/5*c**2.
-c*(c - 2)*(13*c + 2)/5
Find r such that 8/11*r + 2/11*r**4 + 32/11*r**3 - 114/11*r**2 + 152/11 = 0.
-19, -1, 2
Let n(h) be the second derivative of 0 - 16*h - 1/4*h**4 + 0*h**2 + 1/8*h**3 + 9/80*h**5. Factor n(q).
3*q*(q - 1)*(3*q - 1)/4
Let p = -67 + 41. Let z = 29 + p. What is h in -48*h**3 - 63/4*h**4 - 129/4*h**2 + 3*h + z = 0?
-2, -1, -1/3, 2/7
Factor 3/2*a + 3/2*a**2 - 63.
3*(a - 6)*(a + 7)/2
Suppose 27*l = 12*l - 90. Let q(f) = -f**2 - f - 1. Let x(a) be the second derivative of a**4/4 + 3*a**2 + a. Let i(v) = l*q(v) - x(v). Factor i(w).
3*w*(w + 2)
Let p be 558/432 - (-1 + 15/24). Factor -p*b**2 + 10/3*b - 5/3.
-5*(b - 1)**2/3
Let c be 6/9 + 538/3. Let p = 1622/9 - c. Factor 2/9*u**2 + 0*u - p.
2*(u - 1)*(u + 1)/9
Let q be (-455)/169 + -1 + 4. Factor 2/13*a**5 + 0 + 0*a**3 + q*a**2 - 2/13*a - 4/13*a**4.
2*a*(a - 1)**3*(a + 1)/13
Let p(i) be the first derivative of -20/3*i - 4*i**2 - 4/9*i**3 + 18. Suppose p(f) = 0. Calculate f.
-5, -1
Let b(l) = -l**4 - l**3 + l**2 - l - 1. Let w(f) = -f**5 - 27*f**4 - 102*f**3 + 269*f**2 - 149*f - 5. Let j(u) = -15*b(u) + 3*w(u). Factor j(i).
-3*i*(i - 1)**2*(i + 12)**2
Suppose -4/5*n**2 + 12/5*n + 1/5*n**5 - 9/5*n**3 + 0 + 0*n**4 = 0. What is n?
-2, 0, 1, 3
Factor -168*v + 3*v**2 + 81*v + 84*v + 3*v**3 - 3*v**4.
-3*v*(v - 1)**2*(v + 1)
Let r be 1*-1*(-4)/13. Let m be (295/(-3068))/((-5)/8). Factor 0*n**2 + r*n**3 - 2/13 + m*n**4 - 4/13*n.
2*(n - 1)*(n + 1)**3/13
Suppose -5 - 1 = -3*m. Suppose 0 = -5*d + 8*d - 3*f - 24, 2*d - f - 14 = 0. Determine a, given that 0*a - d - 3/2*a**3 - 9/2*a**4 + 21/2*a**m + 3/2*a**5 = 0.
-1, 1, 2
Let r(s) be the second derivative of 1/16*s**4 - 1/4*s**3 - 5*s - 9/8*s**2 + 0. Determine i, given that r(i) = 0.
-1, 3
Factor 900 - 925 + 3*f**3 + 30*f - 27*f**2 - 2*f**3 + 21*f.
(f - 25)*(f - 1)**2
Factor -5*j**4 - 10*j**3 - 19*j - 32*j + 61*j + 5.
-5*(j - 1)*(j + 1)**3
Suppose 3*p - 5*o = -286, 0 = 6*p - 5*p + o + 106. Let l be p/21 - (-15)/3. Solve -3/7*u + 0 + l*u**2 = 0.
0, 3
Let p be -14 + 3952/273 + 1*(-6)/(-9). Factor 0 - 2/7*n**4 - p*n**2 + 0*n + 10/7*n**3.
-2*n**2*(n - 4)*(n - 1)/7
Let m(a) = 3*a**2 + 14*a - 21. Let b(g) = 2*g**2 + 13*g - 22. Let y = 2 - -20. Let r be 1/(-4) + y/(-8). Let i(u) = r*m(u) + 4*b(u). Factor i(s).
-(s - 5)**2
Let w(a) be the third derivative of -a**6/90 - 11*a**5/45 - 5*a**4/9 - 5*a**2 - 2. Factor w(k).
-4*k*(k + 1)*(k + 10)/3
Let b = -240 + 244. Let 6*z**2 + 10/3*z**3 + 2/3*z**b + 4/3 + 14/3*z = 0. What is z?
-2, -1
Let m(z) = -6*z + 21. Let h(j) = -j**2 + 11*j - 45. Let q(n) = -3*h(n) - 7*m(n). Factor q(k).
3*(k - 1)*(k + 4)
Suppose 4*m = 2*m - h + 62, -2*h = -2*m + 74. Determine b so that b**2 - 38*b + 6 - 3 + b**3 + m*b = 0.
-3, 1
Let v be 7 - (-3585)/(-492) - 2/(-4). Let j = 3/82 + v. Factor -3/8*b**3 + 0 + 0*b + j*b**4 + 0*b**2 + 5/8*b**5.
b**3*(b + 1)*(5*b - 3)/8
Let b be (8/(-12))/((-9)/(-36) + 65/(-36)). Solve 3/7*n + 0 + b*n**3 + 6/7*n**2 = 0.
-1, 0
Let g = -1/1457 + 2917/4371. What is m in -4/3*m**2 - g*m**5 + 2/3*m + 4/3*m**4 + 0 + 0*m**3 = 0?
-1, 0, 1
Let f(r) = -r**2 - 5*r - 1. Let w be f(-4). Let j be (-15)/75 - (-5)/25. Factor j*c**2 - 3/2 - 9/2*c + 6*c**w.
3*(c - 1)*(2*c + 1)**2/2
Let p(n) = -4*n**5 - 22*n**4 - 44*n**3 - 40*n**2 - 16*n. Let x(d) = 4*d**5 + 21*d**4 + 42*d**3 + 40*d**2 + 18*d. Let t(m) = -3*p(m) - 2*x(m). Factor t(y).
4*y*(y + 1)**3*(y + 3)
Let d be -17 - -1*0/(-4). Let x = -15 - d. What is g in 3*g**2 - 2*g**5 - 2*g**x + 4*g**3 - 2*g - g**2 = 0?
-1, 0, 1
Let o(t) be the third derivative of t**6/200 - t**5/50 - 310*t**2. Factor o(f).
3*f**2*(f - 2)/5
Let b(g) be the first derivative of -g**7/49 + 8*g**6/105 - g**5/10 + g**4/21 + 12*g + 7. Let n(x) be the first derivative of b(x). Solve n(k) = 0.
0, 2/3, 1
Suppose -6*m + 1188 = 6*m. Factor -23*a**2 - 55*a**3 + 20 + 10*a**4 + m*a**2 + 29*a**2 - 80*a.
5*(a - 2)**2*(a - 1)*(2*a - 1)
Let r(u) be the third derivative of u**8/5040 + u**7/210 + u**6/20 - u**5/20 + 6*u**2. Let z(l) be the third derivative of r(l). Factor z(y).
4*(y + 3)**2
Solve -169/2 + 559/4*h - 83/2*h**3 - 1/4*h**5 - 20*h**2 + 13/2*h**4 = 0 for h.
-2, 1, 13
Let s be -35 - -41 - 6/(-4)*(-364)/105. Factor s*m - 2/5*m**2 - 2/5.
-2*(m - 1)**2/5
Let s = 2257/24 + -94. Let m(a) be the third derivative of 1/80*a**6 + 0*a + 4*a**2 + s*a**3 - 11/240*a**5 + 1/24*a**4 + 0. Factor m(u).
(u - 1)**2*(6*u + 1)/4
Let v = 96 + -75. Factor v - 6*q + 6*q**3 - 21 - 9*q**4 - 3*q**3 + 9*q**2 + 3*q**5.
3*q*(q - 2)*(q - 1)**2*(q + 1)
Let p(t) be the first derivative of -1/9*t**2 + 38 + 2/27*t**3 + 0*t. Factor p(f).
2*f*(f - 1)/9
Let o = -13454 + 13457. Let 0*k**2 + 0 - 2/15*k**o + 0*k = 0. Calculate k.
0
Let s(l) be the third derivative of 9*l**2 + 1/180*l**6 - 1/36*l**4 + 0 - 1/45*l**5 + 0*l + 2/9*l**3. Let s(r) = 0. What is r?
-1, 1, 2
Let m(p) = p - 1. Let w(b) = 5*b**2 - 9*b**2 - 3 - b**2 + 4*b**2 - 5*b. Let l(d) = -2*m(d) - 2*w(d). Solve l(c) = 0.
-2
Let d(c) be the second derivative of 27*c**5/80 - 137*c**4/16 - 57*c**3/4 + 12*c**2 + 49*c. Factor d(q).
3*(q - 16)*(q + 1)*(9*q - 2)/4
Let h(g) be the second derivative of -g**5/10 + g**4/6 - 2*g - 5. Find j, given that h(j) = 0.
0, 1
Factor -1050*t**3 - 1050*t + 147/2*t**4 + 147/2 + 3897*t**2.
3*(t - 7)**2*(7*t - 1)**2/2
Let z(x) be the third derivative of -x**8/840 - x**7/630 - x**6/1620 + 3*x**3/2 + 5*x**2. Let t(h) be the first derivative of z(h). Factor t(p).
-2*p**2*(3*p + 1)**2/9
Let m(j) be the third derivative of 0*j - 22*j**2 + 35/4*j**4 + 0 + 25/12*j**5 + 1/6*j**6 + 15/2*j**3. Factor m(k).
5*(k + 3)**2*(4*k + 1)
Let g(z) = -z**3 - z**2 + z + 1. Let l(t) = 13*t**3 + 9*t**2 - 11*t - 11. Let f be -2 - (0/3)/(-3). Let o(w) = f*l(w) - 22*g(w). Suppose o(s) = 0. Calculate s.
0, 1
Solve 3/8*z**4 - 9/4*z**3 + 0 + 27/2*z - 93/8*z**2 = 0.
-4, 0, 1, 9
Suppose q - 2*h - 4 = 3*h, 3*h = q - 2. Let f be 306/48 + -5 + q. Factor -3/2*v**3 - 3/4*v + f*v**4 + 0 + 15/8*v**2.
3*v*(v - 2)*(v - 1)**2/8
Let u = 66 - 26. Determine k so that -2*k - 8 - 12*k**3 - u*k**2 - 28*k - 6*k = 0.
-2, -1, -1/3
Let x(h) be the first derivative of -30*h**2 + 28/5*h**5 + 8/3*h**3 + 14*h**4 + 21 - 36*h + 2/3*h**6. Determine i, given that x(i) = 0.
-3, -1, 1
Suppose 162*f + 17 = 40 - 23. Factor 6/5*b**3 - 2/5*b**5 + 0*b + 0 + f*b**4 - 4/5*b**2.
-2*b**2*(b - 1)**2*(b + 2)/5
Let z(n) = -5*n**4 + 10*n**3 + n + 16. Suppose 4*q = -3 - 81. Let b = q + 27. Let t(s) = s**4 - 2*s**3 - 3. Let p(w) = b*z(w) + 33*t(w). Solve p(i) = 0 for i.
-1, 1
Let w = -5 - -10. Suppose -3*k - 3*r + 18 = 0, -5*k - 6*r + w*r = -22. Determine q, given that -4/5 - 8*q - 169/5*q**3 - 88/5*q**k - 133/5*q**2 - 16/5*q**5 = 0.
-2, -1, -1/4
Let w(o) = 2*o**2 - 3*o + 1. Let r be w(2). Suppose -r*n + 10 = 4. Factor -2 + 4*d**2 - d + 4 - 6*d**n + d**2.
-(d - 1)*(d + 2)
Let h be (-39)/(-78) - 26/(-20). What is d in -6/5*d + h*d**2 + 0 - 3/5*d**3 = 0?
0, 1, 2
Let u = -12 - -14. Let v be (-27)/45 + ((-24)/(-10))/4. Let v + 1/2*w**u - 1/2*w - 1/8*w**3 = 0. Calculate w.
0, 2
Let v(k) be the first derivative of -k**4/16 - k**3/6 - 76. What is g in v(g) = 0?
-2, 0
Let g be 5/10*-3*36/(-2). Determine l, given that 30*l**2 + 22*l**2 + g*l**3 - 12*l**3 - 65*l**4 + 20*l**5 + 28*l**2 - 20*l = 0.
-1, 0, 1/4, 2
Factor -15/4*i - 27/8 - 3/8*i**2.
-3*(i + 1)*(i + 9)/8
Let c(x) = -15*x**3 + 15*x**2 + 9*x - 27. Let l(o) = -o**4 - o**2 - o - 1. Let a(b) = c(b) - 3*l(b). Find p, gi