 - i. Let v(m) = c*o(m) - 2*z(m). Factor v(h).
-3*h**2*(h + 1)
Let r(p) be the first derivative of p**4/28 + 4*p**3/21 + 5*p**2/14 + 2*p/7 - 78. Factor r(l).
(l + 1)**2*(l + 2)/7
Let b(d) be the first derivative of -2*d**3/9 - 8*d**2 + 50*d/3 + 1096. Factor b(h).
-2*(h - 1)*(h + 25)/3
Let u(m) be the third derivative of 1/6*m**8 + 7/3*m**5 - 2/3*m**4 - 62/105*m**7 - 8/3*m**3 + 2*m + 0 + 16*m**2 - 1/3*m**6. Suppose u(s) = 0. Calculate s.
-1, -2/7, 1/2, 1, 2
Let l(b) = -6*b**3 + 68*b**2 - 76*b + 42. Let f(o) = 2*o**3 - 23*o**2 + 25*o - 14. Let j(g) = -14*f(g) - 5*l(g). Factor j(w).
2*(w - 7)*(w - 1)**2
Let j(m) be the second derivative of -m**7/120 - m**6/8 - m**5/5 + 7*m**4/12 + 18*m. Let p(b) be the third derivative of j(b). Let p(o) = 0. Calculate o.
-4, -2/7
Let x(a) = -a**2 - 3*a + 1. Let t(q) = -27*q**2 + 3*q + 9. Let j(h) = t(h) - 5*x(h). Suppose j(m) = 0. What is m?
-2/11, 1
Let j(l) be the second derivative of l**4/36 + 7*l**3/9 + 13*l**2/6 + 992*l. Find f such that j(f) = 0.
-13, -1
Let k = -203 + 42631/210. Let u(z) be the third derivative of -1/84*z**4 + z**2 + 0*z + 0 - k*z**5 + 0*z**3. Let u(o) = 0. Calculate o.
-1, 0
Let a(t) be the first derivative of 1/3*t + 1/9*t**3 + 1/3*t**2 - 20. Factor a(z).
(z + 1)**2/3
Let d(p) be the second derivative of 5*p**4/42 - 11*p**3/21 - 12*p**2/7 + 271*p. Find a such that d(a) = 0.
-4/5, 3
Factor -15*c**3 - 36/7*c + 132/7*c**2 + 0 + 24/7*c**4.
3*c*(c - 2)**2*(8*c - 3)/7
Let z(h) = -2*h + 4*h - 9 - 4*h + 0. Let q be z(-6). Factor 3/7*g**q - 3/7 + 3/7*g**2 - 3/7*g.
3*(g - 1)*(g + 1)**2/7
Let y(j) be the first derivative of -j**6/42 + 31*j**5/35 - 255*j**4/28 + 75*j**3/7 + 94. Factor y(d).
-d**2*(d - 15)**2*(d - 1)/7
Let r(i) be the first derivative of -i**7/560 + i**6/120 + 7*i**5/80 + i**4/4 - 17*i**3/3 - 12. Let h(a) be the third derivative of r(a). Solve h(n) = 0 for n.
-1, 4
Let z(t) = 45*t**4 + 70*t**3 - 15*t**2 - 25*t + 50. Let h(o) = 11*o**4 + 17*o**3 - 4*o**2 - 6*o + 12. Let g(s) = -25*h(s) + 6*z(s). Suppose g(b) = 0. What is b?
-2, 0, 1
Let l(z) = 13*z**3 - 3*z**2 - 5*z - 5. Let w(o) = 7*o**3 - o**2 - 3*o - 3. Let c(u) = -u + 14. Let x be c(17). Let s(g) = x*l(g) + 5*w(g). Factor s(k).
-4*k**2*(k - 1)
Let x(w) be the first derivative of 2/25*w**5 + 8/5*w - 11 - 1/5*w**4 - 2/5*w**3 + 4/5*w**2. Find c, given that x(c) = 0.
-1, 2
Let o be 2/2*(-5 + 21). Let w be ((-6)/4 + 1)*(-16 + o). Determine g so that -2/7*g**5 + w*g**2 - 2/7*g**3 + 0*g + 0 - 4/7*g**4 = 0.
-1, 0
Let t(n) be the second derivative of 259*n**7/8 + 679*n**6/40 - 279*n**5/8 + 49*n**4/4 - n**3 - 22*n + 2. Determine y, given that t(y) = 0.
-1, 0, 2/37, 2/7
Let m(h) = h**4 + 3*h**3 + h**2 + h + 1. Let p(f) = 5*f**4 + 14*f**3 + 25*f**2 + 52*f + 30. Let y(s) = 6*m(s) - p(s). Factor y(q).
(q - 4)*(q + 1)**2*(q + 6)
Let u = -3248 + 9760/3. Factor -u*i - 1/3*i**3 + 0 - 8/3*i**2.
-i*(i + 4)**2/3
Factor -6/11*d**4 + 0*d**2 + 18/11*d**3 - 24/11*d + 0.
-6*d*(d - 2)**2*(d + 1)/11
Let f(n) be the third derivative of 0*n + 0 - 1/3*n**3 - 1/6*n**4 - 1/30*n**5 + 7*n**2. Determine s, given that f(s) = 0.
-1
Factor -2/13*f**2 - 50/13*f + 0.
-2*f*(f + 25)/13
Let 21*v**2 + 99*v + 18 + 77*v - 54*v + 7*v = 0. Calculate v.
-6, -1/7
Suppose 12*v + v = -0*v. Let y(j) be the first derivative of 0*j**3 + v*j - 10 - 2/65*j**5 + 1/13*j**4 + 0*j**2. Factor y(h).
-2*h**3*(h - 2)/13
Determine a, given that -15/8 + 3/8*a**2 + 3/2*a = 0.
-5, 1
Let z(w) = w**3 - 12*w**2 + 2*w - 21. Let o be z(12). Suppose 2*r - 9*r**2 + 6*r**2 - o*r + r**2 - r**3 = 0. What is r?
-1, 0
Let 0*i + 1/4*i**4 + 121/4*i**2 + 11/2*i**3 + 0 = 0. What is i?
-11, 0
Let c(d) = 10*d**2 + 5*d. Let z(g) = 5*g**2 + 3*g. Let m be 6/27 + (-47)/9. Let y(a) = m*z(a) + 3*c(a). Solve y(l) = 0.
0
Let r(b) be the first derivative of 0*b**3 + 0*b**2 + 3/35*b**5 + 29 - 3/14*b**4 + 0*b + 1/14*b**6. Factor r(s).
3*s**3*(s - 1)*(s + 2)/7
Let a(w) be the second derivative of -w**6/30 + 3*w**5/20 + w**4/4 - 7*w**3/6 - 3*w**2 - 2*w + 96. Find i, given that a(i) = 0.
-1, 2, 3
Let i be 561/374*(-4)/(-14). Factor -i*f + 2/7*f**2 + 1/7.
(f - 1)*(2*f - 1)/7
Let v(x) be the second derivative of 1/120*x**6 - 1/336*x**7 - 29*x - 1/6*x**4 + 0 - 1/3*x**3 + 1/20*x**5 + 2*x**2. Factor v(t).
-(t - 2)**3*(t + 2)**2/8
Let j(i) = i**2 - 25*i + 45. Let y be j(23). Let u be (y*2/(-4))/(38/380). Factor -4/7*k**4 + 8/7*k**2 + 4/7*k + 4/7*k**u - 4/7 - 8/7*k**3.
4*(k - 1)**3*(k + 1)**2/7
Let p be ((-11)/(231/(-90)) - 4) + (-30)/105. Factor 1/2*a**2 + 0*a + p.
a**2/2
Let z(c) = 7*c**3 + 4*c**2 - 21*c. Let i = 132 + -127. Let f(j) = 6*j**3 + 4*j**2 - 20*j. Let s(m) = i*f(m) - 4*z(m). Factor s(d).
2*d*(d - 2)*(d + 4)
Let d(m) be the second derivative of -m**8/560 - m**7/140 - m**6/120 - 4*m**3/3 + 8*m. Let j(l) be the second derivative of d(l). Factor j(u).
-3*u**2*(u + 1)**2
Let d(r) be the first derivative of 5*r**4/4 - 55*r**3/3 + 95*r**2/2 - 45*r - 70. Solve d(q) = 0 for q.
1, 9
Let v(k) = -2*k**3 - 2*k + 1. Let r(i) = i**4 - 3*i**3 + 74*i**2 - 120*i + 66. Let p(x) = -5*r(x) - 30*v(x). Determine o so that p(o) = 0.
1, 2, 6
Let l(x) = -4*x**3 - 42*x**2 + 294*x - 680. Let t(w) = -3*w**3 - 42*w**2 + 294*w - 681. Let h(f) = -5*l(f) + 6*t(f). Find d, given that h(d) = 0.
7
Factor -4 - 42/5*a - 2/5*a**3 - 24/5*a**2.
-2*(a + 1)**2*(a + 10)/5
Let a be (-1 + -351)*(-4)/8. Determine o, given that -2*o**2 - 175 + 0*o**2 + o**2 + o**3 + a - o = 0.
-1, 1
Let x(k) = 23*k**4 + 45*k**3 + 33*k**2 + 2*k - 3. Let h(f) = 45*f**4 + 90*f**3 + 65*f**2 + 5*f - 5. Let v(d) = 3*h(d) - 5*x(d). Solve v(g) = 0.
-1, -1/4, 0
Let k be (10308/40)/((-2 + 5)*-1). Let r = 86 + k. Factor -2/5 + r*q**3 + 1/10*q**2 - 2/5*q.
(q - 2)*(q + 1)*(q + 2)/10
Let o(m) = 6*m**2 + 3*m + 3. Let h be ((-6)/2)/((-3)/(-4)). Let c(p) = -6*p**2 - 3*p - 4. Let b(d) = h*o(d) - 3*c(d). Factor b(t).
-3*t*(2*t + 1)
Suppose -10 - 26 = -9*u. Let z be 1*(-3)/((-6)/(-8)) + u. Factor -3/4*o**4 - 3/2*o + z + 9/4*o**2 + 0*o**3.
-3*o*(o - 1)**2*(o + 2)/4
Let v be 60/540 - 52/8*8/(-18). What is g in -17*g**2 - 7/3*g**v - 28*g - 20/3 = 0?
-5, -2, -2/7
Suppose 754*b + 161 = 777*b. Let h(v) be the third derivative of 0*v + 0 + 1/2*v**3 + 1/70*v**b - 1/2*v**4 + 7*v**2 + 3/10*v**5 - 1/10*v**6. Factor h(t).
3*(t - 1)**4
Let q(t) be the second derivative of -t**10/105840 - t**9/26460 - t**8/23520 + 3*t**4/2 + 6*t. Let a(p) be the third derivative of q(p). Factor a(i).
-2*i**3*(i + 1)**2/7
Determine m, given that 3/2*m**3 + 0 - 1/4*m - 5/4*m**5 - m**2 + m**4 = 0.
-1, -1/5, 0, 1
Let r = 166/5 + -33. Suppose 2*q + 21 = 96*q - 167. Determine o so that -1/5*o + 2/5*o**q + r*o**5 + 0*o**3 + 0 - 2/5*o**4 = 0.
-1, 0, 1
Let b = 641 + -639. Determine r so that 10/13*r**b + 0 - 4/13*r = 0.
0, 2/5
Let z = -2561 - -2566. Let n(i) be the second derivative of 1/80*i**z - 1/168*i**7 + 9*i + 0*i**2 + 0*i**3 - 1/120*i**6 + 1/48*i**4 + 0. Factor n(v).
-v**2*(v - 1)*(v + 1)**2/4
Factor -4*k**2 - 18*k + 5 + 2*k**3 + 15 + 16.
2*(k - 3)*(k - 2)*(k + 3)
Let l = -16 + 18. Factor -f**3 + 49*f - 25*f + 4*f**3 - 15*f**l - 12.
3*(f - 2)**2*(f - 1)
Let -1/2*v**2 - 2*v + 6 = 0. What is v?
-6, 2
Let s(c) = c**3 - 3*c**2 - c + 1. Let h(x) = -x**3 + 6*x**2 + x - 1. Suppose 3 = -3*d - 0*d. Let r be d/2*5*2. Let i(p) = r*s(p) - 2*h(p). Factor i(t).
-3*(t - 1)**2*(t + 1)
Let i(w) be the third derivative of 2*w**5/15 - 137*w**4/12 + 34*w**3/3 - 2*w**2 - 10*w. Factor i(k).
2*(k - 34)*(4*k - 1)
Let -3/8*d**2 + 3/8 + 1/8*d**3 - 1/8*d = 0. Calculate d.
-1, 1, 3
Let k(d) be the third derivative of -d**5/120 - d**4/16 - d**3/6 + 3*d**2. Factor k(j).
-(j + 1)*(j + 2)/2
Suppose -4*b - 6 = -10*b. Let o(y) = 65*y**2 + 95*y + 35. Let x(i) = -i**2 + i + 1. Let s(f) = b*x(f) + o(f). Determine u, given that s(u) = 0.
-3/4
Suppose 3/7*a**2 + 0 + 3/7*a = 0. Calculate a.
-1, 0
Let g(k) be the third derivative of 0*k + k**3 - 3/80*k**6 + 18*k**2 + 0 + 13/40*k**5 - k**4. Factor g(m).
-3*(m - 2)**2*(3*m - 1)/2
Let a = 1297/5 - 269. Let b = a + 442/45. Suppose -2/9*k**3 - 2/9*k**4 + 2/9*k + 0 + b*k**2 = 0. What is k?
-1, 0, 1
Find g, given that 5 + 0*g - 5/4*g**5 + 5/4*g**3 + 15/4*g**4 - 35/4*g**2 = 0.
-1, 1, 2
Let c(y) be the first derivative of -31 + 8*y**2 - 64/7*y - 83/28*y**4 + 68/21*y**3 - 1/21*y**6 + 23/35*y**5. Determine x, given that c(x) = 0.
-1, 1