z**2 - 9*z - 201 = 0.
4, 10
Let u(c) be the first derivative of -c**5/10 + c**4/3 + c - 2. Let v(k) be the first derivative of u(k). What is w in v(w) = 0?
0, 2
Suppose 3*b = 2*t + 18, -34*t + 5 = -b - 37*t. Let u(v) = 4*v**2 - 2. Let o be u(-2). Factor b*h**3 + h**4 - 2*h**2 - o*h**3 - 9*h**4.
-2*h**2*(h + 1)*(4*h + 1)
Factor 54/11 + 15/11*m + 1/11*m**2.
(m + 6)*(m + 9)/11
Let s(w) = 54*w**2 + 542*w - 540. Let r(q) = -19*q**2 - 181*q + 180. Let z(j) = -14*r(j) - 5*s(j). Factor z(o).
-4*(o - 1)*(o + 45)
Let y = 7039 + -63077/9. Let u = y - 3526/117. Factor u - 14/13*m**2 - 10/13*m.
-2*(m + 1)*(7*m - 2)/13
Let d(h) be the third derivative of -1/60*h**4 + 0 + 0*h - 2/15*h**3 + 1/150*h**5 - 32*h**2. Factor d(m).
2*(m - 2)*(m + 1)/5
Let y(i) = -6*i**3 - 2*i. Let h(n) be the first derivative of 19*n**4/4 + 7*n**2/2 - 15. Let m(p) = -2*h(p) - 7*y(p). Determine r, given that m(r) = 0.
0
Let g be (-4)/14 - (-9)/(-21). Let c = -11/35 - g. Factor -4/5*m**2 + 0 - c*m - 2/5*m**3.
-2*m*(m + 1)**2/5
Let k(p) be the third derivative of p**5/540 + 17*p**4/216 + 7*p**3/9 - 3*p**2 - 21*p. Let k(y) = 0. Calculate y.
-14, -3
Let o(t) be the first derivative of -1/16*t**2 - 1/24*t**3 - 8 + 1/4*t. Let o(r) = 0. What is r?
-2, 1
Let b(v) be the third derivative of -v**7/105 - 14*v**6/15 - 261*v**5/10 + 14*v**4/3 + 784*v**3/3 + 297*v**2. Factor b(w).
-2*(w - 1)*(w + 1)*(w + 28)**2
Let y be (-6)/(-4)*2 - (-9 - -3). Suppose -7*g = -10*g + y. Solve 1 - 11/2*s - 13/2*s**4 + 2*s**5 + 11/2*s**2 + 7/2*s**g = 0.
-1, 1/4, 1, 2
Let y be (2 + (-22)/8)/((-138)/736). Let c(z) be the third derivative of 0 + 0*z - 1/120*z**5 - y*z**2 + 1/24*z**4 + 1/4*z**3. Determine w, given that c(w) = 0.
-1, 3
Let c(t) be the first derivative of 2*t**2 + 0*t - 1/4*t**4 + 0*t**3 + 19. Factor c(p).
-p*(p - 2)*(p + 2)
Let o = 42 - 37. Factor -75 + 5*d**2 - 4*d + 73 - o*d.
(d - 2)*(5*d + 1)
Let b(c) be the second derivative of -c**5/360 + c**4/36 - c**3/9 + 19*c**2/2 - 13*c. Let m(y) be the first derivative of b(y). Factor m(g).
-(g - 2)**2/6
Determine r, given that 1/2*r - 2/3 + 1/6*r**2 = 0.
-4, 1
Let f be (-57)/133 + 19/(-21) + 2. Suppose 4/9 - f*k - 28/9*k**2 = 0. What is k?
-1/2, 2/7
Let f(s) be the first derivative of -s**6/24 - 13*s**5/20 + 15*s**4/16 + 13*s**3/12 - 7*s**2/4 + 101. Suppose f(y) = 0. Calculate y.
-14, -1, 0, 1
Suppose -3*w = -44 - 28. Determine x, given that 8*x - 16*x - 34*x - 15*x**2 - w + 0*x = 0.
-2, -4/5
Let q(p) be the third derivative of -p**7/3360 + p**6/1440 + 7*p**3/6 - 14*p**2. Let k(x) be the first derivative of q(x). Suppose k(l) = 0. Calculate l.
0, 1
Let v(l) be the second derivative of -l**5/20 + l**4/6 + l**3/6 - 12*l. Let i be v(-1). Factor -6*j + 2*j**2 - i*j + 0*j**2.
2*j*(j - 4)
Let o(h) be the first derivative of 0*h - 1/8*h**4 - 4 - 1/3*h**3 - 1/4*h**2. Find s such that o(s) = 0.
-1, 0
Suppose -79*v + 78 = -40*v. What is n in -1/10*n**v + 1/5 - 1/10*n = 0?
-2, 1
Let c(h) be the third derivative of -h**7/350 + 9*h**6/200 + 23*h**5/100 - 9*h**4/40 - 11*h**3/5 + 277*h**2. Determine m, given that c(m) = 0.
-2, -1, 1, 11
Let k(v) be the second derivative of v**6/20 - 9*v**5/20 + v**4 + 3*v**3/2 - 27*v**2/4 - 58*v. Factor k(u).
3*(u - 3)**2*(u - 1)*(u + 1)/2
Let o(w) be the second derivative of -w**7/252 - w**6/15 - 49*w**5/120 - 5*w**4/4 - 19*w**3/9 - 2*w**2 + 4*w + 2. Let o(v) = 0. What is v?
-6, -2, -1
Let p(h) be the first derivative of -h**4/8 - 17*h**3/6 - 31*h**2/4 - 15*h/2 - 218. Solve p(f) = 0 for f.
-15, -1
Suppose 32/11*l**4 + 6/11*l**5 + 46/11*l**3 - 56/11*l - 16/11 - 12/11*l**2 = 0. What is l?
-2, -1/3, 1
Let h be -176 - -166 - 2*39/(-6). Factor 18/13*j**h - 4/13 + 2*j - 40/13*j**2.
2*(j - 1)**2*(9*j - 2)/13
Find h, given that 0 + 0*h - 4/5*h**3 - 24/5*h**2 = 0.
-6, 0
Let k(u) = u**3 + 2*u**2 - 4*u - 5. Let m be k(-2). Factor 35*x**m + 4*x + 10*x**2 + 35*x**3 - 2*x**5 - 64*x**3 - 2*x**4.
-2*x*(x - 2)*(x + 1)**3
Determine a, given that -6/11 - 8/11*a - 2/11*a**2 = 0.
-3, -1
Factor -55*j**4 + 19*j**5 + 314*j - 50*j**2 + 1 - 5*j**5 - 304*j + 80*j**3.
(j - 1)**4*(14*j + 1)
Let r be 8/176 - 595/(-462). Factor -2/3 - r*c - 7/6*c**3 + 19/6*c**2.
-(c - 2)*(c - 1)*(7*c + 2)/6
Let l be ((-28)/((-560)/450))/(6 + 0). Factor -39/8*j - l + 3/8*j**3 - 3/4*j**2.
3*(j - 5)*(j + 1)*(j + 2)/8
Suppose -4*l = -3*l + 2*d - 5, 4*l + d = 13. Suppose l = -7*x + 3. Factor 0 + 2/7*p**4 - 2/7*p**3 + x*p + 0*p**2.
2*p**3*(p - 1)/7
Let v(a) be the second derivative of -5*a**4/12 - 245*a**3/6 + 125*a**2 + 14*a - 17. Factor v(z).
-5*(z - 1)*(z + 50)
Let y(x) = -x**4. Let m = 0 + 3. Let h(i) = -i**5 + 3*i**4 + i**3. Let o be (-2)/4*4*(-3)/6. Let r(j) = m*y(j) + o*h(j). Factor r(f).
-f**3*(f - 1)*(f + 1)
Let d(q) be the third derivative of q**7/7560 + 11*q**6/4320 - q**5/120 + 5*q**4/12 + 6*q**2. Let x(i) be the second derivative of d(i). Factor x(y).
(y + 6)*(2*y - 1)/6
Let t(m) = -2*m - 2. Let i be t(-8). Suppose i*u = 15*u - 4. Factor -5*g**u + 5*g**4 - g**5 + 2*g**5.
g**5
Suppose 0 = 6*t - 3*t - 0*t. Let r(y) be the first derivative of t*y**2 + 0*y - 2/9*y**3 - 1/9*y**6 + 1/6*y**4 + 2/15*y**5 + 2. Factor r(m).
-2*m**2*(m - 1)**2*(m + 1)/3
Let l = 372816 + -4098097/11. Let w = l + -261. Solve -8/11 - w*q - 2/11*q**2 = 0 for q.
-2
Let -15/2*m**2 + 3/4*m**3 - 21/4*m + 147 = 0. Calculate m.
-4, 7
Let b(y) = -9*y**4 + 51*y**3 - 63*y**2 + 27*y - 6. Let r(z) = -7*z**4 + 51*z**3 - 63*z**2 + 25*z - 6. Let o(g) = -4*b(g) + 3*r(g). Factor o(x).
3*(x - 1)**3*(5*x - 2)
Factor -1826132/5*x - 308/5*x**3 + 1/5*x**4 + 35153041/5 + 35574/5*x**2.
(x - 77)**4/5
Suppose 4*l - 171 = -3*d + 261, -4*d + 4*l + 604 = 0. Factor 105*v**3 + 38*v**3 + 264*v**2 + d*v + 28*v + 5*v**3 + 28*v**4 + 32.
4*(v + 1)*(v + 2)**2*(7*v + 2)
Let q = -21 - -26. What is g in -4*g**2 - q*g**5 + 7*g**4 + 2*g + 3*g**5 - 3*g**4 = 0?
-1, 0, 1
Let a be (-10)/(-100)*15*(-8)/(-6). Let h(y) be the second derivative of 0*y**3 + 0 + 5*y - 1/12*y**4 + 0*y**a. Factor h(s).
-s**2
Suppose -21*i = -44*i + 69. Let c(s) be the third derivative of 0*s + 0 + 0*s**3 - 1/840*s**7 - 1/240*s**5 + 0*s**4 - 1/192*s**6 - i*s**2. Factor c(a).
-a**2*(a + 2)*(2*a + 1)/8
Let q(v) be the first derivative of -3*v**5/5 + 3*v**4/4 + 2*v**3 - 321. Factor q(d).
-3*d**2*(d - 2)*(d + 1)
Let f(q) be the third derivative of q**7/42 - q**6/6 + q**5/4 + 5*q**4/6 - 10*q**3/3 - 239*q**2. Factor f(n).
5*(n - 2)**2*(n - 1)*(n + 1)
Let w(j) be the first derivative of j**5/15 + 47*j**4/12 - 50*j**3/9 - 16*j**2 - 381. Factor w(u).
u*(u - 2)*(u + 1)*(u + 48)/3
Factor -2874*l - 6*l + 3360*l**2 - 7*l**5 - 7*l**5 + 3*l**5 - 1220*l**3 + 6*l**5 + 140*l**4.
-5*l*(l - 12)**2*(l - 2)**2
Let v(j) be the first derivative of 3*j**5/5 + 9*j**4/2 + 8*j**3 - 9*j**2 - 27*j - 169. Let v(n) = 0. What is n?
-3, -1, 1
Let o = -7124 + 14281/2. Factor o*y - 324*y**4 + 1 + 81*y**2 + 54*y**3.
-(3*y - 2)*(6*y + 1)**3/2
Solve -5*o**3 + 5*o - 3*o**2 - o**2 + 5 - o**2 - 4*o**2 + 4*o**2 = 0 for o.
-1, 1
Let -1/4 - 25/4*c**2 + 5/2*c = 0. Calculate c.
1/5
Find i, given that -338/7 + 52/7*i - 2/7*i**2 = 0.
13
Let r(o) = -o**3 - 5*o**2 + 2*o + 7. Let l be r(-6). Determine n, given that 14*n - 46*n - 8 - 2*n**5 - 38*n**3 - 50*n**2 - l*n**4 + 17*n**4 = 0.
-2, -1
Let m(q) be the second derivative of q**4/6 + 7*q**3/3 + 10*q**2 + 89*q. Determine c so that m(c) = 0.
-5, -2
Let k(p) be the first derivative of 8 - 9/2*p**2 - p**3 - 6*p. Solve k(v) = 0.
-2, -1
Let o(q) be the first derivative of -q**9/10584 + q**8/5880 + q**7/1470 - 10*q**3/3 - 1. Let t(a) be the third derivative of o(a). Solve t(j) = 0 for j.
-1, 0, 2
Suppose 5*t + 4*r = -10, -15 = -5*t - 2*r + 3*r. Suppose -2 = t*m - 8. Find p, given that -36/5*p + 4/5 - 21/5*p**5 + 97/5*p**4 - 159/5*p**m + 23*p**2 = 0.
2/7, 1/3, 1, 2
Let p(n) be the third derivative of n**7/630 - n**6/30 + 11*n**5/90 + 7*n**4/6 + 49*n**3/18 + 70*n**2 + 3*n. Factor p(a).
(a - 7)**2*(a + 1)**2/3
Let p be 24/(-32)*28/(-6). Let q(o) be the first derivative of 2*o + 6 - 5/4*o**4 + 3*o**3 - p*o**2 + 1/5*o**5. Factor q(d).
(d - 2)*(d - 1)**3
Let w(q) be the second derivative of q**5/20 + 25*q**4/9 - 34*q**3/9 - 555*q. Factor w(i).
i*(i + 34)*(3*i - 2)/3
Let s(t) = -t**4 + t**2 - t + 1. Let k(m) = m**4 - 25*m**3 - 116*m**2 - 24*m + 164. Let y(u) = -k(u) + 4*s(u). Factor y(j).
-