 + 2)/2
Let r(h) be the third derivative of 4/9*h**3 + 0*h - 1/90*h**5 + 0 - h**2 + 1/12*h**4. Suppose r(y) = 0. What is y?
-1, 4
Let m be 27/24*(-12)/9*-4. Let i be (-9)/(-5)*(4/m)/2. Suppose -i*v**2 + 0*v - 1/5*v**3 + 0 = 0. What is v?
-3, 0
Let y(f) be the first derivative of 2/15*f**3 + 1/6*f**4 - 24 - 1/45*f**6 + 0*f + 0*f**2 + 2/75*f**5. Let y(g) = 0. Calculate g.
-1, 0, 3
Factor 4*u**2 + 79*u + 20 + 42*u - 97*u.
4*(u + 1)*(u + 5)
Let i(h) be the third derivative of -h**7/70 - h**6/30 + 7*h**5/60 + h**4/6 - 2*h**3/3 - 78*h**2 - h. Let i(t) = 0. What is t?
-2, -1, 2/3, 1
Let u(y) be the first derivative of -y**6/15 + 2*y**5/5 + 3*y**4/5 - 64*y**3/15 - 32*y**2/5 + 481. Determine q so that u(q) = 0.
-2, -1, 0, 4
Let f be 4 + 0/((-4)/(-4)). Factor -5*w + 4*w**3 + 5*w - 16 + w**f - 16*w.
(w - 2)*(w + 2)**3
Suppose k = 2*r - 5*r + 40, r + 2*k = 20. Suppose 2*d = -2 + r. Factor i**4 - 5/8*i**d - 1/4*i**2 - 1/8*i**3 + 0*i + 0.
-i**2*(i - 1)**2*(5*i + 2)/8
Let l(a) be the third derivative of a**6/300 + a**5/10 + 9*a**4/20 - 81*a**3/5 + 630*a**2. Factor l(v).
2*(v - 3)*(v + 9)**2/5
Let h(u) be the first derivative of -5*u**4/48 + 5*u**3/12 - 28*u - 37. Let m(w) be the first derivative of h(w). Factor m(c).
-5*c*(c - 2)/4
Let a = 4168/3 + -1389. Suppose -6*z + z = 0, 5*k + z - 15 = 0. Factor -7/2*u**2 + 25/6*u**k - 3/2*u**4 + a + 1/2*u.
-(u - 1)**3*(9*u + 2)/6
Suppose 0 = k - 0*k - 2. Let b(x) = -10*x**2 + 4*x - 7. Let s(y) be the second derivative of y**4/12 + y**2/2 - 20*y. Let g(v) = k*b(v) + 22*s(v). Factor g(f).
2*(f + 2)**2
Let m = -1415/3 - -472. Find v such that -m*v**2 + 1 + 2/3*v = 0.
-1, 3
Factor 16/7*o - 2/7*o**2 + 0.
-2*o*(o - 8)/7
Let s = 27977 - 27977. Find k such that -1/2*k**5 - k**4 + 2*k**3 + 0 + 4*k**2 + s*k = 0.
-2, 0, 2
Let o(n) be the second derivative of -5/6*n**3 + 5/2*n**2 - 5/12*n**4 + 0 - n + 1/4*n**5. Solve o(b) = 0.
-1, 1
Suppose 5*b + 5*k - 45 = 0, -12 = -5*b + 2*k + 5. Let -19 - b*h**2 + 2*h + 8*h - 10 + 24 = 0. Calculate h.
1
Let p(y) be the second derivative of -y**10/80640 + y**8/8960 - y**6/1920 + y**4/12 - 17*y. Let n(g) be the third derivative of p(g). Factor n(o).
-3*o*(o - 1)**2*(o + 1)**2/8
Let x = 18 - 16. Solve 0*l**3 + 2*l + x*l**4 - 8*l**4 - 2*l**3 + 7*l**2 - l**4 = 0 for l.
-1, -2/7, 0, 1
Let y(i) be the third derivative of 3*i**5/4 - 167*i**4/8 + 11*i**3 + 202*i**2. Factor y(x).
3*(x - 11)*(15*x - 2)
Let x(v) be the second derivative of 0 - 1/4*v**2 - 1/24*v**4 + 11*v - 1/6*v**3. Find r such that x(r) = 0.
-1
Suppose 63 = -3*c + 156. Suppose -c*w = -28*w - 3. Suppose -3/2*z**2 - w + 7/2*z = 0. Calculate z.
1/3, 2
Determine q so that 4/7*q**4 + 0 + 8/7*q**2 + 12/7*q**3 + 0*q = 0.
-2, -1, 0
Suppose -5*o + 6 = -3*o. Suppose -x + 0*x = -o. Factor -4*k**2 - 83*k + 2*k**5 + 4*k**4 + 80*k + 2*k**x - k**5.
k*(k - 1)*(k + 1)**2*(k + 3)
Let w(u) = 3*u**3 + 15*u**2 + 9*u - 31. Let p(a) = 6*a**3 + 30*a**2 + 18*a - 61. Let r(t) = 4*p(t) - 7*w(t). Factor r(o).
3*(o - 1)*(o + 3)**2
Determine f, given that 2/3*f**2 + 20*f + 150 = 0.
-15
Let c(t) be the third derivative of t**6/420 + 6*t**5/35 + 2*t**2 + 139*t. Factor c(i).
2*i**2*(i + 36)/7
Let d(f) = -20*f**2 - 260*f. Let y(s) = 3*s**2 + 40*s. Let g(q) = 5*d(q) + 32*y(q). Factor g(i).
-4*i*(i + 5)
Let k(v) be the first derivative of v**5 - 40*v**4 + 1430*v**3/3 - 1200*v**2 + 1125*v - 56. Let k(o) = 0. Calculate o.
1, 15
Let 15*u + 25*u**2 - 35*u - 15 + 10*u = 0. What is u?
-3/5, 1
Let u(o) be the third derivative of o**5/75 - 3*o**4/5 - 88*o**2. Let u(s) = 0. Calculate s.
0, 18
Let c be 87/15 + -2 - 4/(-20). Let c*n - 2*n + 2*n**2 - n - 9*n = 0. What is n?
0, 4
Let f = -47386/11 + 4308. Factor -14/11*b**4 + f*b**5 - 40/11*b**2 + 16/11*b + 36/11*b**3 + 0.
2*b*(b - 2)**3*(b - 1)/11
Let l(x) be the third derivative of -x**5/60 - x**4/2 - 6*x**3 - 4*x**2 - 11*x. Factor l(o).
-(o + 6)**2
Let u(j) be the first derivative of j**5/110 - j**4/33 + j**3/33 - 2*j + 11. Let w(d) be the first derivative of u(d). Factor w(b).
2*b*(b - 1)**2/11
Let w(b) be the third derivative of b**6/540 + b**5/60 - 3*b**3/2 - 2*b**2. Let o(l) be the first derivative of w(l). Suppose o(c) = 0. Calculate c.
-3, 0
Let a(u) be the first derivative of -4*u**5/5 - u**4 + 8*u**3/3 - 91. Determine y so that a(y) = 0.
-2, 0, 1
Let i(h) be the third derivative of h**6/30 - 8*h**5/45 - h**4/6 + 2*h**2 - 37. Determine c so that i(c) = 0.
-1/3, 0, 3
Let f(i) = 20*i**2 + i - 2. Let q be f(1). Let r = q + -16. Factor 378 + 768*k + 390 + 288*k**2 + 14*k**4 + 48*k**r + 8*k**4 - 19*k**4.
3*(k + 4)**4
Let l(j) be the first derivative of -j**5/10 + 11*j**4/8 + 20*j**3/3 + 7*j**2 - 6. Factor l(u).
-u*(u - 14)*(u + 1)*(u + 2)/2
Let l = 133 + -106. Factor -21 - l*r - 775*r**2 - 3 + 772*r**2.
-3*(r + 1)*(r + 8)
Let f(o) be the third derivative of -o**5/15 + 53*o**4/24 - 139*o**3/6 + 24*o**2. Let a(u) = u + 1. Let m(y) = -5*a(y) + f(y). Let m(t) = 0. What is t?
6
Let b(o) be the first derivative of -o**6/7 - 8*o**5/35 + 25*o**4/14 + 92*o**3/21 - 4*o**2/7 - 48*o/7 - 2. What is s in b(s) = 0?
-2, -1, 2/3, 3
Factor 16/7 - 138/7*g**2 - 548/7*g.
-2*(g + 4)*(69*g - 2)/7
Let a(p) be the third derivative of p**5/360 - p**4/48 + p**3/18 + 4*p**2 - 5. Factor a(y).
(y - 2)*(y - 1)/6
Let s(d) be the first derivative of -5*d**4/7 - 92*d**3/21 + 20*d**2/7 + 460. Solve s(q) = 0 for q.
-5, 0, 2/5
Let c(q) = -5*q**3 + 8*q**2 - q + 5. Let d = -32 + 35. Let h(t) = 2*t**3 - 3*t**2 - 2. Let v(k) = d*c(k) + 7*h(k). Factor v(f).
-(f - 1)**3
Let r(c) be the first derivative of -1/27*c**6 + 9 + 0*c**2 + 0*c**3 - 4/45*c**5 + 0*c - 1/18*c**4. What is i in r(i) = 0?
-1, 0
Let b(x) be the first derivative of -x**4/2 - 148*x**3/27 - 151*x**2/9 - 20*x/3 + 817. Let b(w) = 0. Calculate w.
-5, -3, -2/9
Let x = -457 - -785. Factor 18 - 132*t - x*t**3 + 338*t**2 - 97*t**3 + 128*t**4 + 73*t**3.
2*(t - 1)**2*(8*t - 3)**2
Suppose -2883/4 - 93/2*y - 3/4*y**2 = 0. What is y?
-31
Let q(a) = -3*a + 39. Let l be q(7). Find z such that 11*z**5 - 75*z - 50*z**3 - 24*z**5 - 20 - 100*z**2 + l*z**5 = 0.
-1, 4
Suppose -43*w + 45*w = 6. Let j(u) be the third derivative of u**2 - 3/28*u**5 - 1/56*u**4 + 0*u + 1/7*u**w + 0. Factor j(p).
-3*(3*p - 1)*(5*p + 2)/7
Let l(m) be the third derivative of m**5/60 + 7*m**4/12 + 49*m**3/6 - 15*m**2 + 7*m. What is c in l(c) = 0?
-7
Let v = -35 - -40. Let q(t) = -t**3 - 3*t**2 - 6*t + 14. Let x(l) = 3*l**3 + 7*l**2 + 11*l - 29. Let i(k) = v*q(k) + 2*x(k). Factor i(h).
(h - 2)**2*(h + 3)
Let r(h) be the third derivative of -h**5/360 - 71*h**4/72 - 5041*h**3/36 + 4*h**2 + 2*h. Factor r(x).
-(x + 71)**2/6
Let y(u) be the second derivative of -u**4/6 - 41*u**3/2 - 61*u**2/2 - 394*u. What is h in y(h) = 0?
-61, -1/2
Suppose -3738*u = -3748*u + 50. Let a(o) be the first derivative of 0*o - 12 - 805/4*o**4 - 196*o**u - 220/3*o**3 - 10*o**2. Solve a(l) = 0 for l.
-2/7, -1/4, 0
Let d(n) = -3*n - 60. Let v be d(-21). Let m be -6*v/14*(-32)/24. Solve -m*p - 3/7*p**4 + 0 + 9/7*p**3 + 0*p**2 = 0.
-1, 0, 2
Let k = -605 - -610. Let s(b) be the second derivative of -1/50*b**k - 2/15*b**3 + 0 + 0*b**2 + 7*b - 1/10*b**4. Solve s(u) = 0.
-2, -1, 0
Let l(t) be the third derivative of -t**5/210 + t**4/14 - 5*t**3/21 - 80*t**2. Factor l(w).
-2*(w - 5)*(w - 1)/7
Let x(w) be the first derivative of w**4/12 + w**3/3 - 6*w**2 + 32*w/3 - 256. Let x(g) = 0. What is g?
-8, 1, 4
Let j = 22 - 27. Let r be -2*(0 - (-2)/4). Let t(w) = -w**3 + 1. Let o(c) = 4*c**3 - 2*c**2 - c - 5. Let u(p) = j*t(p) + r*o(p). Factor u(z).
z*(z + 1)**2
Let z(n) be the second derivative of -n**4/6 + 116*n**3/3 - 3364*n**2 + 152*n. What is j in z(j) = 0?
58
Let l(g) be the second derivative of -g**5/110 - g**4/22 + 2*g**3/11 + 8*g**2/11 + 311*g. Determine c, given that l(c) = 0.
-4, -1, 2
Suppose -l = -4*q - 165, q - 2*q = 3*l - 443. Let d = 753/5 - l. Suppose -4/5*x**2 + 2/5*x**3 - d*x + 16/5 = 0. Calculate x.
-2, 2
Let o(g) be the second derivative of 0*g**2 + 1/54*g**4 + 2/27*g**3 - 13*g + 0. Factor o(s).
2*s*(s + 2)/9
Factor -5*y**3 - 55*y + 79/3*y**2 + 100/3 + 1/3*y**4.
(y - 5)**2*(y - 4)*(y - 1)/3
Suppose 43*h = -62*h + 840. Let m(y) be the first derivative of 5/2*y + 5/12*y**6 + 5/4*y**2 + 1/2*y**5 + h - 5/4*y**4 - 5/3*y**3. Factor m(t).
5*(t - 1)**2*(t + 1)**3/2
Let o(m) = -1