07*j - 240*j.
-3*(j - 11)*(j - 6)*(2*j - 1)
Suppose 3*k = -2*m - 0 + 18, k - m = 1. Solve 64*w**4 + w**5 - 9*w**3 + 2*w**5 - 64*w**k + 6*w**2 = 0.
-2, 0, 1
Let i be (414/(-1449))/((-4)/42). Let -3/4*f**4 + 3/4*f**5 + 15/4*f**2 + i*f - 15/4*f**3 - 3 = 0. What is f?
-2, -1, 1, 2
Let w(z) be the first derivative of 58 + 60*z - 40*z**2 + 35/3*z**3 - 5/4*z**4. Factor w(a).
-5*(a - 3)*(a - 2)**2
Let f(h) be the third derivative of h**6/840 - 11*h**5/420 + 17*h**4/84 - 4*h**3/7 - 337*h**2. Factor f(m).
(m - 6)*(m - 4)*(m - 1)/7
Let u = 26158/3177 - 4/353. Let w = -287/36 + u. Factor 0*q**3 + 0 + w*q**5 - 1/2*q**4 + 0*q**2 + 0*q.
q**4*(q - 2)/4
Let y be 12/(-30)*(-31)/(7812/180). Factor 0*p - 2/7*p**3 + 0 - y*p**2.
-2*p**2*(p + 1)/7
Suppose a - 5*a = 5*u - 111, -54 = -2*a - 2*u. Suppose 0 = 58*l - 59*l + 2. Solve 7*n**l - n**2 + 4*n**4 + 14*n**2 + a*n**3 = 0.
-5, -1, 0
Let c(l) be the second derivative of l**4/48 + 7*l**3/3 - 1316*l. Determine n so that c(n) = 0.
-56, 0
Suppose h = -0*h + 41. Suppose -h = -2*m - 25. What is a in 3*a + 9*a - m*a**2 - 7 + 3 = 0?
1/2, 1
Let d be -83 - -5*(-44)/(-20). Let n be (1 - 1) + -9*32/d. Factor 1/4*l**5 + 0*l**2 + 1/2*l**n + 0 + 0*l**3 + 0*l.
l**4*(l + 2)/4
Suppose 1422*u - 3158 = -314. Factor 5/4*n**u + 55/2*n + 605/4.
5*(n + 11)**2/4
Let w(y) be the second derivative of -y**6/75 - 49*y**5/25 - 116*y**4 - 10720*y**3/3 - 60800*y**2 - 10140*y. Suppose w(j) = 0. What is j?
-38, -20
Let w(x) be the second derivative of x**7/231 - 2*x**6/33 + 3*x**5/55 + 16*x**4/33 - 47*x**3/33 + 18*x**2/11 - 10403*x. What is t in w(t) = 0?
-2, 1, 9
Determine r so that -289/2 + 144*r + 1/2*r**2 = 0.
-289, 1
Let l(p) = 6*p**2 - 124*p + 1930. Let k(y) = -1029 + 124*y - y**2 - 903 + y**2 - 7*y**2. Let r(s) = -4*k(s) - 5*l(s). Factor r(a).
-2*(a - 31)**2
Determine k, given that 1459*k + 20*k**2 + 6*k**2 + 2 - 1481*k - 6*k**2 = 0.
1/10, 1
Let v(j) be the second derivative of 0*j**4 - 1/3*j**3 + 0 - 6/7*j**2 + 1/70*j**5 - 92*j. Let v(z) = 0. Calculate z.
-2, -1, 3
Let u(j) be the second derivative of j**7/21 + 6*j**6/5 + 36*j**5/5 - 9*j**4 - 243*j**3 - 972*j**2 - 5*j - 359. Suppose u(n) = 0. What is n?
-12, -3, 3
Let a be -66 + 2 + (-1)/(-1). Let o be a/(-5) + (-30)/50. Factor b**2 + 40*b**3 - 41*b**3 + 5*b**2 + 8 - o*b.
-(b - 2)**3
Factor -14371*a**2 - 3*a**4 - 122*a + 51 + 14463*a**2 + 0*a**4 - 3*a**4 + 7*a**4 - 22*a**3.
(a - 17)*(a - 3)*(a - 1)**2
Let r(v) be the second derivative of v**4/4 - 4*v**3/3 + 5*v**2/2 - 7*v. Let k(b) = 5*b**2 - 16*b + 11. Let y(x) = -4*k(x) + 7*r(x). Factor y(d).
(d - 1)*(d + 9)
Let b(h) be the third derivative of h**7/42 + 23*h**6/24 + 21*h**5/4 + 305*h**4/24 + 50*h**3/3 + 719*h**2. Determine w, given that b(w) = 0.
-20, -1
Suppose -2*b - 5*j - 6 = 0, 9*b - 5*j = 6*b + 16. Factor -4583*s**b + 4581*s**2 - 164 - 147 - 52*s - 27.
-2*(s + 13)**2
Let c(o) = -o**3 + 6*o**2 - 6*o - 2. Let d(j) = -16*j - 10*j - 3*j**3 + 16*j + 13*j**2 - 2*j - 3. Let h(q) = -5*c(q) + 3*d(q). Factor h(f).
-(f - 1)**2*(4*f - 1)
Factor -g**5 + 4255 - 2129 - 2126 - 224*g**4.
-g**4*(g + 224)
Factor 101878*i**2 - 85*i**3 - 32*i**3 - 101422*i**2 - 252*i.
-3*i*(3*i - 2)*(13*i - 42)
Let w(n) be the third derivative of 0 - 1/30*n**5 - 5*n**2 - n**4 + 0*n**3 + 4*n. Factor w(o).
-2*o*(o + 12)
Let j(a) be the second derivative of -5/36*a**4 + 0 + 1/252*a**7 + 0*a**2 + 49*a + 1/12*a**3 + 1/10*a**5 - 1/30*a**6. Factor j(t).
t*(t - 3)*(t - 1)**3/6
Factor -4/7*z**3 - 3744/7 - 1392/7*z - 152/7*z**2.
-4*(z + 6)**2*(z + 26)/7
Let o(i) be the second derivative of i**4/6 - 874*i**3/3 + 190969*i**2 + 674*i. Suppose o(q) = 0. What is q?
437
Let p(f) be the first derivative of -1/2*f**2 + 0*f - 8/3*f**3 - 176. Find n, given that p(n) = 0.
-1/8, 0
Let r(g) be the first derivative of 0*g + 84 + 1/10*g**2 - 1/15*g**3 + 1/25*g**5 - 1/20*g**4. Solve r(t) = 0.
-1, 0, 1
Suppose 62 + 35/2*g + 1/2*g**2 = 0. What is g?
-31, -4
Let s(o) = -o**3 + 174*o**2 + 561*o + 366. Let m(t) = 10*t**3 - 1915*t**2 - 6175*t - 4025. Let k(l) = 4*m(l) + 45*s(l). Solve k(u) = 0.
-2, -1, 37
Solve -122*d + 282*d**2 + 70*d**3 + 180060 - 220*d - 180070 = 0 for d.
-5, -1/35, 1
Let c = 6274/7 - 896. Suppose 156/7*y**2 + 40*y + c*y**4 - 38/7*y**3 - 400/7 = 0. What is y?
-2, 1, 10
Suppose -1/3*p**4 - 5504/3*p - 4352/3 - 85/3*p**3 - 412*p**2 = 0. What is p?
-68, -8, -1
Let f(q) = q**2 - 6*q - 5. Let r be f(-1). Let g(m) be the first derivative of -m**r - 2/3*m**3 - 3 + 0*m. Factor g(h).
-2*h*(h + 1)
Let h(y) = 6*y**2 - 52*y - 19. Let f be h(9). Let k be (f/3)/(2/(-9)). Determine z, given that k*z**3 + 3/2 - 3/2*z - 3/2*z**2 = 0.
-1, 1
Let b(r) = 2*r**3 + 14*r**2 - 20*r - 37. Let z be b(-8). Let u be 6 + (-168)/30 + 1/z. Let -1/5 + 1/5*i**2 - 1/5*i**3 + u*i = 0. What is i?
-1, 1
Let o = -156 + 181. Factor -2*y**3 + 10 + o*y - 16*y**4 + 10*y**2 - 5*y**3 - 13*y**3 - 5*y**5 - 4*y**4.
-5*(y - 1)*(y + 1)**3*(y + 2)
Let h(l) be the second derivative of 3/5*l**5 - 1 + 1/15*l**6 + 11/6*l**4 + 0*l**2 + l + 2*l**3. Factor h(c).
2*c*(c + 1)*(c + 2)*(c + 3)
Suppose 0 = 2*d - 2*h + 1270, -24*d + 5*h = -20*d + 2541. Let o = d - -636. Solve 1/2*v + 1 - 1/2*v**o = 0.
-1, 2
Solve 0 - 4*y**4 + 4/3*y**3 + 4*y**2 - 4/3*y**5 + 0*y = 0.
-3, -1, 0, 1
Let b be 10/(-16)*(124/(-70) - (-1960)/3430). Factor -3/4*r**3 - b*r**2 + 3*r + 3.
-3*(r - 2)*(r + 1)*(r + 2)/4
Let u be (-7)/(-28)*-1 - (-2 + 27/(-12)). Let q(h) be the second derivative of -1/45*h**5 + 0 + 14*h - 4/9*h**3 + 0*h**2 - 5/27*h**u. Find r such that q(r) = 0.
-3, -2, 0
Let g(b) be the second derivative of b**4/24 - 485*b**3/6 + b + 279. Factor g(h).
h*(h - 970)/2
Let b(q) be the third derivative of q**9/60480 - q**8/6720 + q**5/20 - q**3/3 - 2*q**2 - 10*q. Let d(k) be the third derivative of b(k). Factor d(h).
h**2*(h - 3)
Suppose 46*q = 45*q - 5. Let z be (q + 11)/((-10)/(-4) - 2). Suppose -5*l - 5*l**2 + 5*l - 8*l**4 - 3*l**2 - 2*l - 2*l**5 - z*l**3 = 0. Calculate l.
-1, 0
Suppose 0 = -3*p - 0*m - 3*m + 6, 3*p - 10 = -m. Determine d so that 3*d**5 + 19*d - 14*d + 24*d**2 + 75*d**3 + 25*d + 27*d**2 + 30*d**2 + 27*d**p = 0.
-5, -2, -1, 0
Let v(d) = d**3 + 15*d**2 + 54*d - 12. Let w be v(-8). Let h(m) be the second derivative of 0 - 2*m**2 - 12*m + 4*m**3 - 5/3*m**w. Factor h(u).
-4*(u - 1)*(5*u - 1)
Let d(r) be the first derivative of 0*r + 3 + 13/12*r**3 + 1/4*r**2. Suppose d(h) = 0. Calculate h.
-2/13, 0
Let l(m) be the first derivative of -15*m**2 + 6*m - 7*m**2 - 35*m**3 - 82 - 33*m**2 - 10*m**4 - 46*m - m**5. Factor l(x).
-5*(x + 1)**2*(x + 2)*(x + 4)
Let o(h) be the first derivative of 5*h**3/3 - 11495*h**2 + 26427005*h + 8053. Factor o(s).
5*(s - 2299)**2
Suppose -2*a + 6*a = 20. Let u(h) = -15*h - 33*h + 8 + 6 + 13*h**2 + 11 + 10. Let d(p) = 20*p**2 - 72*p + 52. Let x(r) = a*d(r) - 8*u(r). Solve x(s) = 0 for s.
1, 5
Determine i, given that 172/5*i - 56/5*i**2 + 4/5*i**3 - 24 = 0.
1, 3, 10
Let n(k) be the third derivative of -1 - 3/2*k**3 + 0*k - 210*k**2 - 1/60*k**5 + 5/12*k**4. What is i in n(i) = 0?
1, 9
Let m(t) be the third derivative of -t**6/600 + 29*t**5/300 + 43*t**4/40 + 33*t**3/10 - 603*t**2 - 3. Let m(o) = 0. What is o?
-3, -1, 33
Let a(y) = -20*y**2 + 60*y - 36. Suppose 182*o + 5 = 187*o. Let h(c) = c**3 - 2*c**2. Let t(r) = o*a(r) + 4*h(r). Determine n, given that t(n) = 0.
1, 3
Let v(d) be the second derivative of -d**5/100 - 33*d**4/40 + 7*d**3 + 47*d**2/2 + 292*d. Let p(k) be the first derivative of v(k). Find l, given that p(l) = 0.
-35, 2
Let z(k) = -3*k**2 + 9. Let g(b) = 3*b**2 - 2*b - 9. Suppose 0 = -6*i - 59 + 41. Let l(c) = i*g(c) - 4*z(c). Factor l(f).
3*(f - 1)*(f + 3)
Let h(n) be the second derivative of 459*n**5/130 + 48*n**4/13 + n**3 - 2*n**2/13 - 3*n + 40. Suppose h(d) = 0. Calculate d.
-1/3, 2/51
Let t = 234522/55 + -4264. Let f(b) be the first derivative of -5/22*b**4 + 9 + 6/11*b**3 + 4/11*b + t*b**5 - 7/11*b**2. Solve f(d) = 0 for d.
1, 2
Let k(i) = -2*i**4 + 196*i**3 - 6334*i**2 + 65332*i + 71876. Let x(l) = 196*l + 194*l + l**2 - 394*l + 1. Let a(n) = -k(n) + 2*x(n). Factor a(m).
2*(m - 33)**3*(m + 1)
Let f be (-972)/24*(855/(-63) - -13)/3. Suppose 3/7*d**3 - f - 27/7*d - 30/7*d**4 + 276/7*d**2 = 0. Calculate d.
-3, -2/5, 1/2, 3
Suppose 88/9*t - 2/9*t**2 + 200/3 = 0. What is t?
-6, 50
Let n(a) = a**3 - 22*a**2 + 