e of 1/8*w**3 - 117/4*w - 21 + 111/16*w**2. Determine n so that d(n) = 0.
-39, 2
Factor 1008*a**3 + 18600*a**2 + 5*a**4 - 19220*a + 22 - 393*a**3 - 22.
5*a*(a - 1)*(a + 62)**2
Let y be 14 - (-7)/((112/32)/(-7)). Let -5/4*z**2 + y + 5/2*z = 0. Calculate z.
0, 2
Suppose -16*f = -11*f - 10. Solve 1 + 4*j**2 - 50*j**2 - 7*j + 2 + 47*j - 46*j**f = 0 for j.
-3/46, 1/2
Let h = 200 + -192. Factor -6*g + h*g**3 + 11*g - 14*g**2 + g.
2*g*(g - 1)*(4*g - 3)
Suppose -841*s - 2393 = -6683*s + 7356 + 1935. Suppose 232*v - 32/3 - 1682*v**s + 24389/6*v**3 = 0. What is v?
4/29
Suppose -f + 3 = -0. Suppose 0 = -242*d + 598 - 114. Factor -3/10*l**d + 0 - 1/5*l - 1/10*l**f.
-l*(l + 1)*(l + 2)/10
Factor 223*n**3 - 2*n**4 - 69*n**3 - 118*n**2 + 150*n - 72*n**2 - 112*n**2.
-2*n*(n - 75)*(n - 1)**2
Let c(a) be the first derivative of a**6/24 + a**5/3 - 25*a**4/24 - 55*a**2/2 + 43. Let n(p) be the second derivative of c(p). Factor n(i).
5*i*(i - 1)*(i + 5)
Let p(g) be the second derivative of 22 - 1/2*g**4 - g - 23/90*g**5 - 13/27*g**3 - 7/135*g**6 - 2/9*g**2. Factor p(x).
-2*(x + 1)**3*(7*x + 2)/9
Let l be (5/(-20) - (-25)/(-4))*-2. Factor 2*g**3 + 30*g**2 + 3*g**3 + l*g - 13*g - 160.
5*(g - 2)*(g + 4)**2
What is r in 180*r + 16*r**2 - r**5 - 8*r**2 - 53*r**4 - 20*r**5 + 88 + 17*r**5 - 176*r**3 - 43*r**4 = 0?
-22, -1, 1
Let j be 336/(-32)*(-7)/(6342/8). Let c = j - -53/1057. Suppose 0 + 1/7*p - 2/7*p**2 + c*p**3 = 0. What is p?
0, 1
Let o(j) = -1001*j + 95097. Let g be o(95). Suppose -15/7*x - 25/7 - 1/7*x**3 + 9/7*x**g = 0. What is x?
-1, 5
Let y(v) be the third derivative of -11*v**5/4 - 4*v**4 - 2*v**3 + 4048*v**2. Suppose y(g) = 0. Calculate g.
-2/5, -2/11
Solve 16*c**2 + 1071 - 27*c - c**3 - 981 - 20*c - 22*c = 0.
3, 10
Let d(y) be the first derivative of 0*y - y**3 + 46 - 9/4*y**4 + 0*y**2. Let d(r) = 0. Calculate r.
-1/3, 0
Let o(m) be the third derivative of -1/840*m**8 + 0*m - 7/150*m**6 + 0 - 3/20*m**4 - 2/15*m**3 - 8/75*m**5 - 60*m**2 - 2/175*m**7. Find q, given that o(q) = 0.
-2, -1
Let n(j) = 3*j + 22. Let b be n(-7). Suppose -b + 16 = 5*i. Suppose -119*a**3 + 2*a**5 - 3*a + 5*a + 115*a**i = 0. What is a?
-1, 0, 1
Let u(g) be the first derivative of -g**6/24 - 87*g**5/10 - 10091*g**4/16 - 97469*g**3/6 + 2523*g**2/2 + 48778*g + 1515. Factor u(t).
-(t - 1)*(t + 1)*(t + 58)**3/4
Suppose 5*w + m = 37, -5*w + 3*m = 128574 - 128543. Factor -2/15*d + 0 + 0*d**3 + 2/15*d**5 + 4/15*d**w - 4/15*d**2.
2*d*(d - 1)*(d + 1)**3/15
Let j(f) be the second derivative of -f**4/16 - 1219*f**3/8 - 1827*f**2/4 - 1324*f - 1. Factor j(s).
-3*(s + 1)*(s + 1218)/4
What is w in -9*w**3 - 48 - 1983*w**2 + 3*w**4 - 4*w + 2019*w**2 - 4*w**4 = 0?
-12, -1, 2
Let h(m) be the second derivative of 3*m**5/40 + 7*m**4/4 - 31*m**3/4 + 12*m**2 + 1906*m. Factor h(q).
3*(q - 1)**2*(q + 16)/2
Let v(r) = -10*r**2 + 171*r - 495. Let o(n) = -8*n**2 + 170*n - 486. Let m(x) = 3*o(x) - 2*v(x). Solve m(w) = 0.
3, 39
Let s(r) = 7769*r - 38841. Let w be s(5). Find c, given that -3/2*c**w + 0*c**3 - 18 - 6*c + 27/2*c**2 = 0.
-3, -1, 2
Let f(p) = -p. Let x be f(1). Let z be (0 + x)/(-1) + 2. Suppose 8*k + 32*k**3 + 12*k**4 - 62*k**2 - 4*k**z - 4*k**4 + 90*k**2 = 0. What is k?
-2, -1, -1/2, 0
Let l(o) be the third derivative of -o**8/2352 - 13*o**7/147 - 35*o**6/24 - 50*o**5/7 + 3*o**2 - 982. Suppose l(u) = 0. Calculate u.
-120, -5, 0
Let k(w) = 22*w**2 + 1180*w + 1078. Let p(t) = 7*t**2 + 393*t + 361. Let q(x) = -5*k(x) + 16*p(x). Let q(y) = 0. What is y?
-193, -1
Let x(p) = -p**2 + 27*p + 256. Let u be x(0). Let a be 6/9 + u/(-456). Find y, given that -a*y + 2/19*y**2 + 2/19*y**3 - 2/19 = 0.
-1, 1
Suppose -116 = -33056*i + 33027*i. Suppose -c**3 + 9/4 + 1/4*c**i - 1/2*c**2 + 3*c = 0. Calculate c.
-1, 3
Let r be (-185)/(-111)*4/(-5)*-12 - 7. Let v(x) be the first derivative of r*x + 1/12*x**3 + 28 + 3/2*x**2. Factor v(s).
(s + 6)**2/4
Suppose 25*z + 63 = 138. Factor -5*m**2 - z*m**2 + 30*m - 3*m**3 + 72 + m**2 - 3*m**2 + m**2.
-3*(m - 3)*(m + 2)*(m + 4)
Let d = 1222396075/444 + -2753143. Let g = d - -3/148. Factor -u**3 + 4/3*u - g*u**2 + 2/3*u**4 + 1/3*u**5 + 0.
u*(u - 1)**2*(u + 2)**2/3
Factor -304*r**2 + 692220*r + 1970*r**2 - 1391112 + 83*r**3 - 82*r**3.
(r - 2)*(r + 834)**2
Let 76*u**4 + 72*u**3 + 1178*u - 1023*u**5 - 4634*u - 3456*u**2 + 1027*u**5 = 0. What is u?
-12, -1, 0, 6
Let b(h) be the first derivative of -34*h**2 - 4/3*h**3 + 0*h - 128. Solve b(r) = 0.
-17, 0
Let q(l) be the second derivative of 7/3*l**4 + 0 - 39/40*l**5 + 54*l - 49/24*l**3 + 0*l**2 + 2/15*l**6 - 1/168*l**7. Factor q(z).
-z*(z - 7)**2*(z - 1)**2/4
Let l(s) be the first derivative of -s**2 + 78 - 1/3*s**3 + 3*s. Factor l(j).
-(j - 1)*(j + 3)
Suppose 58*x + 245 = 160*x + 41. Let z(m) be the third derivative of 12*m**x - 1/2*m**5 - 2/3*m**4 - 4/9*m**3 + 0*m + 0 - 5/36*m**6. Factor z(b).
-2*(b + 1)*(5*b + 2)**2/3
Let m(c) be the third derivative of 1 + 0*c**3 + 1/360*c**5 + 131*c**2 + 0*c - 1/72*c**4 + 1/720*c**6. Solve m(u) = 0.
-2, 0, 1
Let l(k) be the third derivative of k**6/630 + 4*k**5/105 + 17*k**3/2 + 32*k**2. Let p(q) be the first derivative of l(q). What is m in p(m) = 0?
-8, 0
Let c(s) be the first derivative of -s**4/36 + 32*s**3/9 - 512*s**2/3 + 80*s - 114. Let u(r) be the first derivative of c(r). Factor u(g).
-(g - 32)**2/3
Determine j so that -56/9*j**4 - 3200/3 + 64/9*j**2 - 48*j**3 - 2/9*j**5 + 6880/9*j = 0.
-12, -10, 2
Let y(c) be the third derivative of -c**8/181440 - 17*c**7/22680 - c**5/20 - 5*c**4/24 + 105*c**2. Let m(b) be the third derivative of y(b). Factor m(x).
-x*(x + 34)/9
Let r(a) be the second derivative of -2 - 37/9*a**3 + 19/3*a**2 + 17/18*a**4 + 28*a + 1/30*a**5. Factor r(c).
2*(c - 1)**2*(c + 19)/3
Find f such that -55*f**2 + 485/2*f**3 + 170*f**4 - 120*f + 0 - 15/2*f**5 = 0.
-1, 0, 2/3, 24
Let h be -10 - -5 - -19 - ((-25 - 11) + 45). Factor 1/4*j**2 + 0 - 1/4*j**h + 0*j + 3/4*j**4 - 3/4*j**3.
-j**2*(j - 1)**3/4
Let g(p) be the second derivative of 1/45*p**6 - 2/9*p**3 - 1/4*p**4 + 11*p - 1/30*p**5 + 0 - p**2. Let n(b) be the first derivative of g(b). Factor n(t).
2*(t - 2)*(t + 1)*(4*t + 1)/3
Suppose 4*l = 4*q - 28, 347*q + 2*l + 14 = 342*q. Let n(m) be the first derivative of 1/9*m**2 + q*m**3 + 0*m - 1/18*m**4 - 3. Factor n(t).
-2*t*(t - 1)*(t + 1)/9
Let g(k) be the first derivative of -5*k**4/4 - 85*k**3/3 - 150*k**2 - 3532. Factor g(x).
-5*x*(x + 5)*(x + 12)
Suppose 110*h - 220 + 2165 + 5*h**2 + 455 + 0*h**2 + 150*h = 0. Calculate h.
-40, -12
Let y(n) be the second derivative of -n**5/5 + 8*n**4 - 382*n**3/3 + 1008*n**2 - 6758*n. Factor y(m).
-4*(m - 9)*(m - 8)*(m - 7)
Factor 0*g - 72/7 + 2/7*g**2.
2*(g - 6)*(g + 6)/7
Let n = 3066615/13 - 235893. What is h in -n - 12/13*h**2 + 38/13*h = 0?
1/6, 3
Let a = -6/1015 - -2084/9135. Let 0 + a*b + 1/9*b**3 - 1/3*b**2 = 0. What is b?
0, 1, 2
Let z(r) = 4*r**2 - 803*r + 1614. Let b(o) = 4*o**2 - 800*o + 1616. Let m(k) = -3*b(k) + 4*z(k). Factor m(g).
4*(g - 201)*(g - 2)
Let h(t) = -t**3 - 4*t**2 + 8*t + 10. Let o be h(-5). Let k be ((-12)/o)/((-10)/(-25)). Determine v so that -2*v**2 + 0*v**2 - k*v + 3 + v**2 + 4*v**2 = 0.
1
Let s(m) = 14*m + 171. Let d be s(-12). Factor -44*z**2 - 40*z - 7*z**2 - 9*z**4 - z**5 - 738*z**3 + 707*z**d - 12.
-(z + 1)**2*(z + 2)**2*(z + 3)
Find j, given that 6*j**5 - 8*j**5 + 118*j**3 - 42*j**3 + 6 - 60*j**4 + 366 + 408*j**2 - 794*j = 0.
-31, -3, 1, 2
Let t be 87/(-261) + (-2)/(-3). Let u(o) be the second derivative of 0 + t*o**3 + 0*o**2 - 1/30*o**6 + 0*o**5 - 4*o + 1/4*o**4. Suppose u(k) = 0. What is k?
-1, 0, 2
Let v(d) = -2*d**2 + 148*d - 2592. Let c(k) = 2*k + 11*k + k - 16*k. Let i(w) = 2*c(w) + v(w). Solve i(z) = 0.
36
Let p = -1838 - -29409/16. Let f(k) be the first derivative of 15 + 0*k - 1/40*k**5 - 1/8*k**3 + 3/32*k**4 + p*k**2. Find l, given that f(l) = 0.
0, 1
Suppose -4*p = 12, q + 3*p = -7 - 0. Let -84*d - 90 - 211*d + 15*d**q + 30*d = 0. Calculate d.
-1/3, 18
Let d(s) be the first derivative of s**3/3 - s**2 - 2*s - 1. Let g(n) = -9*n + 421 - 404 + 17*n - 8*n**2 + 9*n. Let l(w) = -51*d(w) - 6*g(w). Factor l(q).
-3*q**2
Suppose 12*c - 2376 = 48*c. Let q be 88/c*(-6)/4. Let -12/13 + 14/13*l**q - 2/13*l**4 + 10/13*l**3 - 10/13*l = 0. Calculate l.
-1, 1, 6
Factor -2/3*q**3 - 24*q + 0 + 74/3*q**2.
-2*q*(