Solve x(z) = 0.
-50, 1/5
Suppose -13*d + 6011 = -4064. Let y be (62/d)/((-1)/(-5)). Suppose y*w**2 + 6/5 - 8/5*w = 0. Calculate w.
1, 3
Let q be 7/(343/42) - ((-605)/(-77) + -11). Find r, given that 4/7*r**q - 46/7*r + 2/7*r**5 - 36/7*r**3 + 12/7 + 64/7*r**2 = 0.
-6, 1
Let c(s) be the first derivative of -2*s**5/35 - 10*s**4/7 + 146*s**3/21 + 92*s**2/7 + 3060. Find x, given that c(x) = 0.
-23, -1, 0, 4
Let u(p) = 8*p**3 + 4*p**2 + 26*p - 30. Let x(s) = -9*s**3 - 3*s**2 - 29*s + 35. Let k(t) = -7*u(t) - 6*x(t). Factor k(l).
-2*l*(l + 1)*(l + 4)
Factor 1394*a**2 + 1386*a**2 + 1387*a**2 - 276*a - 4170*a**2.
-3*a*(a + 92)
Let u = 416331 - 2912130/7. Determine h so that 9477/7*h**4 + 10344/7*h**2 + 144/7 - 2064/7*h + u*h**5 - 20088/7*h**3 = 0.
-6, 2/9, 1
Factor -2*i**2 - 4490*i - 5848*i - 186*i - 13844322.
-2*(i + 2631)**2
Let b(u) be the second derivative of u**5/30 + 123*u**4 + 181548*u**3 + 133982424*u**2 - 2872*u + 2. Factor b(n).
2*(n + 738)**3/3
Determine v, given that -1918/17*v + 480/17 - 8/17*v**2 = 0.
-240, 1/4
Let n(i) = -i**3 - 8*i**2 - 2*i - 10. Let t be n(-9). Suppose 113*r + 188 = 115*r. Suppose -v**2 + 183*v - t*v - r*v = 0. What is v?
0
Let i(h) be the third derivative of -h**5/60 - h**4/4 - h**3/3 - 22*h**2. Let n be i(-4). Suppose -u + n*u - 7 - 5*u**2 + 17 = 0. Calculate u.
-1, 2
Let z(k) = k**3 - 2*k**2 + k - 1. Let y(c) = 24*c**3 + 2804*c**2 + 506960*c + 504080. Let a(d) = -y(d) + 20*z(d). Factor a(n).
-4*(n + 1)*(n + 355)**2
Let k(r) be the second derivative of -3/10*r**6 + 3/4*r**4 + 0*r**2 + 3*r + 14 + 0*r**3 - 3/20*r**5 + 1/14*r**7. Factor k(c).
3*c**2*(c - 3)*(c - 1)*(c + 1)
Let z(w) be the third derivative of w**8/84 - 11*w**6/30 - 6*w**5/5 - 4*w**4/3 - 1147*w**2. Factor z(g).
4*g*(g - 4)*(g + 1)**2*(g + 2)
Let h(u) = -2*u**2 + u - 1. Let n(z) be the first derivative of -29*z**4/4 + 27*z**3 - 30*z**2 - 314. Let m(q) = 12*h(q) - 3*n(q). Find f such that m(f) = 0.
2/29, 1, 2
Let o(c) = -15*c - 25. Let x be o(-3). Let s = -10 + x. Suppose -12*y**5 - 20*y**2 + 20*y**4 + 7*y**5 - 10*y**3 + s*y + 5*y + 0*y = 0. What is y?
-1, 0, 1, 3
Let d be 3 + (37 - (9 + 31)). Let 16/25*t**3 - 2/25*t**4 + d + 4/5*t - 34/25*t**2 = 0. Calculate t.
0, 1, 2, 5
Solve -53504*f + 4/7*f**4 + 247808/7 - 1420/7*f**3 + 128136/7*f**2 = 0.
1, 2, 176
Let m(j) be the third derivative of j**8/1344 - 11*j**7/105 + 17*j**6/24 - 7*j**5/5 - 5046*j**2. Factor m(d).
d**2*(d - 84)*(d - 2)**2/4
Let i(b) be the first derivative of -b**6/900 - 7*b**5/150 - 2*b**4/5 + 48*b**3/5 - 91*b**2/2 - 294. Let o(s) be the second derivative of i(s). Factor o(m).
-2*(m - 3)*(m + 12)**2/15
Let k(p) be the third derivative of -p**8/6720 + p**6/240 - p**5/30 - 5*p**3/6 - 56*p**2. Let g(m) be the third derivative of k(m). Solve g(v) = 0.
-1, 1
Let b(i) be the first derivative of 23*i**5/15 - 5*i**4 + 14*i**3/3 + 2*i**2/3 + i + 80. Let d(y) be the first derivative of b(y). Factor d(t).
4*(t - 1)**2*(23*t + 1)/3
Let h be 3*(-2)/24 - (-9)/4. Suppose -3*d - 3 + 13 = 4*f, -2*d = -h*f - 2. Factor 6/17*w + 6/17*w**d + 2/17*w**3 + 2/17.
2*(w + 1)**3/17
Let d(x) = -2*x**3 + 86*x**2 - 2*x + 126. Let g be d(43). Let v be (-20)/g + (-57)/(-12). What is z in -1 + z + v*z**2 + 23/4*z**4 - 35/4*z**3 - 5/4*z**5 = 0?
-2/5, 1, 2
Let s(w) be the second derivative of -w**6/75 - 21*w**5/50 - 17*w**4/15 + 28*w**3/5 + 152*w**2/5 + 3210*w. Find u, given that s(u) = 0.
-19, -2, 2
Let d(c) be the third derivative of 31*c**2 + 1/270*c**6 + 0*c - 11/270*c**5 - 1/9*c**4 + 1/945*c**7 + 0 + 4/3*c**3. Suppose d(k) = 0. Calculate k.
-3, 2
Find d such that -133*d**5 - 20414*d**2 + 346 + 1296*d**4 + 4633*d - 12487*d - 12114*d**3 - 1228 + 101*d**5 = 0.
-1, -1/4, 21
Factor -123*h**2 - 21*h**2 - 2*h**3 + 36431*h + 2*h**4 - 36431*h.
2*h**2*(h - 9)*(h + 8)
Let p be (3/(-21))/((-115)/(72450/180)). Let 33/2*f**2 + 0 + 8*f + p*f**4 + 9*f**3 = 0. What is f?
-16, -1, 0
Let o = -2678/5 + 72842/45. Let n = -1080 + o. Factor 2/3*j**3 + 0 - 10/9*j - n*j**2.
2*j*(j - 5)*(3*j + 1)/9
Let r(z) = 40*z + 1725. Let d be r(-43). Let a(o) be the first derivative of 0*o**2 + 0*o**3 + 1/16*o**4 - 1/10*o**d + 0*o + 25. Factor a(x).
-x**3*(2*x - 1)/4
Factor -1/3*z**2 - 30 + 23/3*z.
-(z - 18)*(z - 5)/3
Let a be (-36)/(-33)*143/273. Factor 0 - a*b**5 + 0*b + 32/7*b**2 + 16/7*b**3 - 8/7*b**4.
-4*b**2*(b - 2)*(b + 2)**2/7
Let p(w) = -5*w**2 - 1542*w - 1513. Let i(c) = -6*c**2 - 1552*c - 1514. Let j(h) = -3*i(h) + 4*p(h). Factor j(d).
-2*(d + 1)*(d + 755)
Let u be 9/4*264/198. Let g(j) be the first derivative of -3/2*j**2 - 1/4*j**4 + j + j**u - 9. Find l, given that g(l) = 0.
1
Let v(x) = -18*x**2 - x - 24. Let o be v(0). Let u be o/18*10/(-8)*3. Determine m so that 0*m + 0 - 1/11*m**4 + 1/11*m**u + 0*m**2 - 2/11*m**3 = 0.
-1, 0, 2
Let o(i) be the second derivative of i**5/25 + 77*i**4/15 - 322*i**3/15 - 474*i**2/5 + 2*i - 1713. Factor o(l).
4*(l - 3)*(l + 1)*(l + 79)/5
Let o = 119791/18 - 6655. Let n(r) be the first derivative of o*r**3 + 2 - 1/2*r + 1/6*r**2. Factor n(z).
(z - 1)*(z + 3)/6
Let t(s) = -4*s**2 + 33*s - 32. Let b(m) = -4*m**2 + 32*m - 32. Let x = 190 + -193. Let v(n) = x*b(n) + 4*t(n). Factor v(h).
-4*(h - 8)*(h - 1)
Suppose -14 = m + 4*u, 3*u + 16 = -518*m + 520*m. Let y = 67/126 - 2/63. Solve 2*t + y*t**m + 2 = 0 for t.
-2
Let r = -75 - -78. Determine x so that 29*x + 557*x**4 + 48 - 12*x**r + 19*x - 560*x**4 = 0.
-2, 2
Let a(y) = -y**3 - 9*y**2 + 21*y - 12. Let h be a(-11). Let q = 1 - h. Let -289*j**q - 20*j + 85*j**2 - 32*j**4 + 140*j**2 - 4*j**5 - 72*j**3 = 0. What is j?
-5, -1, 0
Let c(a) be the second derivative of 2/27*a**4 - 4/9*a**2 - 1/27*a**3 + 1/90*a**5 + 0 + 131*a. Factor c(p).
2*(p - 1)*(p + 1)*(p + 4)/9
Factor 23*x**4 + 15131*x**2 - 15089*x**2 + x**5 + 59*x**3 + 21*x**4 - 26*x**4.
x**2*(x + 1)*(x + 3)*(x + 14)
Let h(k) be the first derivative of 64 - 1/2*k + 1/2*k**2 - 1/6*k**3. Find u, given that h(u) = 0.
1
Let i be -53 + (788095/(-165))/(-89). Factor 578/3*f + 0 + i*f**3 + 68/3*f**2.
2*f*(f + 17)**2/3
Suppose 5*p + 3*w = 26, 0 = -p - 2*w - 577 + 585. Let u(c) be the first derivative of 0*c - 3/4*c**2 - 3/5*c**5 + 1/4*c**6 + c**3 + 16 + 0*c**p. Factor u(r).
3*r*(r - 1)**3*(r + 1)/2
Let q(o) be the third derivative of -o**6/8 + 151*o**5/12 - 9625*o**4/24 + 3125*o**3/6 - 8*o**2 + 4*o. Find k, given that q(k) = 0.
1/3, 25
Let u(f) be the second derivative of -f**7/350 + f**6/50 - f**5/20 + f**4/20 - 25*f**2/2 + 93*f. Let k(z) be the first derivative of u(z). Solve k(o) = 0.
0, 1, 2
Let t be (-2)/(-8)*-4*-48. Let y be ((-4)/t*-4)/((-7)/(-42)). Suppose 0*k + 1/3*k**y + 4/3*k**4 + 5/3*k**3 + 0 = 0. What is k?
-1, -1/4, 0
Let z(q) be the first derivative of q**4/46 + 16*q**3/23 - 25*q**2/23 - 1172. Factor z(f).
2*f*(f - 1)*(f + 25)/23
Suppose 0 = 2*o + 8, -4*o + 56 + 9 = -3*z. Let v be (-6)/(6 + -3)*3/z. Factor 16/9*a + v*a**3 - 10/9*a**2 - 8/9.
2*(a - 2)**2*(a - 1)/9
Suppose -8*u + 10 = -6. Let h be (-5 - 28/(-5))*(u - 1). Factor -3/5*d**3 + h*d + 6/5 - 6/5*d**2.
-3*(d - 1)*(d + 1)*(d + 2)/5
Let -2*g**3 - 221*g + 7251*g**2 - 7291*g**2 + 448 + 85*g = 0. What is g?
-14, -8, 2
Factor 2/11*r**3 - 162/11*r**2 + 0 - 164/11*r.
2*r*(r - 82)*(r + 1)/11
Let b = -2/1827 - 122173/215586. Let c = -4/59 - b. Determine a so that c*a - 1/4*a**2 + 0 = 0.
0, 2
Suppose -2*o + 116 = 2*f - 4*f, 0 = 2*f + 2*o + 124. Let c = f + 76. Factor -3*a**4 - 6*a**3 - a**3 + c*a**3.
-3*a**3*(a - 3)
Suppose -1/3*o**3 - 169/3 - 143/3*o + 25/3*o**2 = 0. Calculate o.
-1, 13
Factor 275*t - 74*t**4 + 90 + 2*t**5 + 101*t + 218*t**2 - 82*t**3 - 21 + 56 + 27.
2*(t - 38)*(t - 2)*(t + 1)**3
Solve 6*j**3 - 3*j**4 + 148*j**2 - 157 - 35 - 38*j**3 + 5*j**4 - 102 - 112*j = 0 for j.
-1, 3, 7
Let p be (-34)/10880*-8*10. Solve c**2 + p*c**3 + 3/4*c + 0 = 0 for c.
-3, -1, 0
Factor -3*v**3 + 24*v**2 - 12*v**4 + 147*v + 7*v**4 + 4*v**4 + 25*v**2.
-v*(v - 7)*(v + 3)*(v + 7)
Let f = 6753 + -6749. Let b(j) be the third derivative of 0 - 49/3*j**3 - 1/30*j**5 + 0*j - 7/6*j**4 + f*j**2. Factor b(g).
-2*(g + 7)**2
Let d(v) be the second derivative of v**5/90 + v**4/6 + 20*v**3/27 + 4*v + 66. What is n in d(n) = 0?
-5, -4, 0
Let k be 0/(((-9)/3 - -5) + -3). Suppose -3*q + 6*q = v + 14, k = -5*q + v + 22. Let 0 + 8/3*u**2 + 0*u - 8/3*u**3 + 2*u**5 - 10/3*u**q = 0. What is u?
