 + 98. Let i(b) be the third derivative of p(b). Solve i(a) = 0.
-1, 0, 1
Let i be (177/7 - 29) + 4. Factor 10/7 - i*r**2 + 8/7*r.
-2*(r - 5)*(r + 1)/7
Let i = -115006 - -115011. Suppose 88*k - 14/3*k**i + 80/3 + 36*k**4 - 178/3*k**3 - 116/3*k**2 = 0. Calculate k.
-1, -2/7, 2, 5
Let h(q) = 24786*q**4 - 10519*q**3 - 15720*q**2 + 1488*q - 35. Let l(f) = 2*f**4 - f**3 - 1. Let m(x) = -h(x) + 3*l(x). Suppose m(p) = 0. What is p?
-2/3, 2/59, 2/35, 1
Let a(n) = 6*n**2 + 5390*n + 3634214. Let i(h) = -20*h**2 - 16169*h - 10902645. Let b(c) = 7*a(c) + 2*i(c). Let b(w) = 0. Calculate w.
-1348
Let k(i) be the second derivative of -3*i**6/50 + 2109*i**5/100 - 117*i**4/10 - 2*i + 583. Factor k(x).
-3*x**2*(x - 234)*(3*x - 1)/5
Let b be ((-1)/15*3)/((-763)/70 + 10). Let s(c) be the second derivative of b*c**4 + 0 - 23*c + 0*c**2 + 1/30*c**5 - 5/9*c**3. Let s(g) = 0. What is g?
-5, 0, 1
Let a(m) be the second derivative of 125/3*m**3 - 1/15*m**6 + 0*m**2 + 2 - 25/2*m**4 + 3/2*m**5 + 3*m. Determine q so that a(q) = 0.
0, 5
Let y = -57179/30 + 1906. Let m(s) be the third derivative of 0*s - y*s**5 + 1/12*s**4 + 0*s**3 + 4*s**2 + 0. Determine x, given that m(x) = 0.
0, 1
Let i = 541 + -518. Factor 50 - i*a - 79 + 10*a**2 - 91 - 5*a**2 + 73*a.
5*(a - 2)*(a + 12)
Let m be 88/24 - (-2)/6. Let g = 279 - 276. Find f such that 8*f - 10 + 23*f**2 - g*f + 5*f**4 - 8*f**2 - 10*f**m - 5*f**3 = 0.
-2, -1, 1
Let b(m) = 176*m - 350. Let x be -11*(36/90 - (-96)/(-165)). Let w be b(x). Factor w*h**2 + 16/5*h - 8/5.
2*(h + 2)*(5*h - 2)/5
Suppose 13*c - 7*c = -41*c. Let s(q) be the third derivative of 0*q**5 - 1/280*q**6 + 0*q + 0 + c*q**3 + 1/56*q**4 - 9*q**2. Find b such that s(b) = 0.
-1, 0, 1
Let t(d) be the second derivative of 2*d**7/105 + 19*d**6/150 + 3*d**5/50 - 3*d**4/4 + 3*d + 5. Factor t(j).
j**2*(j + 3)**2*(4*j - 5)/5
Let r(j) = -21*j**3 + 483*j**2 - 489*j + 108. Let d(t) = -3*t**3 + 69*t**2 - 70*t + 16. Let s(x) = -27*d(x) + 4*r(x). Factor s(g).
-3*g*(g - 22)*(g - 1)
Let c(l) be the third derivative of -37*l**6/60 + 7*l**5/6 + l**4/6 + 5*l**2 - 7. Factor c(f).
-2*f*(f - 1)*(37*f + 2)
Let s = 161053/10280 - 137/2056. Determine t so that s*t**2 + 363/5*t**3 - 363/5*t - 18 + 12/5*t**4 = 0.
-30, -1, -1/4, 1
Let h(w) be the second derivative of -w**4/4 + 171*w**3/2 + 87*w + 10. Let h(n) = 0. Calculate n.
0, 171
Determine f so that -4/5*f**3 - 1856/5*f + 368 + 476/5*f**2 = 0.
2, 115
Suppose 5*c + 4 = -5*m + 49, 5*c - 10 = 2*m. Suppose 0 = r - m - 12. Factor 16*w**5 - 13*w + 4*w**4 - 12*w**3 + r*w + 12*w**4 - 8*w**2.
4*w*(w + 1)**2*(2*w - 1)**2
Let u = 20/823 + 1226/17283. Let a(g) be the first derivative of -3/7*g**2 + u*g**3 + 0*g + 1. Find m such that a(m) = 0.
0, 3
Suppose -12*o + 26 = -13*o. Let k = -23 - o. Suppose 1 - 8 + k*h**2 - 5 = 0. What is h?
-2, 2
Solve 2*j**5 - 64277 - 608*j**2 + 1197*j + 65109 - 349*j - 428*j**3 + 2*j**5 + 200*j**4 = 0 for j.
-52, -1, 2
Let o(g) be the first derivative of 18 - 1/24*g**4 + 0*g - 1/6*g**3 + 5/6*g**2. Factor o(z).
-z*(z - 2)*(z + 5)/6
Suppose 52 - 152 = 20*t. Let w(p) = -p**2 + 25*p - 36. Let c(s) = 2*s**2 - 50*s + 68. Let h(v) = t*w(v) - 3*c(v). Factor h(i).
-(i - 24)*(i - 1)
Let v be 100/((-57)/(-171)*(42 - 0)). Factor 54/7*m**2 + 16/7 + 2/7*m**4 - v*m - 22/7*m**3.
2*(m - 8)*(m - 1)**3/7
Let f be (21/(1890/(-12)))/((-12)/18). Let c(q) be the second derivative of 0*q**3 - f*q**5 + 0*q**4 + 0*q**2 + 0 + 2/15*q**6 + 10*q. Factor c(z).
4*z**3*(z - 1)
Let b = -31 + 44. Let o = b + -9. Solve 14*k**2 + 9*k**5 + 0*k**3 - 12*k**o + 9*k - 12*k**5 - 2*k**2 - 6*k**3 = 0.
-3, -1, 0, 1
Let k = -1040 - -1047. Let d(r) be the third derivative of 1/8*r**4 + 1/140*r**k + 6*r**2 + 1/448*r**8 + 0 - 3/160*r**6 + 0*r - 1/20*r**5 + 0*r**3. Factor d(p).
3*p*(p - 1)**2*(p + 2)**2/4
Let h(a) be the first derivative of -3*a**4/4 + 5*a**3 + 27*a**2 - 216*a + 679. Let h(p) = 0. Calculate p.
-4, 3, 6
Let q = 170 + -167. Factor 144*m**2 + 30*m - 42*m**q - 462 + 3*m**4 + 315 + 12*m.
3*(m - 7)**2*(m - 1)*(m + 1)
Let r = -6685 + 6689. Let w(b) be the third derivative of 10*b**3 + 0 - 1/40*b**6 - 3*b**r + 0*b + 9/20*b**5 - b**2. Factor w(h).
-3*(h - 5)*(h - 2)**2
Let j(n) be the first derivative of 17*n**4/10 + 56*n**3/3 + 304*n**2/5 + 128*n/5 - 5898. Determine v, given that j(v) = 0.
-4, -4/17
Let l(g) be the third derivative of -g**6/30 + 8*g**5/15 - g**4/6 - 28*g**3 - 6*g**2 - 2*g - 340. Factor l(y).
-4*(y - 7)*(y - 3)*(y + 2)
Suppose -2*n - 11 = 3*l, 3*l + 199*n - 196*n + 21 = 0. Factor 2/3*x - 1/2*x**2 - 1/6*x**l + 2.
-(x - 2)*(x + 2)*(x + 3)/6
Let x(a) = 3*a**3 + 2070*a**2 + 369599*a + 4. Let n(j) = 15*j**3 + 10341*j**2 + 1847994*j + 21. Let s(i) = -4*n(i) + 21*x(i). Factor s(b).
3*b*(b + 351)**2
Let z = 221989/9 - 24665. Solve 2/3*v**3 + z*v - 10/9*v**2 + 0 - 2/9*v**5 + 2/9*v**4 = 0 for v.
-2, 0, 1
Let o(b) be the first derivative of b**4/22 - 4*b**3/11 + 9*b**2/11 + 94*b - 66. Let r(p) be the first derivative of o(p). Factor r(q).
6*(q - 3)*(q - 1)/11
Let z = 25749 + -25749. Find b such that 14/9*b**2 + 16/9*b - 2/9*b**3 + z = 0.
-1, 0, 8
Factor 3010*v + 2007/2 + 1002*v**3 + 3009*v**2 - 1/2*v**4.
-(v - 2007)*(v + 1)**3/2
Find z such that -18*z**2 - 25*z - 2*z**3 + 4*z**3 + 42 + z**3 - 2*z = 0.
-2, 1, 7
Factor -12*p - 645 + 2*p**2 - p**3 + 645 + 6*p**2 + 0*p**3.
-p*(p - 6)*(p - 2)
Let q(s) = s**3 + 2*s**2 - 1. Let r be (-6)/(-12) + -2 - (-10)/4. Let c be q(r). Factor -2*g + 25*g + 2*g + c*g**2 - 49*g + 72.
2*(g - 6)**2
Let b(l) be the first derivative of l**6/10 + 3*l**5/10 - 3*l**4/4 + 43*l + 32. Let g(v) be the first derivative of b(v). Factor g(z).
3*z**2*(z - 1)*(z + 3)
Let f(c) be the third derivative of 11/80*c**6 + 0*c + 1/280*c**7 + 343/8*c**3 + 0 + 21/10*c**5 + 90*c**2 + 245/16*c**4. Factor f(l).
3*(l + 1)*(l + 7)**3/4
Let u(a) = a**2 - a + 4. Let n(k) = 81*k**2 + 42*k - 23. Let m(r) = -n(r) - 5*u(r). Let m(t) = 0. What is t?
-1/2, 3/43
Factor -336 + 3/2*r**3 - 33*r**2 + 192*r.
3*(r - 14)*(r - 4)**2/2
Let o(l) be the first derivative of -l**4/8 - 149*l**3/6 - 295*l**2/4 - 147*l/2 + 506. Determine z so that o(z) = 0.
-147, -1
Let 4378*b**2 - 8627*b**2 + 88 - 564*b + 5385*b**2 - 904*b**3 + 216*b**4 + 28*b**5 = 0. Calculate b.
-11, 2/7, 1
Let a(v) = 9*v**2 - v - 1. Let i(n) = 77*n**2 - 1483*n + 10949. Let d(y) = -3*a(y) + i(y). Determine h, given that d(h) = 0.
74/5
What is x in 47/2*x**2 - 81*x + 44 + 41/2*x**3 - 15/2*x**4 + 1/2*x**5 = 0?
-2, 1, 4, 11
Let z(i) be the second derivative of -2 + 2/15*i**6 + 25*i + 2*i**2 - 7/3*i**3 + 7/5*i**5 - 1/3*i**7 - 2/3*i**4. Solve z(s) = 0 for s.
-1, 2/7, 1
Let x be 96459/53280 - (-9)/(-5). Let q(u) be the third derivative of -11*u**2 + 13/240*u**5 - 1/6*u**3 + x*u**6 + 0*u + 1/24*u**4 + 0. Solve q(w) = 0.
-2, -1, 2/5
Let s = -2084/47 - -774010/17437. Let r = s + 5/53. Factor 1/7*l**2 - 1/7*l**4 - 1/7*l + 0 + r*l**3.
-l*(l - 1)**2*(l + 1)/7
Let l(t) = 43*t**2 + 95*t - 2. Let w(y) = -y**2 - y - 2. Suppose 114 = 5*s + 119. Let f(k) = s*l(k) + 5*w(k). Find z such that f(z) = 0.
-2, -1/12
Let l(x) be the second derivative of 49*x**6/20 - 2163*x**5/40 + 141*x**4 - 117*x**3 - 13390*x. Solve l(v) = 0.
0, 6/7, 13
Let f(x) be the third derivative of 6*x**2 + 8 + 1/6*x**4 - 7/2*x**3 + 1/60*x**5 + 0*x. Factor f(t).
(t - 3)*(t + 7)
Let x = 72522/11 + -217027/33. Factor -192 + 208*v + 1/3*v**3 - x*v**2.
(v - 24)**2*(v - 1)/3
Factor 409*j**3 + 197*j + 379*j + 2*j**4 + 10*j**4 + j**5 - 517*j**3 + 32*j**2.
j*(j - 4)**2*(j + 2)*(j + 18)
Let o be (-4)/7 - (-69905)/434. Let v = o - 2885/18. Factor 0 + 2/9*t**3 + 4/9*t**2 + 0*t - v*t**4.
-2*t**2*(t - 2)*(t + 1)/9
Suppose -4*r = 4, -2*n - r = 3*n - 9. Find c, given that 947*c**4 - 902*c**4 - 88*c**3 - 320*c**n + 60*c + 303*c**3 = 0.
-6, 0, 2/9, 1
Suppose 3*m + 90 = -10*l, 332 = 5*m - l + 323. Determine j, given that 5/6*j**3 + m - 5/6*j**2 + 5/6*j**4 + 1/6*j**5 - j = 0.
-3, -2, -1, 0, 1
Let w = 4549 + -4543. Let b(p) be the third derivative of 0*p - 2/3*p**3 - 1/45*p**5 + 5/18*p**4 + 0 + 10*p**2 - 1/90*p**w. Factor b(u).
-4*(u - 1)**2*(u + 3)/3
Let o(x) be the third derivative of 1/84*x**8 + 0 - 2/35*x**7 - 1/15*x**5 + 65*x**2 + 0*x**4 + 0*x + 1/10*x**6 + 0*x**3. Determine t so that o(t) = 0.
0, 1
Let z(n) be the third derivative of 0*n + 3/10*n**5 - 28*n**2 + 4*n**3 + 3/