1/4
Factor -12/5*j**2 + 41/5*j - 42/5 + 1/5*j**3.
(j - 7)*(j - 3)*(j - 2)/5
Let s(v) be the second derivative of v**5/140 + v**4/28 - 2*v**3/21 - 6*v**2/7 + 86*v - 3. Suppose s(r) = 0. Calculate r.
-3, -2, 2
Let q be 0 + 1*(0 - -2) + -28. Let z = -23 - q. Factor -6*y**2 + 3*y**4 + z*y**4 - 18*y**3 + 9*y + 6*y**3 + y**5 + 2*y**5.
3*y*(y - 1)**2*(y + 1)*(y + 3)
Let c(k) be the first derivative of 1/4*k**3 + 61 + 0*k + 9/8*k**2. Solve c(m) = 0 for m.
-3, 0
Let l(t) = t**3 - t**2 + 5*t + 7. Let r(y) = -7*y**2 + 5*y - 3. Let p(f) = -3*f**2 + 2*f - 1. Let n(a) = 5*p(a) - 2*r(a). Let k(j) = l(j) - 5*n(j). Factor k(w).
(w + 1)**2*(w + 2)
Let n(p) be the first derivative of -p**7/168 + p**5/80 + 48*p + 22. Let d(k) be the first derivative of n(k). Factor d(o).
-o**3*(o - 1)*(o + 1)/4
Let o(h) = 10*h - 77. Suppose 23*q = 28*q - 40. Let x be o(q). Factor -6/7 - 2/7*y**x - 10/7*y**2 - 2*y.
-2*(y + 1)**2*(y + 3)/7
Suppose -30 - 18 = -3*h. Suppose -k + 4*q - 24 = -2*k, h = -k + 4*q. Solve -12 + k*i - 6*i - 10*i - 3*i**2 = 0 for i.
-2
Find m, given that 41/5*m**4 + 186/5*m**3 + 1/5*m**5 - 288/5 + 212/5*m**2 - 152/5*m = 0.
-36, -2, 1
Suppose -2*i + 8 = 0, m - 5*i = 2 - 24. Let n be ((-68)/187)/(m/11). What is y in -1/5 + 0*y + 1/5*y**n = 0?
-1, 1
Let r(x) be the third derivative of 0*x**5 + 1/1575*x**7 + 1/150*x**6 + 37*x**2 + 0 - 8/45*x**4 + 0*x**3 + 0*x. Suppose r(s) = 0. Calculate s.
-4, 0, 2
Let b(f) be the third derivative of -1156/3*f**3 + 0 + 17/3*f**4 + 0*f - 103*f**2 - 1/30*f**5. Factor b(l).
-2*(l - 34)**2
Let v(c) = 95*c**2 - 103*c - 3. Let r(w) = w**2 + 11*w - 1. Let o(p) = r(p) + v(p). Solve o(k) = 0.
-1/24, 1
Suppose -6*q + 121 - 43 = 0. Let y(i) be the first derivative of -19*i**2 + i**3 + 21 + q*i**2 + 0. Factor y(g).
3*g*(g - 4)
Let r(c) be the first derivative of 1/15*c**6 + 5 + 1/10*c**5 - 1/6*c**4 - 1/3*c**3 + 0*c**2 - 21*c. Let w(k) be the first derivative of r(k). Factor w(h).
2*h*(h - 1)*(h + 1)**2
Let u(k) be the first derivative of k**6/24 + 9*k**5/10 - 5*k**4/2 + k**3/6 + 39*k**2/8 - 5*k + 2803. Find f such that u(f) = 0.
-20, -1, 1
Let y(k) be the third derivative of k**6/160 + 13*k**5/40 + 5*k**2 - 11*k. Determine z, given that y(z) = 0.
-26, 0
Let b(d) be the third derivative of -d**7/105 - 7*d**6/15 - 128*d**5/15 - 64*d**4 + 2742*d**2. Find o, given that b(o) = 0.
-12, -8, 0
Let q(p) = 8*p**3 - 6*p**2 + 4*p - 4. Let s be q(2). Find v, given that 10 - s*v - 35*v**2 + 31*v**2 - 50 = 0.
-10, -1
Let z(r) be the third derivative of -r**6/30 + 2*r**5/5 - 90*r**2. Let o(q) = -q**3 + 8*q**2. Let g(a) = 20*o(a) - 6*z(a). Solve g(c) = 0 for c.
-4, 0
Let a be (960/175)/(2 + 9 - 1026/95). Factor 48*b - 93/7*b**2 + 6/7*b**3 + a.
3*(b - 8)**2*(2*b + 1)/7
Let m(b) be the second derivative of 0*b**4 + b**2 - 1/60*b**5 - 121*b + 0 + 7/18*b**3. Determine x so that m(x) = 0.
-2, -1, 3
Suppose 528*z**2 + 450*z**2 - 3*z**3 + 137*z**2 + 910*z**2 = 0. What is z?
0, 675
Let o(i) = i - 8. Let q = -15 + 25. Let x be o(q). Find t, given that 4*t**2 - 4*t + t**x + 0*t**2 - 7*t**2 = 0.
-2, 0
Let a(i) = -2*i**2 + 458*i - 508. Let y(b) = -b**2 - 12*b. Let z(s) = a(s) - 4*y(s). Factor z(r).
2*(r - 1)*(r + 254)
Factor 10784/7*p - 14536832/7 - 2/7*p**2.
-2*(p - 2696)**2/7
Let a(w) = -45*w**2 + 996*w - 1966. Let q(l) = 66*l**2 - 999*l + 1965. Let h(z) = 3*a(z) + 2*q(z). Factor h(y).
-3*(y - 328)*(y - 2)
Let l be 12 + (-48)/(6/1). Let s(i) be the third derivative of -7/480*i**6 + 0*i + 2*i**2 + 1/20*i**5 + 1/24*i**l + 0*i**3 + 0. Factor s(d).
-d*(d - 2)*(7*d + 2)/4
Let s(f) = 2*f**2 + 8*f - 1. Let b be s(-5). Suppose -25 = -4*a - b. Suppose -24*w + 12 + 0*w - 33*w**2 - 14*w**5 + 21*w**a + 39*w**3 - w**5 = 0. Calculate w.
-1, 2/5, 1, 2
Let u(p) be the third derivative of -2/3*p**3 + 1/40*p**6 + 1/12*p**5 - 1/210*p**7 + 6 + 0*p + p**2 - 1/8*p**4. Factor u(v).
-(v - 4)*(v - 1)*(v + 1)**2
Let d be (-816)/119*-2*(-1)/(-4). Let q(g) be the first derivative of -18/7*g**2 + 27 - 3/28*g**4 + d*g + 6/7*g**3. Suppose q(w) = 0. Calculate w.
2
Let g be (-4559)/(-1692) + (-45)/20. Suppose -8/9*h**3 + 10/9*h**2 + 0 - g*h + 2/9*h**4 = 0. What is h?
0, 1, 2
Let x = 139/6 + -401/18. Let a(q) be the first derivative of 1/27*q**3 + x*q**2 + 64/9*q - 26. Factor a(o).
(o + 8)**2/9
Suppose 287*m + 128 = 702. Let f(g) be the first derivative of 8 + 0*g - 1/16*g**m + 0*g**3 + 1/32*g**4. Solve f(s) = 0.
-1, 0, 1
Let l(g) = 3*g**2 - 13*g. Let h be l(6). Suppose -80 = -10*q - h*q. Factor 3/2*r**q - 6 - 9/2*r.
3*(r - 4)*(r + 1)/2
Let j = 30312 + -30307. Let w(t) be the second derivative of 6*t - 2/45*t**6 + 0*t**2 + 0*t**3 + 0 - 1/6*t**4 - 7/30*t**j. Determine v, given that w(v) = 0.
-3, -1/2, 0
Let u(r) be the third derivative of -r**6/120 - 89*r**5/20 + 179*r**4/8 - 269*r**3/6 + 398*r**2 + 5*r. Let u(i) = 0. Calculate i.
-269, 1
Let i(n) be the second derivative of 26 + 1/24*n**4 + 1089/4*n**2 + 3*n - 11/2*n**3. Factor i(z).
(z - 33)**2/2
Let z(y) = 2*y**3 + 18*y**2 - 697*y + 554. Let t be z(-24). Find n such that -2/3*n**t + 0 - 2/3*n = 0.
-1, 0
Let s(b) = 0*b**3 - 8987 - 2*b + b**3 + 8987 + b**2. Let a(q) = 6*q**3 + 36*q**2 + 68*q + 40. Let r(g) = a(g) - s(g). Let r(k) = 0. What is k?
-4, -2, -1
Solve -17891883440*a - 12140*a**3 + 22106940*a**2 + 5/2*a**4 + 5430186624040 = 0 for a.
1214
Find j, given that 68 + 10*j**5 + 155 - 189*j + 45*j**4 - 145*j**3 + 24*j - 700*j**2 - 255*j + 177 = 0.
-5, -2, 1/2, 4
Let o = 1000 + -996. Suppose 5*z = 4*i - 10, 4*z + 15 = o*i + 3. Factor -4/7*k**z + 10/7*k - 4/7.
-2*(k - 2)*(2*k - 1)/7
Let q be (-1222)/14 - 8/(-28). Let g = q + 101. Determine b so that 19*b + g*b**2 + 10*b + 2*b**3 - 17*b = 0.
-6, -1, 0
Let s(k) be the third derivative of -3/350*k**7 + k + 10*k**2 + 0 + 0*k**5 + 0*k**3 - 1/140*k**8 + 1/200*k**6 + 0*k**4. What is j in s(j) = 0?
-1, 0, 1/4
Let t be (154 - 164) + 64/6. Let m(g) be the second derivative of 0 + 1/45*g**6 - 1/6*g**4 + 1/30*g**5 + 5*g - 5/9*g**3 - t*g**2. Factor m(i).
2*(i - 2)*(i + 1)**3/3
Let n(p) = 2131*p - 6391. Let j be n(3). Solve 4*a**j + 4 - 22/3*a - 2/3*a**3 = 0.
1, 2, 3
Factor 6/7*k**3 + 204/7 + 566/7*k - 136/7*k**2.
2*(k - 17)*(k - 6)*(3*k + 1)/7
Find o such that -16 - 151/2*o**3 + 80*o - 21*o**2 + 37*o**4 - 9/2*o**5 = 0.
-1, 2/9, 1, 4
Factor -1/2*q**3 + 27/2*q**2 + 0 - 25*q.
-q*(q - 25)*(q - 2)/2
Let i = -251 - -316. Solve -336*j**3 - 49*j + 157*j + 124*j - 16*j**4 - 49*j - 84 + i*j + 12*j**2 = 0.
-21, -1, 1/2
Let f(a) be the first derivative of -a**5/20 + 51*a**4/16 - 33*a**3/4 + 49*a**2/8 + 5384. Let f(p) = 0. What is p?
0, 1, 49
Let y(f) be the first derivative of -f**4/12 + 2647*f**3/3 - 7006609*f**2/2 + 18546494023*f/3 + 3227. Suppose y(o) = 0. Calculate o.
2647
Let j(a) be the first derivative of a**3/3 + 174*a**2 + 347*a + 2274. Factor j(d).
(d + 1)*(d + 347)
Suppose -235*t**4 - 700*t**5 + 96 + 425*t**4 + 3*t + 1741*t**4 - 612*t**3 + 13*t - 1240*t**2 + 509*t**4 = 0. What is t?
-2/5, 2/7, 1, 3
Let f(c) be the second derivative of c**5/480 - 7*c**4/192 + 13*c**2 - 7*c + 3. Let h(y) be the first derivative of f(y). Suppose h(z) = 0. What is z?
0, 7
Let u(d) be the first derivative of -57 - 7/2*d**2 - 8/3*d**3 - 2*d + 1/6*d**6 - 1/2*d**4 + 2/5*d**5. Find h, given that u(h) = 0.
-1, 2
Let p(d) = 467*d**3 + 84*d**2 - 216*d + 83. Let u(b) = 85*b**3 + 17*b**2 - 43*b + 17. Let j(k) = 2*p(k) - 11*u(k). Let j(y) = 0. Calculate y.
-21, 1
Factor -5/8*x**2 + 1511/4 + 7553/8*x.
-(x - 1511)*(5*x + 2)/8
Let s(y) be the first derivative of -7*y**5/20 + 13*y**4/4 - 13*y**3/3 - 6*y**2 + 10373. Factor s(q).
-q*(q - 6)*(q - 2)*(7*q + 4)/4
Let k be 3 - ((-124620)/4950 + 2/11). Let f = k - 305/11. Factor -f*l + 16/15 - 2/15*l**2.
-2*(l - 2)*(l + 4)/15
Factor 95 + 69*j + 31 + 60*j**2 - 3*j**3 - 5*j**2 - 65*j**2 - 50*j**2.
-3*(j - 2)*(j + 1)*(j + 21)
Let m = -817 - -369. Let w = 448 + m. Let w - 1/10*i**2 + 2/5*i = 0. What is i?
0, 4
Suppose -5*h = 3*v - 200, -2*v - 2*v = -h + 40. Let 1244 + 94*w - 611 - 16*w + 6*w**3 - 597 + h*w**2 = 0. What is w?
-3, -2/3
Let 117/4*z + 0 + 1/4*z**2 = 0. What is z?
-117, 0
Let 7066*c + 4*c**2 - 3867*c + 618 - 3819*c - c**2 - c**2 = 0. Calculate c.
1, 309
Let c be (-9)/(-34) - 412/(-1751). Let f(o) be the first derivative of 1/25*o**5 + 19 + 0*o + 0*o**2 + c*o**4 + 5/3*o**3. Factor f(l).
l**2*(l