hat z(r) = 0.
0
Find x such that 34/15*x**2 + 16/15*x + 0 + 10/3*x**4 - 36/5*x**3 + 8/15*x**5 = 0.
-8, -1/4, 0, 1
Let f(m) = 6*m**4 - 24*m**3 + 38*m**2 + 20*m - 24. Let u(o) = -2*o**3 + o**2 + 3. Let v(d) = -f(d) - 8*u(d). Factor v(g).
-2*g*(g - 5)*(g - 2)*(3*g + 1)
Let p be (5 - 1)*(-1)/(-2). Let g = -60497 - -181493/3. Find u, given that -g - 1/3*u**p + u = 0.
1, 2
Let b = -1673 + 1676. Let w(h) be the third derivative of 0 + 1/40*h**5 + 0*h**b - 29*h**2 + 0*h**4 - 1/80*h**6 + 0*h. Factor w(m).
-3*m**2*(m - 1)/2
Let p(g) = -30*g - 4*g - 2*g**2 - 103 + 6*g. Let x(d) be the first derivative of d**3/3 + 7*d**2 + 52*d + 11. Let a(l) = -3*p(l) - 5*x(l). Factor a(u).
(u + 7)**2
Let o = -751 + 753. Suppose 5*q - k - 1 = 17, -9 = -o*q + k. Factor -2*r**2 - 8/3*r + 2/3*r**q + 0.
2*r*(r - 4)*(r + 1)/3
Let b be 4/(2/((-23)/((-414)/27))). Find d such that 2/3 + 5/3*d + 1/3*d**b - 4*d**2 + 4/3*d**4 = 0.
-2, -1/4, 1
Factor 23/3*h + 0 - 1/3*h**2.
-h*(h - 23)/3
Find x, given that -x**2 + 0 - 1/2*x - 1/2*x**3 = 0.
-1, 0
Let s(i) be the second derivative of 3*i**7/7 + 52*i**6/15 + 48*i**5/5 + 11*i**4 + 7*i**3/3 - 6*i**2 + 2693*i. Let s(q) = 0. Calculate q.
-3, -1, 2/9
Let d = -165861 - -165861. Factor 13/9*m**3 + 1/9*m**5 + d + 0*m + 8/9*m**4 + 2/3*m**2.
m**2*(m + 1)**2*(m + 6)/9
Let y = 204221/10 + -203977/10. Solve y*k**2 + 0 - 1/5*k**3 - 3721/5*k = 0.
0, 61
Let g(m) = -6*m**2 + 20*m - 2. Let l be g(3). Let b(s) be the third derivative of 0*s - 1/100*s**5 + 0*s**l + 0 + 1/10*s**3 - 6*s**2. Factor b(j).
-3*(j - 1)*(j + 1)/5
Let v(b) = b - 28. Let l be v(31). Suppose -5*a + a = -4*i - 28, -l*a = -i - 11. Suppose -6/5*z**a + 12/5*z + 0 = 0. Calculate z.
0, 2
Factor 280/3*z + 18*z**2 + 0 + 2/3*z**3.
2*z*(z + 7)*(z + 20)/3
Suppose 30 - 80*g**2 - 30 - 75*g**2 + 127*g**2 + 360*g = 0. Calculate g.
0, 90/7
Let t = 66805/133618 + 2/66809. Let k(p) be the first derivative of -5/6*p**3 - 1/10*p**5 - 4 + 1/2*p**4 + 0*p + t*p**2. Factor k(q).
-q*(q - 2)*(q - 1)**2/2
Let a(n) be the first derivative of -2*n**3/21 + 4*n**2 + 58*n/7 + 2775. Find t, given that a(t) = 0.
-1, 29
Suppose -2*w + 13 = m, 4*w + 0 = 8. Suppose m = 24*d - 21*d. Suppose 5*a**5 - 6*a**3 - 20*a**4 + 18*a**d + 2*a**3 + 6*a**3 = 0. Calculate a.
0, 2
Let m(d) be the first derivative of -2*d**6/3 - 8*d**5 - 9*d**4 + 972. Determine g so that m(g) = 0.
-9, -1, 0
Let h(y) be the third derivative of 67*y**2 + 2 + 0*y + 1/120*y**6 - 2/3*y**3 + 1/60*y**5 - 1/6*y**4. Solve h(g) = 0.
-2, -1, 2
Let v(s) = -s**5 - s**2 - 2*s + 2. Let q(k) = 4*k**5 - 2*k**4 + 26*k**3 + 56*k**2 + 36*k - 12. Let n(g) = q(g) + 6*v(g). Find l such that n(l) = 0.
-3, -1, 0, 4
Let g(y) be the third derivative of -3/280*y**7 + 0 + 0*y - 298*y**2 + 1/60*y**6 + 0*y**3 + 0*y**4 + 1/240*y**5. Find u, given that g(u) = 0.
-1/9, 0, 1
Let y be -104*(-7)/1120 + (-5)/(75/6). Let n be (-9)/(-12) + (-1)/4. Factor y*a**4 + n*a - 1/2*a**3 + 0 - 1/4*a**2.
a*(a - 2)*(a - 1)*(a + 1)/4
Let z be (14/1 - 994/71)/(-2). Factor 0 - 30/7*j**4 + z*j + 72/7*j**3 - 24/7*j**2.
-6*j**2*(j - 2)*(5*j - 2)/7
Let b(c) be the second derivative of -c**4/20 - 47*c**3/10 - 4*c + 122. Suppose b(k) = 0. Calculate k.
-47, 0
Let o(x) be the second derivative of x**6/540 - x**4/27 - 17*x**2/2 + x. Let i(b) be the first derivative of o(b). Solve i(a) = 0.
-2, 0, 2
Suppose -275*f = -279*f + 100. Let b be (-50)/6*(-30)/f. What is a in -6*a - 2/5*a**3 - 18/5*a**2 + b = 0?
-5, 1
Find k such that -2/7*k**3 - 50307514/7 - 1758/7*k**2 - 515094/7*k = 0.
-293
Suppose 3864 = 68*b + 116*b. Factor -131/2*w**2 + b*w**3 + 9/2*w**4 - 14 + 54*w.
(w - 1)*(w + 7)*(3*w - 2)**2/2
Let v be (2 - 8) + 27/3. Factor 0*g - 2*g**2 + g - 3*g**3 + 4*g**v.
g*(g - 1)**2
Let r be 27*(-6)/(-18) + -10 + (-3)/(-2). Let p(z) be the first derivative of -1/8*z**2 + r*z - 7 - 1/6*z**3 + 1/16*z**4. Factor p(x).
(x - 2)*(x - 1)*(x + 1)/4
Let b be (4/(-3) - -2)*3. Let w = -914 - -1759. Factor 5*o**3 - 2560 - 103*o**2 + 607*o + w*o - 492*o - 17*o**b.
5*(o - 8)**3
Factor 1/2*g**2 - 162 - 323/2*g.
(g - 324)*(g + 1)/2
Let 409/9*g + 136/9 + 1/3*g**2 = 0. Calculate g.
-136, -1/3
Let n = 1136931/7 + -162417. Let n + 2/7*d**3 - 12/7*d**2 - 2/7*d = 0. Calculate d.
-1, 1, 6
Let q(b) be the first derivative of 0*b + 4/9*b**5 + 7/9*b**4 - 6 + 4/9*b**3 + 0*b**2 + 2/27*b**6. Suppose q(n) = 0. Calculate n.
-3, -1, 0
Determine w so that -276/13 - 2/13*w**2 - 278/13*w = 0.
-138, -1
Factor -2/3*n**2 + 430/3 - 76/3*n.
-2*(n - 5)*(n + 43)/3
Solve 6/5 - 4/5*k**2 + 1/5*k**3 + 1/5*k = 0 for k.
-1, 2, 3
Let h be -12 + (-24 - 3944/(-102)). Factor -h*x**3 + 22/3*x**2 + 8/3 + 38/3*x.
-2*(x - 4)*(x + 1)*(4*x + 1)/3
Let h(p) be the second derivative of p**5/120 - p**4/18 + p**3/36 + p**2/2 - 17*p - 4. Factor h(s).
(s - 3)*(s - 2)*(s + 1)/6
Let v(w) be the first derivative of 5*w**4/4 - 135*w**3 - 1740*w**2 - 7120*w - 756. Suppose v(g) = 0. Calculate g.
-4, 89
Let o(m) = -8*m**2 - 252*m - 250. Let g(a) = -a**2 + a. Suppose 3*f + 0*f - 6 = 3*k, 2*k - f = 1. Let v(i) = k*g(i) - o(i). Suppose v(s) = 0. What is s?
-50, -1
Suppose 3*q + 77*v - 72*v = 55, 22 = -5*q + 2*v. Factor -1/4*f**3 + f + 0 + q*f**2.
-f*(f - 2)*(f + 2)/4
Determine u, given that 69*u**2 - 40*u + 11*u**2 + 745*u**4 - 747*u**4 - 288 + 10*u**3 = 0.
-4, -2, 2, 9
Let s be (-43)/(-5160)*4220 + -35. Factor s*x**5 + 0 + 0*x - 1/6*x**2 - 1/6*x**3 + 1/6*x**4.
x**2*(x - 1)*(x + 1)**2/6
Find t such that 2097152/7 - 48768/7*t**2 - 2048000/7*t - 383/7*t**3 - 1/7*t**4 = 0.
-128, 1
Let s(p) = -7*p**5 - 5*p**3 - 10*p**2 - 38*p + 5. Let b(m) = -2*m**5 - m**4 - m**2 - 8*m + 1. Let x(j) = 5*b(j) - s(j). Find t, given that x(t) = 0.
-2, -1, 0, 1/3, 1
Let q(z) be the first derivative of z**9/16632 - z**7/4620 + 3*z**3 + 6*z**2 - 140. Let m(p) be the third derivative of q(p). Factor m(f).
2*f**3*(f - 1)*(f + 1)/11
Let r = 681 + -681. Let p(n) be the third derivative of r*n**3 + 0*n + 0*n**4 - 1/160*n**5 + 1/1680*n**7 + 0 - 45*n**2 - 1/480*n**6. Find j such that p(j) = 0.
-1, 0, 3
Let s be -5 + (-17)/((-43180)/14712). Let z = 1/127 + s. Factor -z + 2/3*y - 2/15*y**2.
-2*(y - 3)*(y - 2)/15
Let h(u) be the third derivative of -u**6/540 - 61*u**5/27 - 23707*u**4/27 - 182408*u**3/9 + 27*u**2 + 80*u - 1. Factor h(q).
-2*(q + 6)*(q + 302)**2/9
Factor -139*a - 1255*a**3 + 1250*a**3 + 709*a + 2200 - 15*a**2.
-5*(a - 11)*(a + 4)*(a + 10)
Let v be 96/(-12) + (-24)/(-3). Let i be (-6 + v)/(5 + (-246)/24). Solve 8/7 + 2/7*l**2 - i*l = 0.
2
Suppose -s - j = -6, -5 = -j - 3. Let u = s - 2. Suppose 0*l**2 + 4*l**3 - 10 + 8*l**2 - 4*l + 0*l**u + 2 = 0. What is l?
-2, -1, 1
Let x(m) be the second derivative of -13*m**6/75 + m**5/25 + m**4/2 + 643*m. Suppose x(v) = 0. What is v?
-1, 0, 15/13
Let c be (-117)/65*(0 + -5). Let l(j) be the first derivative of -25 + c*j**2 + 81*j + 1/3*j**3. Factor l(s).
(s + 9)**2
Factor 33200*l**3 + 155 - 33201*l**3 + 153*l**2 + 115*l + 194*l.
-(l - 155)*(l + 1)**2
Let h = 1086122/5 + -217224. Factor h*m**3 - 12/5*m**2 + 18/5*m + 0.
2*m*(m - 3)**2/5
Let q be 40/42 + 7/((-294)/12). Let a = 1929 + -1929. Factor 14/3*h + a + q*h**2.
2*h*(h + 7)/3
Suppose -4*j + 332 = 13*y - 9*y, -y + 89 = 3*j. Suppose 110*u**2 + 64 + 145*u**2 - y*u**2 - 84 - 20*u = 0. Calculate u.
-2/7, 2/5
Suppose 0 = 16*b - 8422 + 8150. Let r(y) be the third derivative of -1/120*y**5 - 49/12*y**3 - b*y**2 + 0 + 0*y + 7/24*y**4. Solve r(k) = 0.
7
Suppose -2 = 5*k - 4*m, -m - 186 = 4*k - 197. Factor 1/3*q**k + 3025/3 + 110/3*q.
(q + 55)**2/3
Let p = -427/4 + 2423/20. Let n(i) be the first derivative of p*i + 17 + 2/15*i**3 - 12/5*i**2. Factor n(o).
2*(o - 6)**2/5
Let f(q) = -989*q + 988*q + 4 - 4. Let k(l) = -2*l**2 - 2*l + 16. Let i(o) = -2*f(o) - k(o). Suppose i(d) = 0. What is d?
-4, 2
Suppose -340*p**3 - 149*p**5 - 146*p**5 + 170 + 437*p**5 + 10*p**2 - 147*p**5 + 345*p - 180*p**4 = 0. What is p?
-34, -1, 1
Suppose 0 = -3*l - 21, 0 = -206*x + 201*x - 7*l - 29 - 20. Let 4/3*f + x + 3/2*f**4 - 1/6*f**5 - 3/2*f**2 - 7/6*f**3 = 0. Calculate f.
-1, 0, 1, 8
Determine t so that -62/13*t**3 + 0 - 1162/13*t**2 + 2/13*t**4 - 4410/13*t = 0.
-7, 0, 45
Suppose -140/3*k + 8/3*k**3 + 2/3*k**4 - 134/3*k**2 + 0 = 0. What is k?
-10, -1, 0, 7
Let s be (3/(-3))/(26/8 - -5 - 9). What is z in -2/3*z**2 + s*z + 0 - 2/3*z**3 = 0?
-2, 0, 1
Let w = 15