405*q. Solve p(j) = 0 for j.
9
Find c such that 977*c - 7976018 - 72*c**2 - 7396*c + 70*c**2 - 489*c - 1080*c = 0.
-1997
Let r(b) be the first derivative of -12*b - 16/5*b**5 + 53 - 30*b**4 - 52*b**3 - 37*b**2. Determine o, given that r(o) = 0.
-6, -1/2
Let g = -1949 - -13675/7. Let s(a) = -a**2 - 7*a - 4. Let h be s(-6). Factor -2/7*x**h - g - 16/7*x.
-2*(x + 4)**2/7
Let b(a) be the second derivative of -a**7/21 + 4*a**6/15 + 4*a**5/5 - 32*a**4/3 + 112*a**3/3 - 64*a**2 + 797*a. Factor b(x).
-2*(x - 2)**4*(x + 4)
Suppose 29*s - 10 = 34*s + 5*x, -2*s - 10 = 3*x. Let o(m) be the second derivative of -1/6*m**3 + 0*m**2 + 0 + 1/80*m**5 + 0*m**s + 39*m. Factor o(l).
l*(l - 2)*(l + 2)/4
Let q(v) be the first derivative of -v**6/2 - 78*v**5/5 - 579*v**4/4 - 312*v**3 - 216*v**2 + 1078. Solve q(s) = 0 for s.
-12, -1, 0
Let v be 4/(6/42 + (-45)/21). Let u be v*(108/14 + -8). Factor u*l**2 + 20/7*l - 4/7*l**3 + 12/7.
-4*(l - 3)*(l + 1)**2/7
Let -2/3*x**5 + 0*x - 28/3*x**2 - 46/3*x**3 - 20/3*x**4 + 0 = 0. What is x?
-7, -2, -1, 0
Let s be (-3 - 71183/(-63)) + 1 - 4. Let r = 1124 - s. Factor r*g**3 + 1/9 - 1/9*g**2 - 1/9*g.
(g - 1)**2*(g + 1)/9
Let b(t) be the second derivative of t**4/36 - 11*t**3/6 + 58*t**2/3 + 38*t + 2. Factor b(n).
(n - 29)*(n - 4)/3
Suppose 3/2*q**2 + 0 - 153*q = 0. Calculate q.
0, 102
Solve 708 - 2589 + 4*j**2 + 1117*j + 1701*j - 514*j - 427 = 0 for j.
-577, 1
Let m be 270/81*6/5*1. Factor -3*k**5 - 3*k**3 - 3*k**5 - 2*k**m + 10*k**5 - 3*k**5.
k**3*(k - 3)*(k + 1)
Let o(w) be the third derivative of -7*w**6/990 - 17*w**5/660 - w**4/44 - 32*w**3/3 - 46*w**2. Let r(a) be the first derivative of o(a). Factor r(z).
-2*(z + 1)*(14*z + 3)/11
Factor -2149 + 16316*m**2 + 1600*m + 2*m**3 - 987 - 16528*m**2.
2*(m - 98)*(m - 4)**2
Suppose -2*p + 7 = -3. Let s(n) = 7 + 230*n + 180*n - 401*n - 3*n**2. Let f(c) = -4*c**2 + 10*c + 8. Let i(w) = p*f(w) - 6*s(w). Find z, given that i(z) = 0.
-1
Let z(y) be the second derivative of -27*y**5/5 - 18*y**4 - 24*y**3 - 16*y**2 + 40*y + 11. Determine a so that z(a) = 0.
-2/3
Factor -1994 - 12*t - 5*t**2 - 403*t + 148 + 266.
-5*(t + 4)*(t + 79)
Suppose 12 = 3*u - 3*r - 12, 0 = -4*u - 2*r + 2. What is y in -3*y + u*y + 4*y**3 + 96*y**2 - 100*y**2 = 0?
0, 1
Let t(d) be the second derivative of d**6/160 - 9*d**5/160 - 17*d**4/64 - 3*d**3/8 - 66*d**2 - 79*d. Let g(c) be the first derivative of t(c). Factor g(u).
3*(u - 6)*(u + 1)*(2*u + 1)/8
Let b be 40/(3 - 1) - (8 - 9). Suppose -2*o + 2 = -2*s - 2, -3*o = 2*s - b. Solve -3*n - 3*n**4 - 16*n**s + 6 + 3*n**2 + 19*n**3 - 6 = 0 for n.
-1, 0, 1
Suppose 4*n + 5 - 37 = -2*b, 0 = 2*b + n - 11. Factor 3/4 + p + 1/4*p**b.
(p + 1)*(p + 3)/4
Let r(x) = 318*x - 954. Let k be r(3). Let b(v) be the third derivative of 14*v**2 + 1/15*v**3 - 1/30*v**4 + 1/150*v**5 + k*v + 0. Factor b(g).
2*(g - 1)**2/5
Let u be (8196/(-54))/(8/(-6)). Let g = u - 340/3. Factor 0 + 0*i**3 - g*i**4 + 1/2*i**2 + 0*i.
-i**2*(i - 1)*(i + 1)/2
Let m(x) be the second derivative of 5*x**8/336 + x**7/42 - x**6/24 - x**5/12 - 43*x**2/2 - 4*x + 1. Let v(c) be the first derivative of m(c). Factor v(a).
5*a**2*(a - 1)*(a + 1)**2
Let m(t) = 29*t**2 + 28*t + 2. Let u(g) = g**2 + g - 1. Let a(o) = m(o) + 3*u(o). Factor a(n).
(n + 1)*(32*n - 1)
Suppose -26*r - 89 = -193. Let m(y) be the third derivative of -y**2 + 1/120*y**5 + 0*y**3 - 1/48*y**r + 0*y + 0. Factor m(k).
k*(k - 1)/2
Suppose 841*q + 502 = 3025. Let 46/3*m - 34/5*m**2 - 8/15*m**4 - 14/3*m**q - 10/3 = 0. Calculate m.
-5, 1/4, 1
Let p(z) = -z**2 - 9738*z + 4723878. Let t(l) = 2*l**2 + 29211*l - 14171641. Let x(d) = -17*p(d) - 6*t(d). Factor x(s).
5*(s - 972)**2
Let v(k) be the third derivative of 4*k + 5/3*k**3 + 0 + 7/30*k**5 + 4*k**2 - 1/60*k**6 - 11/12*k**4. Determine h so that v(h) = 0.
1, 5
Let u(i) = -3*i**2 - 92*i + 130. Let v(t) = -6*t**2 - 192*t + 261. Let q(w) = -9*u(w) + 5*v(w). Determine h so that q(h) = 0.
-45, 1
Suppose 281216/7*y**5 + 19548*y + 3888352/7*y**4 - 378 + 13100984/7*y**3 - 2345670/7*y**2 = 0. What is y?
-7, 3/52
Let u(s) be the first derivative of s**3/6 - 21*s**2/4 + 2467. Solve u(c) = 0.
0, 21
Let o(m) = -8*m. Let c(s) = s**3 - 3*s**2 - s + 1. Let v be c(3). Let d(t) = t**2 - 38*t. Let k(p) = v*d(p) + 11*o(p). Solve k(l) = 0.
-6, 0
Factor 1/5*f**3 + 1/5*f**4 - 13/5*f - 7/5*f**2 - 6/5.
(f - 3)*(f + 1)**2*(f + 2)/5
Let l(k) = -k**3 - 99*k**2 + 152*k + 5202. Let i be l(-100). Suppose -5/6*v**i + 0 + 5/3*v = 0. What is v?
0, 2
Let l = -623 - -628. Let p(y) be the second derivative of -1/4*y**4 + 18*y - 1/2*y**2 - 1/20*y**l + 0 - 1/2*y**3. Factor p(r).
-(r + 1)**3
Let s(y) be the third derivative of y**5/300 - 22*y**4/15 - 24*y**3 - 22*y**2 - 4. Factor s(a).
(a - 180)*(a + 4)/5
Suppose 4 = -84*i + 82*i - 4*r, 3*i - r = 15. Factor -i*n - 10/7*n**2 + 4/7*n**3 + 16/7.
2*(n - 4)*(n + 2)*(2*n - 1)/7
Let d(i) be the third derivative of -i**7/560 - i**6/120 + 7*i**5/80 - i**4/4 + 5*i**3 + 43*i**2. Let u(f) be the first derivative of d(f). Factor u(h).
-3*(h - 1)**2*(h + 4)/2
What is i in -279/7*i**3 + 3/7*i**5 + 0 + 276/7*i - 132/7*i**2 + 132/7*i**4 = 0?
-46, -1, 0, 1, 2
Let m be (-1 - (2 - 0)) + 38 + 88. Factor -4*l**2 - 7*l - m*l + 33*l - 47*l - 140.
-4*(l + 1)*(l + 35)
Let m be ((2 - -18) + -22)/(1 - (-42)/(-27)) - 2. Determine a, given that 1/5*a**5 + 4/5*a**2 + m*a**3 + 0*a + 0 + a**4 = 0.
-2, -1, 0
Solve 0*p**2 + 2/11*p**5 + 0 + 0*p + 42/11*p**4 + 108/11*p**3 = 0.
-18, -3, 0
Let n be (-68)/(-20) - (-2)/(-10)*-3. Let c(u) be the second derivative of -1/4*u**3 + 9/8*u**2 + 0 + 16*u - 1/16*u**n. Factor c(t).
-3*(t - 1)*(t + 3)/4
Let y(j) be the third derivative of -j**6/280 - 3*j**5/28 - 13*j**4/28 - 81*j**2 - 2*j. Determine s, given that y(s) = 0.
-13, -2, 0
Let c(j) = -8*j**3 + 111*j**2 + 513*j - 6983. Let m be c(14). Suppose 0 + 4/7*t - 4/7*t**m + 0*t**2 = 0. Calculate t.
-1, 0, 1
Let z(l) be the first derivative of -l**4/8 - 4*l**3 + 51*l**2/4 + 126*l + 33. Let c(i) be the first derivative of z(i). Factor c(d).
-3*(d - 1)*(d + 17)/2
Factor -182/3*n + 1/6*n**3 - 430/3 + 35/6*n**2.
(n - 10)*(n + 2)*(n + 43)/6
Suppose -3*h - 2*l - 304 = 0, -5*h = -2*l + 6*l + 506. Let s = 720/7 + h. Factor -w**3 - 30/7*w**2 - 29/7*w - s.
-(w + 1)*(w + 3)*(7*w + 2)/7
Let i = 349 - 346. Factor 26*z**3 + 12 - 57*z**3 + 13*z + 30*z**i.
-(z - 4)*(z + 1)*(z + 3)
Let u(c) = -45*c**2 + 749*c + 78. Let w(m) = -91*m**2 + 1497*m + 158. Let t(j) = 7*u(j) - 3*w(j). Find y, given that t(y) = 0.
-2/21, 18
Factor 1/2*x**3 - 22326 + 7076*x + 241/2*x**2.
(x - 3)*(x + 122)**2/2
Let c(w) be the second derivative of 1/9*w**3 + 1/90*w**4 + 4/15*w**2 - 69*w + 0. Determine q so that c(q) = 0.
-4, -1
Factor -2408400 - 888*q**2 - 161376*q - 2*q**3 + 731*q**2 - 6413488 - 827*q**2.
-2*(q + 164)**3
Let d(b) be the third derivative of 11*b**2 - 1/180*b**6 + 0*b + 0*b**4 + 0*b**5 + 0 - 5/2*b**3. Let y(i) be the first derivative of d(i). Factor y(r).
-2*r**2
Let p be (1/1)/6*(-109 + 143). Let r(l) be the second derivative of -p*l**4 + 4*l - 2/5*l**6 + 0 + 0*l**2 - 4*l**3 - 14/5*l**5. Find w, given that r(w) = 0.
-3, -1, -2/3, 0
Let y(r) be the second derivative of r**7/210 + 22*r**6/75 - 69*r**5/20 + 154*r**4/15 + 94*r**3/15 - 408*r**2/5 + 1113*r. Determine v so that y(v) = 0.
-51, -1, 2, 4
Let u(m) be the second derivative of 0 + 184*m + 1/18*m**4 - 2/3*m**3 + 0*m**2. Factor u(p).
2*p*(p - 6)/3
Let v(g) = -g**2 + 14*g + 2. Let y be v(14). Factor 8 - 12877*j**3 + j - 6*j**y + 12873*j**3 + 2*j**4 + 7*j.
2*(j - 2)**2*(j + 1)**2
Let b(q) be the first derivative of 5*q**4/4 - 260*q**3 + 3055*q**2/2 - 2280*q - 3709. Factor b(p).
5*(p - 152)*(p - 3)*(p - 1)
Let g = 103 - 95. Let w be 45/(-27)*(g/10 + -2). Determine y so that -6*y**3 - 6*y**5 + 12*y**2 - 15*y**4 - 2*y + 12*y + 4 - 1 + w*y = 0.
-1, -1/2, 1
Let i(r) = -47*r + 429. Let b be i(9). Let d(q) = 6*q - 36. Let x be d(b). Determine j, given that 0*j**2 - 1/3*j**4 + 1/6*j**5 + 1/6*j**3 + x*j + 0 = 0.
0, 1
Let y = 38 - 33. Factor -7*r**2 - 5*r - 3*r**2 + 5 + 0*r**4 - y*r**5 + 7*r**3 + 5*r**4 + 3*r**3.
-5*(r - 1)**3*(r + 1)**2
Let x(g) be the second derivative of 1/30*g**6 + 0*g**2 - 4/5*g**5 + 0*g**4 + 126 - g + 0*g**3. Find w, given that x(w) = 0.
0, 16
Let j(m) be the second derivative of m**7/5040 - m**6/240 + 3*m**5/80 