 - 4/15*a**5 + 1/3*a**3 + 5/2*a**2 + 1/90*a**6 + 1 - 3/2*a**4. Let r(n) be the second derivative of s(n). Factor r(x).
4*(x - 9)*(x + 1)
Let n = -342 - -655. Let x = -139 + n. Determine b so that x*b**2 + 4*b - 4*b - b**3 - 177*b**2 = 0.
-3, 0
Let q(y) be the first derivative of 4*y**5/35 - 3*y**4/7 - 20*y**3/21 + 6*y**2/7 + 16*y/7 - 1248. What is r in q(r) = 0?
-1, 1, 4
Let u = -500 + 729. Determine h, given that 7*h**3 - 27*h**2 - 25*h**3 + 69*h - u*h + 79*h + 69*h - 3*h**4 = 0.
-4, -1, 0
Let o = 31/24604 + 48681/418268. Let -o*x**2 - 12/17*x + 8/17*x**3 - 2/17*x**4 + 0 = 0. Calculate x.
-1, 0, 2, 3
Let j be (-1040)/(-66) + -12 + 22/(-6). Solve -2/11*n + j + 1/11*n**2 = 0 for n.
1
Let o be -5 - (98217/2183)/(-9) - 0. Let b = o - -8774/45843. Factor 8/21*j**3 + 2/21*j**2 + 0 - 2/7*j**4 - b*j.
-2*j*(j - 1)**2*(3*j + 2)/21
Let j(a) = -a**2 - 23*a + 15. Let x be j(-23). Suppose -8*p + 13*p - x = 0. Factor 1/7*d**p + 27/7 + 27/7*d + 9/7*d**2.
(d + 3)**3/7
Let w be 10562/(-7530) + 1 - 148/(-370). Let l = 6781/1506 + w. Solve 0*m + l*m**5 + m**3 + 0 + 0*m**2 + 11/2*m**4 = 0.
-1, -2/9, 0
Let x(b) be the second derivative of -b**7/315 - 11*b**6/225 + b**5/150 + 11*b**4/90 + 2*b - 457. Let x(g) = 0. Calculate g.
-11, -1, 0, 1
Let h be (26/(-2613))/(260/(-14205)). Let v = -11/134 + h. Determine m so that 6/13*m**3 + 2/13*m**4 - v*m + 2/13*m**2 - 4/13 = 0.
-2, -1, 1
Let o(d) be the first derivative of d**7/240 - 19*d**6/960 - d**5/80 + 53*d**2/2 + 47. Let x(r) be the second derivative of o(r). Factor x(b).
b**2*(b - 3)*(7*b + 2)/8
Let z(w) = -5*w**3 - 14*w**2 - 48*w - 35. Let v(n) = -4*n**3 - n**2 - n. Let a(s) = 4*v(s) - 4*z(s). Factor a(d).
4*(d + 1)*(d + 5)*(d + 7)
Find q, given that 18/5*q - 2/5*q**3 - 6/5*q**2 + 54/5 = 0.
-3, 3
Let x(c) be the first derivative of -c**6/21 - 2*c**5/7 - 5*c**4/14 + 10*c**3/21 + 6*c**2/7 - 1119. Find t such that x(t) = 0.
-3, -2, -1, 0, 1
Let s(n) = -26*n**3 + 98*n**2 - 68*n - 42. Let l(t) = t**3 - t**2 - 2*t - 1. Let b be ((-1)/6*6)/(2/(-2)). Let u(m) = b*s(m) + 6*l(m). Factor u(g).
-4*(g - 3)*(g - 2)*(5*g + 2)
Suppose -4*i + 8 = g, 43*i = 42*i + 4*g + 2. Let k(z) be the second derivative of 7*z + 1/120*z**5 + 0*z**3 + 0 + 0*z**i + 1/36*z**4. Factor k(p).
p**2*(p + 2)/6
Let l(h) be the second derivative of h**6/120 + h**5/4 + 25*h**4/8 + 61*h**3/3 - 142*h - 2. Let m(s) be the second derivative of l(s). Factor m(v).
3*(v + 5)**2
Let q(o) = 5*o**2 + o - 1. Let p be q(-1). Determine x, given that 50*x**p + 40*x**3 - 208*x - 93*x**3 + 64 + 49*x**2 = 0.
1/3, 8
Let v be 66 - (-33 + 99 + -20). Factor -8*f - 4/5*f**2 - v.
-4*(f + 5)**2/5
Find p such that -170/3*p**2 - 546 + 358*p - 2/3*p**3 = 0.
-91, 3
Let t be 0/4 + 10/2. Suppose -5*r = -2*l - 70, 4*r = -0*r + t*l + 73. Factor -z - 4*z**2 + 8 - r*z + 9*z.
-4*(z - 1)*(z + 2)
Factor -1612*s**3 - 10*s - 3*s**2 - 19*s**2 + 801*s**3 + 797*s**3 - 2*s**4.
-2*s*(s + 1)**2*(s + 5)
Let w be 12/(-110)*35/(-6)*312/1092. Factor 32/11*a**3 - 26/11 - w*a**4 - 84/11*a**2 + 80/11*a.
-2*(a - 13)*(a - 1)**3/11
Let o(m) = -m**3 + 1. Let n(y) = 164*y**2 - 1536*y + 4172. Let i(p) = -n(p) - 4*o(p). Factor i(l).
4*(l - 29)*(l - 6)**2
Let s(y) be the second derivative of 3*y**4 + 110*y**3/3 + 168*y**2 + 2323*y. Factor s(n).
4*(n + 3)*(9*n + 28)
Let g(o) be the third derivative of 2/3*o**4 + 29/30*o**6 - 27*o**2 + 0 + 0*o**3 - 8/5*o**5 + 0*o - 6/35*o**7. Factor g(y).
-4*y*(y - 2)*(y - 1)*(9*y - 2)
Let l(g) be the third derivative of -g**8/336 - g**7/42 - g**6/15 - g**5/15 + 6*g**2 + 57. Factor l(x).
-x**2*(x + 1)*(x + 2)**2
Let 594 + 815*a + 0*a**4 + a**4 + 185*a**2 - 67*a**3 - 53*a**3 + 122*a**3 - 37*a**3 = 0. What is a?
-2, -1, 11, 27
Let n be ((-16)/280*-5)/((-48)/(-70)). Let y(z) be the second derivative of 20*z + n*z**4 - 5/3*z**3 + 0 + 0*z**2. Find i, given that y(i) = 0.
0, 2
Let l = 4 + 3. Let o = 15648 - 15646. Factor 7*d + 25*d**2 - l*d**o + 15*d - 5 + 9.
2*(d + 1)*(9*d + 2)
Let h(k) be the third derivative of k**8/60480 - 13*k**7/3024 + 17*k**5/6 + 84*k**2. Let z(f) be the third derivative of h(f). Factor z(u).
u*(u - 65)/3
Let j = -362200/17 - -21306. Factor 6/17 - 10/17*p + 2/17*p**2 + j*p**3.
2*(p - 1)**2*(p + 3)/17
Let q(i) = -27*i - 20. Let o be q(-1). Let g be (o - 103/18) + (-2)/(-9). Determine y so that -g + 3*y - 3/2*y**2 = 0.
1
Let o(x) be the second derivative of -7 + 7*x + 5/4*x**2 - 1/5*x**5 + 3/4*x**4 - 4/3*x**3 + 1/60*x**6. Factor o(s).
(s - 5)*(s - 1)**3/2
What is u in 131*u + 439*u + 265*u**4 - 1715*u**2 + 334*u**3 - 25*u**5 - 1850*u**2 + 900 - 30*u + 1551*u**3 = 0?
-6, -2/5, 1, 15
Let u(n) be the second derivative of -186*n + 5/3*n**4 + 5*n**2 - 1/42*n**7 + 9/2*n**3 - 1/5*n**6 - 1/10*n**5 + 0. Suppose u(j) = 0. What is j?
-5, -1, 2
Factor -37*r**2 + 12892*r**3 + 2*r**5 - 96*r**4 - 6354*r**3 - 6372*r**3 + 10*r**4 - 45*r**2.
2*r**2*(r - 41)*(r - 1)**2
Suppose 121*j + 132 - 616 = 0. Let d(x) be the third derivative of 0*x**j + 0*x + 1/60*x**5 + 0 - 1/600*x**6 + 27*x**2 + 0*x**3. Factor d(s).
-s**2*(s - 5)/5
Let h(o) be the first derivative of -o**5 + 5*o**4 + 15*o**3 - 90*o**2 + 1450. Let h(y) = 0. Calculate y.
-3, 0, 3, 4
Suppose 4 = 4*w - 2*p, -5*w - p = -6*p. Let d(h) = h**3 + 35*h**2 - 241*h + 207. Let o be d(-41). Factor -3 + 19*k**o - 16*k**2 + 2 - w.
3*(k - 1)*(k + 1)
Suppose -97*b = 174 - 465. Let m(p) be the first derivative of -5/3*p**b - 7 + 35/2*p**2 + 0*p. Factor m(l).
-5*l*(l - 7)
Let r(n) be the second derivative of -13*n**6/24 + 2*n**5 + 5*n**4/6 + 59*n**2/2 - 3*n - 3. Let o(p) be the first derivative of r(p). Factor o(s).
-5*s*(s - 2)*(13*s + 2)
Let v(l) = 4*l + 102. Let c be v(-27). Let t be 18 + -19 + (-16)/c. Factor -5*q**3 + 5*q - t*q**2 + 5/3.
-5*(q - 1)*(q + 1)*(3*q + 1)/3
Let o = -3606/5 - -729. Let f be ((-915)/(-300) - 49/(-28))*(-6)/(-4). Factor o*c**3 + f*c**4 + 3/5*c + 0 + 18/5*c**2 + 12/5*c**5.
3*c*(c + 1)**2*(2*c + 1)**2/5
Factor -6556730207 - 25320*y**2 + 42740160*y - 4401104216 - 13090628937 + 5*y**3.
5*(y - 1688)**3
Let s be -1 + 354/(-4)*(-7)/441. Let h = s - -2/21. Let 1/2*w**4 + 0 + 0*w - 1/2*w**3 + h*w**5 - 1/2*w**2 = 0. Calculate w.
-1, 0, 1
Let k = -1367/966 - -215/138. Factor 13/7*o**3 - 62/7*o**2 + 128/7*o - k*o**4 - 96/7.
-(o - 4)**2*(o - 3)*(o - 2)/7
Let k = 1121 - 2014. Let y = k + 895. Factor 10/3*m**y + 16/3*m + 8/3 + 2/3*m**3.
2*(m + 1)*(m + 2)**2/3
Let r(p) be the second derivative of -110*p + 4*p**2 + 5/6*p**4 - 1/10*p**5 + 0 - 8/3*p**3. Factor r(x).
-2*(x - 2)**2*(x - 1)
Let p(x) be the first derivative of 2*x**5/5 + 2*x**4 + 4*x**3/3 - 4*x**2 - 6*x + 11902. Solve p(f) = 0 for f.
-3, -1, 1
Suppose -3 = 4*q - 3*a, -4*q + 2*a + 6940 - 6938 = 0. Solve 0 - 8*c + 1/2*c**3 + q*c**2 = 0 for c.
-8, 0, 2
Let r = -19963 - -19963. Solve -2/3*w**4 + 4/3*w**3 + r + 0*w + 2*w**2 = 0.
-1, 0, 3
Let s = 27 + -22. Factor 10*x**2 - 8*x**3 - 27*x**2 - x**5 + s*x**4 + 21*x**2.
-x**2*(x - 2)**2*(x - 1)
Let k(m) = m**4 - m**3 + 7*m. Let n(x) = 10*x**4 + 45*x**3 + 65*x**2 + 105*x. Let y(a) = 15*k(a) - n(a). Determine g, given that y(g) = 0.
-1, 0, 13
Let z(b) be the first derivative of -12 - 8/21*b**2 + 1/126*b**4 - 1/9*b**3 + 3*b. Let t(d) be the first derivative of z(d). Find k, given that t(k) = 0.
-1, 8
Let b(i) be the first derivative of -1/4*i**4 + 4/3*i**3 + 2*i - 5/2*i**2 - 57. Solve b(l) = 0 for l.
1, 2
Suppose p - 12 = -2*p + 5*a, 0 = p - 5*a - 4. Suppose f = 3*s - 10, 3*s = 2*f + s + p. Factor 15*b**3 - 10 + 35*b - 73*b**f + 65*b**2 - 32*b**2.
5*(b - 1)**2*(3*b - 2)
Let i = -27/1303 - 1107469/3909. Let z = -283 - i. Factor 3 - z*q**3 - 5*q + 7/3*q**2.
-(q - 3)**2*(q - 1)/3
Factor 31*x**4 - 62*x**4 + 428*x**3 - 2734575*x + 12679*x**2 + 5144250 - 1289*x**3 + 34*x**4 + 70256*x**2.
3*(x - 95)**3*(x - 2)
Let q be ((-24)/(-15))/((-6)/(-30)). Let l be 0/(q/(-2)) + 16/6. Factor -2/3*a**5 - 8/3*a**2 + 4/3*a**4 - l*a + 0 + 2*a**3.
-2*a*(a - 2)**2*(a + 1)**2/3
Solve 2*o**4 - 2*o**5 + 0*o**5 - 80*o - 293*o**2 + 151*o**2 + 150*o**2 + 28*o**3 - 64 = 0.
-2, -1, 2, 4
Let r(n) be the first derivative of -59 + 0*n + 9/4*n**4 + n**3 + 0*n**2. Factor r(d).
3*d**2*(3*d + 1)
Factor 4/3*j**4 - 88/3*j**3 + 0 + 88/3*j - 4/3*j**2.
4*j*(j - 22)*(j - 1)*(j + 1)/3
Let p = 108 - 105. Find k, given that 75*k**4 - 1396*k**5 + 1331*k**5 - 8*k**3 - 2*k**p = 0.
0, 2