*3 - 5*j**2 + 4*j + 8. Let g(d) = 4*r(d) + 3*s(d). Find h such that g(h) = 0.
-2, -1, 1, 2
Factor 5*b**3 - 25/4*b**2 - 5/4*b**4 + 5/2*b + 0.
-5*b*(b - 2)*(b - 1)**2/4
Let f = -3820/27 + 1274/9. Let j(u) be the first derivative of 12 + f*u**3 + 8/9*u + 5/9*u**2. What is k in j(k) = 0?
-4, -1
Suppose 0 = -31*l + 29*l + 14. Factor 12*v**3 - 5*v**5 + 2*v**5 - l*v**5 - 8*v**2 + 6*v**5.
-4*v**2*(v - 1)**2*(v + 2)
Let z = -952 + 958. Let c(n) be the third derivative of 1/96*n**4 + 1/120*n**5 + 0*n + 5*n**2 - 1/480*n**z + 0 - 1/12*n**3. Factor c(s).
-(s - 2)*(s - 1)*(s + 1)/4
Let n(a) be the first derivative of 2*a**6/75 - a**5/25 - a**4/3 - 2*a**3/5 - 4*a + 6. Let o(p) be the first derivative of n(p). Factor o(y).
4*y*(y - 3)*(y + 1)**2/5
Suppose -76*n**2 - 25*n**3 + 192*n**2 - 110*n**4 + 254*n**2 - 120*n + 207*n**4 - 112*n**4 = 0. What is n?
-6, 0, 1/3, 4
Let o(y) be the third derivative of 0*y + 0*y**3 + 0 - 1/30*y**4 + 1/2520*y**8 + 5*y**2 + 1/180*y**6 - 1/90*y**5 + 1/315*y**7. Suppose o(k) = 0. Calculate k.
-3, -2, -1, 0, 1
Let h = 196166/212485 + -2/16345. Factor 2/13*q**2 - 2/13*q - h.
2*(q - 3)*(q + 2)/13
Let t(y) = -y**4 + y**3. Let o(f) = -6*f**4 + 2*f**3 + 2*f**2 + 2*f. Let k(p) = o(p) - 4*t(p). Factor k(q).
-2*q*(q - 1)*(q + 1)**2
Let b(p) be the second derivative of 2*p**4/21 + 23*p**3/21 + 15*p**2/7 - 160*p. Factor b(v).
2*(v + 5)*(4*v + 3)/7
Find y, given that 0*y + 0*y**2 + 0 + 20/9*y**3 - 2/9*y**4 = 0.
0, 10
Let r = 2178 + -2176. Suppose 4/3*a + 0*a**r + 0 - 4/3*a**3 = 0. What is a?
-1, 0, 1
Let t be (27 - 18)/(72/16). Let -4/9*c + 2/3 - 2/9*c**t = 0. What is c?
-3, 1
Let a(q) be the first derivative of -q**6/1020 + q**4/68 - 2*q**3/51 + 21*q**2/2 + 12. Let h(v) be the second derivative of a(v). Factor h(z).
-2*(z - 1)**2*(z + 2)/17
Let v = -144 - -148. Factor -94*k + 94*k - 6*k**3 - 3*k**v.
-3*k**3*(k + 2)
Determine c so that -14 - 5/2*c + 1/4*c**2 = 0.
-4, 14
Let y(x) be the second derivative of -x**6/25 + 8*x**5/25 - 29*x**4/30 + 4*x**3/3 - 4*x**2/5 + 35*x + 2. Determine p so that y(p) = 0.
1/3, 1, 2
Let w(b) be the third derivative of -b**8/112 - 2*b**7/7 + 11*b**6/20 + b**5 - 21*b**4/8 + b**2 - 8. Suppose w(v) = 0. Calculate v.
-21, -1, 0, 1
Factor 406/3*c + 8/3*c**2 - 34.
2*(c + 51)*(4*c - 1)/3
Suppose 41*o = 32*o + 18. Solve -4/7*f**o + 12/7*f - 8/7 = 0 for f.
1, 2
Let u(a) = -6*a**2 + 6*a + 8. Let l(t) = -5*t**2 + 6*t + 8. Let o(g) = 4*l(g) - 3*u(g). Factor o(p).
-2*(p - 4)*(p + 1)
Suppose 0 = 4*m - 4, 5*m + 8 = 3*g + 4*m. Let v(t) be the second derivative of 1/2*t**2 - 7/24*t**4 + 0 - 5/12*t**g + 2*t. Factor v(d).
-(d + 1)*(7*d - 2)/2
Let q(j) be the third derivative of -j**5/90 - 19*j**4/36 - 17*j**2 + 2*j. Factor q(m).
-2*m*(m + 19)/3
Let u(c) be the first derivative of -3/4*c**3 - 2 - 1/120*c**5 + 1/8*c**4 + 2*c + 9/4*c**2. Let w(h) be the first derivative of u(h). Solve w(b) = 0.
3
Let w(k) be the second derivative of 0 + 1/3*k**4 + 1/10*k**5 - 1/3*k**3 - 2*k**2 + 9*k. Let w(d) = 0. What is d?
-2, -1, 1
Let m(b) = -6*b**3 - 9*b**2 + 3*b - 2. Let k be m(-2). Find l, given that 2/7*l - 8/7*l**2 + 2/7*l**5 + 4/7 + 4/7*l**k - 4/7*l**3 = 0.
-2, -1, 1
Let c(t) = -5*t**4 + 70*t**3 - 213*t**2 + 148*t - 4. Let f(u) = -135*u**4 + 1890*u**3 - 5750*u**2 + 3995*u - 110. Let l(o) = -55*c(o) + 2*f(o). Factor l(h).
5*h*(h - 10)*(h - 3)*(h - 1)
Let v(g) be the first derivative of 0*g**2 + 0*g + 1/8*g**4 + 1/6*g**3 - 2. What is b in v(b) = 0?
-1, 0
What is m in 0 - 76/5*m**3 - 232/15*m + 154/5*m**2 - 2/15*m**4 = 0?
-116, 0, 1
Let w = -529/30 - -108043/210. Let h = w - 496. What is l in 0 + 10/7*l**2 - h*l**5 - 4/7*l + 10/7*l**3 - 10/7*l**4 = 0?
-2, -1, 0, 1/3, 1
Let f be 1/(2*(-2)/(-16)). Find z, given that -4*z**3 - 2*z**2 + 2*z**5 - 1332*z**f - z**5 + 1334*z**4 + 3*z = 0.
-3, -1, 0, 1
Let q(o) = -31*o**2 - 112*o - 233. Let d(h) = 20*h**2 + 75*h + 155. Let l(v) = -8*d(v) - 5*q(v). Factor l(m).
-5*(m + 3)*(m + 5)
Let q be 69 + 2 + -3 + 4. Let p be ((-4)/6)/((-1)/q). Solve p*b - 4 - 46*b + b**2 + 5*b**2 = 0.
-1, 2/3
Let k(j) be the third derivative of j**8/70560 + j**5/10 - 3*j**2. Let h(a) be the third derivative of k(a). Factor h(o).
2*o**2/7
Let j = 109433/4650 - 1/1550. Let k = j + -61/3. Factor -32/5 - 2/5*z**2 - k*z.
-2*(z + 4)**2/5
Find x such that -54/13 + 2/13*x**2 - 4*x = 0.
-1, 27
Let h(t) = -4*t**3 - 7*t**2 - 7*t. Let p(r) = 7*r**3 + 13*r**2 + 13*r. Let n(s) = 11*h(s) + 6*p(s). Let l be n(0). Factor -2/9*z + 2/9*z**3 + l + 0*z**2.
2*z*(z - 1)*(z + 1)/9
Let d(y) be the first derivative of -36*y**5/5 + 3*y**4 - y**3/2 - 11*y**2 + 4. Let q(f) be the second derivative of d(f). Factor q(u).
-3*(12*u - 1)**2
Let m(s) be the first derivative of -35/3*s**3 - 5*s + 1 + 35/2*s**2 + 40/3*s**6 - 115/4*s**4 + 8*s**5. Solve m(g) = 0 for g.
-1, 1/4, 1
Let r be (500/1800)/((-4)/(-36)). Find p, given that -r*p**4 + p - 7/2*p**2 + 0 + 1/2*p**5 + 9/2*p**3 = 0.
0, 1, 2
Let w = -16936 - -135491/8. Factor 3/4*m**3 + 3/8*m**5 - 9/8*m + w + 3/4*m**2 - 9/8*m**4.
3*(m - 1)**4*(m + 1)/8
Let o be (11 - 1)*(0 + -1). Let m be (-8)/o + (-156)/270. Find k, given that m + 0*k - 4/9*k**2 + 2/9*k**4 + 0*k**3 = 0.
-1, 1
Factor -72*d + 432/7 + 75/7*d**2 - 3/7*d**3.
-3*(d - 12)**2*(d - 1)/7
Let y(z) be the first derivative of z**3 - 12*z**2 + 45*z + 315. Solve y(g) = 0 for g.
3, 5
Let z(u) be the first derivative of -15 - 1/18*u**6 + 1/15*u**5 + 1/3*u**3 + 5/12*u**4 + 0*u + 0*u**2. Let z(v) = 0. Calculate v.
-1, 0, 3
Let m be (1 + 2 + -2)*(3 + 14). Let t = 69/4 - m. Factor t*a - 1/2*a**3 - 1/2*a**2 + 1/4*a**5 + 1/4 + 1/4*a**4.
(a - 1)**2*(a + 1)**3/4
Let n(z) be the second derivative of 7*z**6/150 + 107*z**5/100 + 157*z**4/20 + 469*z**3/30 + 49*z**2/5 + 584*z. Factor n(s).
(s + 1)*(s + 7)**2*(7*s + 2)/5
Suppose -2*w = -w - 22. Suppose -w*m + 10 = -17*m. Let m*l - 6*l - 2*l**2 - l**2 - 3 - 2*l = 0. What is l?
-1
Let f(l) be the first derivative of -l**6/15 + 4*l**5/25 + 7*l**4/10 - 16*l**3/15 - 12*l**2/5 - 140. Find h such that f(h) = 0.
-2, -1, 0, 2, 3
Let c(n) be the second derivative of 0 - 9*n + 0*n**2 - 2/27*n**3 - 1/54*n**4. Find z, given that c(z) = 0.
-2, 0
Let q(u) be the first derivative of u**5/12 - 5*u**4/24 - 5*u**3/3 - 5*u**2/2 + 27. Let i(r) be the second derivative of q(r). Factor i(x).
5*(x - 2)*(x + 1)
Factor -1/7 + 62/7*g**2 + 61/7*g.
(g + 1)*(62*g - 1)/7
Let l(p) be the second derivative of 6 + 0*p**2 + p - 4/25*p**5 - 1/5*p**4 + 0*p**3. Factor l(n).
-4*n**2*(4*n + 3)/5
Let c(f) be the third derivative of f**5/600 + f**4/240 + 10*f**2 + 3. Solve c(g) = 0 for g.
-1, 0
Let m(j) be the second derivative of j**4/30 + 73*j**3/15 + 142*j**2/5 - 557*j. Find u, given that m(u) = 0.
-71, -2
Let y(p) be the second derivative of 2*p**6/5 + 9*p**5/5 - 15*p**4/4 + 2*p**3 - 3*p + 101. Factor y(u).
3*u*(u + 4)*(2*u - 1)**2
Suppose -6/11*w**2 - 54/11*w - 120/11 = 0. What is w?
-5, -4
Let i(b) be the second derivative of b**7/10080 + b**6/1440 - 19*b**4/6 - 14*b. Let v(k) be the third derivative of i(k). Find f, given that v(f) = 0.
-2, 0
Solve 5*m**2 + 2*m**2 - 2*m**2 - 379*m + 2434 + 11086 - 141*m = 0.
52
Let c = 177/139 - 13/556. Find b such that -c*b**2 + 0 - 45/4*b**4 + 0*b - 5*b**5 - 15/2*b**3 = 0.
-1, -1/4, 0
Determine i, given that -3*i**2 - 48/5*i - 1/5*i**3 + 64/5 = 0.
-8, 1
Factor -26*r**5 + 18*r**3 + 40*r - 26*r**5 + 47*r**5 + 11*r**2 + 25*r**4 - 48*r**3 - 31*r**2.
-5*r*(r - 2)**3*(r + 1)
Let m(w) be the third derivative of w**7/315 + 7*w**6/120 + 19*w**5/45 + 35*w**4/24 + 2*w**3 + 785*w**2. Let m(f) = 0. What is f?
-4, -3, -1/2
Find v, given that -8/7*v + 5/7*v**2 - 48/7 + 1/7*v**3 = 0.
-4, 3
Factor 30*m**3 - 11*m**4 + m**2 - 11*m**2 - 40*m + 2*m**5 + 27*m**4 + 2*m**2.
2*m*(m - 1)*(m + 2)**2*(m + 5)
Let p(y) be the first derivative of 5*y**6/6 + 13*y**5 + 105*y**4/2 + 290*y**3/3 + 185*y**2/2 + 45*y + 68. Let p(b) = 0. What is b?
-9, -1
Let j(l) be the third derivative of l**5/5 + 13*l**4/12 + 2*l**3/3 + l**2 - 11*l. Find k such that j(k) = 0.
-2, -1/6
Let c = -19 - -24. Factor 27*v**4 + 4*v**5 - 12*v**5 + 5*v**c - 81*v**3 + 81*v**2.
-3*v**2*(v - 3)**3
Let v = 152 + -147. Let x(u) be the third derivative of 0*u**4 + 1/150*u**v + 0 + 1/120*u**6 - 1/150*u**7 + 0*u**3 + 6*u**2 + 0*u. What is a in x(a) = 0?
-2/7, 0, 1
Let m be 10/(-27)*(-20 + 2716/140