. Let s(a) = 3*c(a) + 4*k(a). Determine h so that s(h) = 0.
-3/26, 1
Let j = -379/825 - -26/55. Let t(w) be the third derivative of -1/300*w**6 + j*w**5 - 1/60*w**4 + 0*w**3 + 3*w**2 + 0 + 0*w. Factor t(g).
-2*g*(g - 1)**2/5
Let i(t) = t**3 + 5*t**2 - 2*t - 6. Let y be i(-5). Let 0*d**3 - 8*d + 0 + 20*d - y*d**3 - 8 = 0. What is d?
-2, 1
Factor -3/5*l**2 - 3/5 - 6/5*l.
-3*(l + 1)**2/5
Let t(k) be the second derivative of k**6/30 + 11*k**5/60 + 11*k**4/36 + k**3/18 - k**2/3 - 62*k - 1. Factor t(v).
(v + 1)**2*(v + 2)*(3*v - 1)/3
Let t(g) = -g**2 + 6*g + 3. Let w be t(6). Suppose 0*a - 2*a + 28 = -4*p, -5*a = 4*p. Factor x**3 - 5*x**2 + 8*x**2 + 15*x + 6 - a*x**w + 3.
-3*(x - 3)*(x + 1)**2
Factor -11 - 15 - 25*p - 55*p - 24*p**2 + 30*p**2 + 4*p.
2*(p - 13)*(3*p + 1)
Find j, given that 4*j**3 + j**3 - 5*j**3 + 34*j**2 + 62*j + 30 + 2*j**3 = 0.
-15, -1
Let b(l) be the first derivative of l**4 - 140*l**3 - 864*l**2 - 1744*l + 213. What is v in b(v) = 0?
-2, 109
Let b be ((-10)/4)/(-3*(-1)/24). Let n = 20 + b. Suppose n*s + 0 + 2/9*s**2 = 0. What is s?
0
Let v(o) = 4*o**3 + 4*o - 4*o**3 - 7*o**4 + 7 + o**3. Let i(m) be the first derivative of 3*m**5/5 - m**2 - 3*m - 5. Let c(w) = -5*i(w) - 2*v(w). Factor c(x).
-(x - 1)*(x + 1)**3
Factor 188/9*m - 176/9*m**2 - 40/9 + 28/9*m**3.
4*(m - 5)*(m - 1)*(7*m - 2)/9
Let f = 4 - -3. Let p be (-3 - f/(-3))*-3. Determine d, given that p + 0 + 2*d**2 - 5 + d**2 = 0.
-1, 1
Let v(s) be the first derivative of 21/2*s**2 + 6*s + 9/4*s**4 + 8*s**3 - 10. Find p such that v(p) = 0.
-1, -2/3
Let c(r) = -r**2 - 2*r. Let a(b) = b**2 + 5*b. Suppose -7*t + 25 = -10. Let q(m) = t*c(m) + 2*a(m). Suppose q(w) = 0. Calculate w.
0
Suppose w + 1 = -3*y, 6*w - 5*y - 3 = 7*w. Factor -2/11*d**w + 2/11*d + 0.
-2*d*(d - 1)/11
Let r = 531 - 531. Let h(f) be the second derivative of 0*f**3 + 7*f + r*f**2 + 1/130*f**5 + 1/195*f**6 - 1/39*f**4 + 0. Factor h(k).
2*k**2*(k - 1)*(k + 2)/13
Let h be ((-24)/(-30))/(2/5). Let p be 2 + -1 + h - -87. Factor 13 + 19*j - 76*j + p*j**2 - 7.
3*(2*j - 1)*(15*j - 2)
Factor -18/5*y**2 + 3/5*y**3 + 36/5 + 3*y.
3*(y - 4)*(y - 3)*(y + 1)/5
Suppose x = -t + 3*x - 4, 4*x - 32 = -4*t. Let -b**5 - 88*b**2 - 2*b**t + 144*b + 16*b**3 - b**4 + 1 + 6*b**4 - 81 = 0. Calculate b.
-5, 2
Let j(m) be the third derivative of -m**5/690 + 7*m**4/92 - 18*m**3/23 + 373*m**2. Determine s so that j(s) = 0.
3, 18
Let k(j) = -2*j. Let f be k(-3). Let s(i) be the third derivative of 0 + 2*i**2 + 1/40*i**f + 0*i - 1/8*i**4 - 1/10*i**5 + i**3. Factor s(o).
3*(o - 2)*(o - 1)*(o + 1)
Let d(v) be the third derivative of v**5/100 + 59*v**4/40 + 29*v**3/5 + 98*v**2 - 2*v. What is a in d(a) = 0?
-58, -1
Suppose 12*t - 65 = -17. Let k(d) be the third derivative of 1/100*d**5 - 2*d**2 + 0*d + 3/40*d**t + 1/5*d**3 + 0. Factor k(p).
3*(p + 1)*(p + 2)/5
Let h = -197/36 + 103/18. Let m(v) be the first derivative of -5 + 1/4*v + 1/2*v**2 - 1/12*v**3 - h*v**4. Factor m(d).
-(d - 1)*(d + 1)*(4*d + 1)/4
Let i(v) be the second derivative of 2*v**6/15 - 6*v**5/5 + 8*v**4/3 + 4*v**3 - 18*v**2 + 103*v. Determine w so that i(w) = 0.
-1, 1, 3
Let h(k) = -11. Let d(i) = 5. Let n(y) = 13*d(y) + 6*h(y). Let j(q) = -q**2 - q + 6. Let a(m) = 5*j(m) + 30*n(m). Let a(f) = 0. Calculate f.
-1, 0
Suppose -2*b + 3*b = 3*x - 37, 4*b = x - 5. Let v = x + -10. Factor 2*s**2 - v*s**2 + 3*s**4 - 2*s**2 + 0*s**4.
3*s**2*(s - 1)*(s + 1)
Suppose 0*k + 0 + k**3 - 5/4*k**2 + 1/4*k**4 = 0. Calculate k.
-5, 0, 1
Let r(c) be the second derivative of c**6/15 - c**5 + 4*c**4/3 + 10*c**3/3 - 9*c**2 + 215*c. Factor r(b).
2*(b - 9)*(b - 1)**2*(b + 1)
Suppose 1590*j - 126*j**2 - 8232 + 174*j + 3*j**3 + 0*j**3 = 0. Calculate j.
14
Factor 10836/13*n**2 + 148176/13 - 158760/13*n + 2/13*n**4 - 254/13*n**3.
2*(n - 42)**3*(n - 1)/13
Let g = -89 - -91. Factor -1367*q**g + 30 + 1362*q**2 - 10 + 15*q.
-5*(q - 4)*(q + 1)
Suppose 2*v**3 + 15*v - 1 - 4*v**4 + 5*v**3 + 5*v**2 - 18*v - v**3 - 3*v**3 = 0. What is v?
-1, -1/4, 1
Let k(y) be the second derivative of -9/5*y**2 + 11/20*y**4 + 31/10*y**3 + 0 + 36*y. Suppose k(q) = 0. Calculate q.
-3, 2/11
Suppose 6*h = 9*h - 33. Suppose h = 2*d + 1. Let 14/9*k**2 - 4/9*k + 10/9*k**4 - 2*k**3 + 0 - 2/9*k**d = 0. What is k?
0, 1, 2
Let o(s) be the second derivative of s**8/20160 - s**6/720 + s**5/180 - 7*s**4/3 + 3*s. Let i(w) be the third derivative of o(w). Solve i(a) = 0.
-2, 1
Let y = -622/19 + 4962/133. Determine g so that 16/7 + y*g + 12/7*g**2 = 0.
-2, -2/3
Let j(z) be the third derivative of -z**8/2688 + z**7/280 - 51*z**2. Let j(l) = 0. What is l?
0, 6
Let c = -94/55 - -138/55. Determine g, given that 0 + 8/5*g + c*g**2 = 0.
-2, 0
Let h(q) be the second derivative of -3*q**7/14 - 11*q**6/5 - 17*q**5/16 - 7*q**4/48 + 247*q + 1. Determine m so that h(m) = 0.
-7, -1/6, 0
Let b(n) be the second derivative of -1/6*n**6 + 0*n**4 + 43*n - 1/2*n**5 + 5/2*n**2 + 5/3*n**3 + 0. What is h in b(h) = 0?
-1, 1
Let -2*t**3 + 0*t - 38*t**2 + 87*t**2 - 2*t - 45*t**2 = 0. Calculate t.
0, 1
Let k be 16/3 + (-7)/21. Suppose -2*o = k*h - 35 - 1, -h - 4 = -o. Factor -16*a**2 - 2*a**4 + 8 - 8 - o*a - 10*a**3.
-2*a*(a + 1)*(a + 2)**2
Let i be ((-11)/11 - -2)/((-1)/(-2)). Let v be (-172)/645 + i/3. Factor -v*p**4 - 8/5*p - 2/5 - 12/5*p**2 - 8/5*p**3.
-2*(p + 1)**4/5
Let b = -6/1615 - -3418/4845. Let t = -2/57 + b. Suppose -1/3 - 1/3*d**2 - t*d = 0. Calculate d.
-1
Let f(v) be the first derivative of -v**4/4 - 11*v**3/3 - 6*v**2 - 18*v - 41. Let q be f(-10). Solve -1/4 + 0*m + 1/4*m**q = 0.
-1, 1
Let a(r) be the first derivative of r**3/15 + 3*r**2/5 + r - 91. Factor a(t).
(t + 1)*(t + 5)/5
Let m(y) be the first derivative of y**4/12 + 4*y**3/9 - 19*y**2/6 + 14*y/3 - 276. Factor m(k).
(k - 2)*(k - 1)*(k + 7)/3
Suppose k + 5*b = 139, -2*k + 3*k - 2*b - 118 = 0. Let r = k + -124. Factor r + 2/7*g**2 + 2/7*g**3 + 0*g.
2*g**2*(g + 1)/7
Factor 5*p**4 + 4620*p + 26*p**3 + 3002*p**2 - 9*p**3 + 517 - 2*p**4 + 168*p**3 + 1283.
(p + 1)*(p + 30)**2*(3*p + 2)
Suppose 6*p - 15 = 11*p. Let s be p/12 + 81/36. Determine n, given that 0 - 7/3*n**s + n**3 + 2/3*n - 4/3*n**5 + 8/3*n**4 = 0.
-1, 0, 1/2, 2
Let b(s) be the third derivative of -s**8/1050 - s**7/700 + s**6/900 + 49*s**3/6 - 4*s**2 - 2*s. Let c(a) be the first derivative of b(a). Factor c(k).
-2*k**2*(k + 1)*(4*k - 1)/5
Let j(o) = -7*o**2 + 9*o + 10. Suppose 5*z + 7 = 32. Let f(t) = 6*t**2 - 8*t - 9. Let d(h) = z*j(h) + 6*f(h). Factor d(m).
(m - 4)*(m + 1)
Let u(v) be the second derivative of 3*v**5 - 47*v**4/3 - 36*v**3 + 16*v**2 - v + 262. Factor u(b).
4*(b - 4)*(b + 1)*(15*b - 2)
Let q(i) be the first derivative of -4*i**3/9 - 86*i**2/3 - 56*i + 813. Factor q(k).
-4*(k + 1)*(k + 42)/3
Find p such that 0*p + 1/3*p**5 + 1/3*p**4 + 20/3*p**2 - 16/3*p**3 + 0 = 0.
-5, 0, 2
Let y(w) be the third derivative of 2*w**7/735 - 2*w**5/35 - 4*w**4/21 - 2*w**3/7 - 99*w**2. Suppose y(v) = 0. Calculate v.
-1, 3
Let r(x) be the third derivative of x**5/140 - 19*x**4/56 - 40*x**2. Factor r(g).
3*g*(g - 19)/7
Suppose -7*k = -10*k + k. Let i(b) be the second derivative of k - 7/48*b**4 - 1/16*b**5 - b + 1/30*b**6 + 0*b**2 + 1/12*b**3. Factor i(d).
d*(d - 2)*(d + 1)*(4*d - 1)/4
Suppose -1 = -5*q + 4. Let p(g) = -g**2 - 1. Let r(y) = -y**3 - y - 2. Let d(c) = q*r(c) - 2*p(c). Factor d(i).
-i*(i - 1)**2
Suppose 4*p - 20 = -p. Let v be 9/4 - 1/4. Factor h**2 - p*h**v + 2*h + 2*h**2.
-h*(h - 2)
Let o(d) be the third derivative of -d**5/330 + 13*d**4/132 - 4*d**3/11 - 82*d**2. Factor o(a).
-2*(a - 12)*(a - 1)/11
Let p = 1286 - 1283. Let m(n) be the second derivative of -7*n - 1/6*n**4 + 0 - 1/10*n**5 + 1/15*n**6 + 0*n**2 + 1/3*n**p. Factor m(q).
2*q*(q - 1)**2*(q + 1)
Let s(c) = -3*c**2 - 14*c + 4. Let q be s(-6). Let v be (q/16)/(-5)*4. Suppose 1/3*y**2 + 4/3*y + v = 0. What is y?
-3, -1
Let l(i) = -2*i**2 - 18*i + 143. Let a be l(-14). Let r(m) be the first derivative of 1/10*m**4 - 4/5*m + 0*m**a + 6 - 3/5*m**2. Factor r(d).
2*(d - 2)*(d + 1)**2/5
Let i(g) be the third derivative of -g**5/20 + 57*g**4/8 + 59*g**3 - 159*g**2 + 1. Factor i(h).
-3*(h - 59)*(h + 2)
Let h be 270/135 - 16*2/22. Factor 2/11*c**2 + 4/11 + h*c.
2*(c + 1)*(c + 2)/11
Suppose -2*a = k - 16, -a + 23 = -k + 3*k. Suppose -11*n + k*n + 3 = 0. Factor 1/2*m - 3/2*m**2 + 0 - 1/2*