a(p) be the first derivative of -p**6/15 + 2*p**5/5 - p**4/2 - 4*p - 5. Let b(r) be the first derivative of a(r). Suppose b(k) = 0. Calculate k.
0, 1, 3
Suppose 32*f - 37*f = 85. Let s = f + 35/2. Determine m so that 1/2*m**2 - 1/2*m**3 - 1/2 + s*m = 0.
-1, 1
Suppose -5*q + 139*o - 134*o = 0, 0 = 2*o - 8. Factor 9/8*a**q + 0 + 15/8*a**2 + 3/8*a**5 + 0*a - 27/8*a**3.
3*a**2*(a - 1)**2*(a + 5)/8
Let v(h) be the third derivative of 1/24*h**4 + 0*h + 1/420*h**7 + 0*h**6 + 0*h**3 + 0 - 1/40*h**5 + 7*h**2. Factor v(q).
q*(q - 1)**2*(q + 2)/2
Let k(b) be the second derivative of -b**4/78 + 5*b**3/13 + 34*b**2/13 + 53*b - 2. Factor k(h).
-2*(h - 17)*(h + 2)/13
Let a(n) = -n**3 - n. Let i(z) = 3*z**4 - 3*z**3 + 18*z**2 - 3*z + 3. Let c be (-14)/35 + (-77)/(-5). Let k(u) = c*a(u) - i(u). Let k(w) = 0. Calculate w.
-1
Let b(d) be the third derivative of -d**5/120 + 5*d**4/24 - 3*d**3/4 - 70*d**2. Find q such that b(q) = 0.
1, 9
Solve -864 + 48*a - 2/3*a**2 = 0 for a.
36
Let z = -636 + 636. Let l(f) be the second derivative of 0 - 1/2*f**3 + z*f**2 + 1/12*f**4 + 6*f. Factor l(u).
u*(u - 3)
Let w(t) = -54*t**5 + 120*t**4 + 366*t**3 - 282*t**2 - 195*t + 72. Let s(u) = -u**5 - 2*u**4 + u**3 - u. Let j(i) = -9*s(i) - w(i). Let j(a) = 0. What is a?
-2, -2/3, 2/7, 1, 3
Let z(m) be the third derivative of 33/160*m**6 + 3/8*m**4 - 23/40*m**5 - m**2 + m**3 - 1/40*m**7 + 0*m + 0. Let z(d) = 0. Calculate d.
-2/7, 1, 2
Let o(z) be the third derivative of -z**7/210 + 7*z**5/60 - z**4/4 + 10*z**2 - 7*z. Let o(t) = 0. Calculate t.
-3, 0, 1, 2
Let h(r) = -8*r**3 - 9*r**2 - 79*r - 44. Let v(t) = -3*t**3 - 3*t**2 - 27*t - 15. Let g(k) = -6*h(k) + 17*v(k). Find l such that g(l) = 0.
-1, 3
Let a(t) = t**2 + 5*t - 3. Let r be a(-6). Determine d, given that -10*d**5 + 12*d**3 + 16*d**4 - 12*d - 55*d**2 - 70*d**4 - 102*d**r - 3*d**2 = 0.
-3, -1, -2/5, 0
Let u be (1 + -3)/((-18)/(-81)). Let r(h) = -h**3 - 8*h**2 + 10*h + 12. Let d be r(u). Factor 8*g**5 - 18*g**5 - 11*g**5 - 3*g**4 - d*g**4.
-3*g**4*(7*g + 2)
Let t(v) be the third derivative of v**6/60 + v**5/30 - 4*v**4/3 + 20*v**3/3 - 192*v**2. Factor t(o).
2*(o - 2)**2*(o + 5)
Let y = 11240/8439 + 4/2813. Find k such that 0*k - 16/3*k**4 - 8/3*k**2 + y*k**5 + 20/3*k**3 + 0 = 0.
0, 1, 2
Let w(o) = -6*o**3 + 13*o**2 - 9. Let t(q) = -3*q**3 + 6*q**2 - 4. Let d be (4/(-5))/(84/20 - 4). Let s(x) = d*w(x) + 9*t(x). Suppose s(k) = 0. Calculate k.
0, 2/3
Let p(t) = -t**4 - 5*t**2 - 6*t + 2. Let i(a) = -4*a**4 - a**3 - 16*a**2 - 19*a + 5. Let l(o) = -2*i(o) + 7*p(o). Suppose l(b) = 0. What is b?
-2, 1
Let j(x) = x**2 + x + 4. Let b be j(0). Let y(w) be the second derivative of 0 - 1/3*w**b + 4/3*w**3 + 0*w**2 - 7*w. Let y(t) = 0. What is t?
0, 2
What is l in 10/13*l**2 - 60/13 - 146/13*l = 0?
-2/5, 15
Determine s, given that 56/5*s + 406/15*s**2 + 92/5*s**3 + 26/5*s**4 + 8/15*s**5 - 24/5 = 0.
-3, -2, 1/4
Let p(d) be the second derivative of -d**8/420 - 2*d**7/525 + d**6/75 - 24*d**2 + 35*d. Let q(s) be the first derivative of p(s). Suppose q(z) = 0. What is z?
-2, 0, 1
Let k be ((-26)/28 - -1)*2. Let b(t) be the first derivative of -8 - 1/28*t**4 + 0*t - 1/7*t**2 + k*t**3. Find l such that b(l) = 0.
0, 1, 2
Let p = 108 - 107. Let f be p - ((-16)/(-24))/(4/6). Determine l so that -2/7*l**4 + f + 6/7*l**3 - 2/7*l**5 - 4/7*l + 2/7*l**2 = 0.
-2, -1, 0, 1
Let f be (0 - 0)/(63/(-21)). Let m be ((-4)/(-5))/((-84)/(-70)). Factor f*a + m - 2/3*a**2.
-2*(a - 1)*(a + 1)/3
Let v(m) be the first derivative of -m**4/10 + 142*m**3/5 - 11448*m**2/5 + 22472*m/5 - 630. Find n, given that v(n) = 0.
1, 106
Let o(c) = 7*c + 9. Let p be o(-1). Let k(l) be the third derivative of 1/45*l**5 + 1/60*l**6 + 2/9*l**3 + 0*l - 4*l**p - 7/36*l**4 + 0. Factor k(v).
2*(v - 1)*(v + 2)*(3*v - 1)/3
Let j(q) = -2*q**2 + 203*q - 1991. Let v(s) = s**2 + s + 3. Let k(t) = -j(t) + 3*v(t). Solve k(i) = 0 for i.
20
Let -83901*h**2 + 4*h**5 + 170774*h**3 - 1460*h**4 - 39754*h**3 + 135424 + 485761*h**2 + 252863*h + 151937*h = 0. What is h?
-1, 184
Let x(p) be the third derivative of 9*p**2 + 0*p**5 + 0*p + 0 + 1/480*p**6 - 1/96*p**4 + 0*p**3. Factor x(w).
w*(w - 1)*(w + 1)/4
Let i(v) be the second derivative of -v**6/180 + 13*v**4/72 - 3*v**2 + 27*v. Determine y, given that i(y) = 0.
-3, -2, 2, 3
Let q(d) = 4*d**2 - 252*d - 253. Let t be q(64). Let -2/21*z**4 - 10/7*z**2 - 6/7*z - 2/3*z**t + 0 = 0. What is z?
-3, -1, 0
Let l = 79/98 - 15/49. Let k(p) be the third derivative of l*p**4 + 0 + 1/30*p**6 + 6*p**2 + 1/5*p**5 + 0*p + 2/3*p**3. Find d such that k(d) = 0.
-1
Let a = 43 - 34. Let u(j) = -5*j**4 + 2*j**2 + 8*j + 7. Let r(n) = 11*n**4 - 3*n**2 - 16*n - 15. Let v(h) = a*u(h) + 4*r(h). Factor v(x).
-(x - 3)*(x + 1)**3
Suppose -4*f = -3*a + 2*a + 60, -f - 2*a = 15. Let r be ((-22)/55)/(16/f). Find n such that r*n - 9/8 + 1/8*n**3 + 5/8*n**2 = 0.
-3, 1
Let k = -38394 - -191978/5. Determine l so that k - 4/5*l**2 + 14/5*l = 0.
-1/2, 4
Factor 0 - 75/4*p + 3/4*p**2.
3*p*(p - 25)/4
Let f(v) = 23*v**5 + 15*v**4 - 71*v**3 + 7*v**2 + 48*v - 13. Let n(c) = -c**5 - c**4 + c**3 - c**2 - 1. Let m(d) = -f(d) - 3*n(d). Find s such that m(s) = 0.
-2, -1, 2/5, 1
Let p(g) be the first derivative of -2/33*g**3 - 12/11*g + 5/11*g**2 - 9. Factor p(z).
-2*(z - 3)*(z - 2)/11
Let y be (-2755)/(-855) + (0 - 3 - 0). Let r(s) be the first derivative of 2*s**2 - y*s**3 + 1 - 6*s. Find h such that r(h) = 0.
3
Let h(o) be the third derivative of -o**6/1080 + 2*o**5/45 - 5*o**4/24 + 9*o**3/2 + 7*o**2 + 2. Let j(n) be the first derivative of h(n). Factor j(x).
-(x - 15)*(x - 1)/3
Let f(i) be the first derivative of 0*i + 0*i**2 - 16 - 1/6*i**3. Let f(w) = 0. What is w?
0
Let f(j) = -31*j**2 - 212*j + 37. Let u be f(-7). Factor -2/3 - 17/3*p**u - 19/3*p.
-(p + 1)*(17*p + 2)/3
Let m(b) be the third derivative of b**6/60 + 19*b**5/150 + 11*b**4/60 - b**3/5 - 281*b**2. Find y, given that m(y) = 0.
-3, -1, 1/5
Let y = 6 + -2. Determine j so that 7 - 20*j - 11*j**2 + 4*j**y + 4*j**3 - 15 - j**2 = 0.
-1, 2
Suppose -4*k = -3*k - 4. Let l(g) be the second derivative of 4/15*g**3 + 4/15*g**2 + 1/9*g**6 - 1/5*g**5 + 11*g - 11/90*g**k + 0. Suppose l(o) = 0. What is o?
-2/5, 1
Factor -2/5*g**2 + 0 + 56/5*g.
-2*g*(g - 28)/5
Let q(f) = 23*f - 90. Let h be q(4). Let k(g) be the second derivative of 0*g**h - 1/21*g**7 + 0*g**3 + 0 - 2/15*g**6 + 0*g**4 - 6*g - 1/10*g**5. Factor k(l).
-2*l**3*(l + 1)**2
Let g(w) be the first derivative of 5*w**6/6 + 17*w**5/5 + 4*w**4 + 4*w**3/3 + 91. Factor g(c).
c**2*(c + 1)*(c + 2)*(5*c + 2)
Let a be -392 + -1 + 0 + (-2)/1. Let i = a - -2773/7. Factor 0*z**2 - 2/7*z**4 + 32/7 + 32/7*z - i*z**3.
-2*(z - 2)*(z + 2)**3/7
Let u(m) be the first derivative of -m**6/2 + 12*m**5/5 + 9*m**4/2 - 4*m**3 - 15*m**2/2 - 49. Suppose u(z) = 0. What is z?
-1, 0, 1, 5
Let p(q) = -q**4 + 3*q**2 - 1. Let v(i) = -18*i**5 + 144*i**4 + 856*i**3 + 918*i**2 + 288*i + 6. Let r(k) = -6*p(k) - v(k). Solve r(d) = 0 for d.
-3, -2/3, 0, 12
Factor 0 + 0*k + 34/7*k**3 - 30/7*k**4 - 4/7*k**2.
-2*k**2*(k - 1)*(15*k - 2)/7
Let v(n) be the first derivative of -n**3/12 + 253*n**2/4 - 64009*n/4 + 125. Solve v(x) = 0 for x.
253
Solve 75/2 - 3/2*c**2 + 36*c = 0.
-1, 25
Let a(k) be the third derivative of -k**7/13860 - k**6/396 - 5*k**5/132 + k**4/6 - 3*k**2. Let f(c) be the second derivative of a(c). Solve f(m) = 0 for m.
-5
Let l(f) be the third derivative of -f**8/168 + 2*f**7/105 - 146*f**2. Factor l(x).
-2*x**4*(x - 2)
Let f be ((-11)/(308/32))/((-45)/63). Let 4/5 - 1/5*w**5 - 7/5*w**3 + 1/5*w**2 + f*w - w**4 = 0. Calculate w.
-2, -1, 1
Let p(u) be the third derivative of 0 - 1/15*u**5 + 0*u**3 + 0*u**6 + 1/168*u**8 - 1/12*u**4 + 2/105*u**7 + 0*u - 10*u**2. Find z such that p(z) = 0.
-1, 0, 1
Find p such that 0*p**2 - 2/7*p + 0 + 0*p**4 - 2/7*p**5 + 4/7*p**3 = 0.
-1, 0, 1
Let w(p) = 2*p**2 + 8*p. Suppose b + 85 = 6*b. Let v(n) = -6*n**2 - 23*n. Suppose -4*o + 15*o = 66. Let r(m) = b*w(m) + o*v(m). Suppose r(s) = 0. Calculate s.
-1, 0
Factor 2/3*p**2 + 2/3 + 4/3*p.
2*(p + 1)**2/3
Factor 10/3*b + 1/3*b**2 + 4 - 1/6*b**3.
-(b - 6)*(b + 2)**2/6
Let z(x) = -x**2 - 5*x. Let m(j) = 2*j**2 + 14*j. Suppose 0 = 4*p - 4 + 32. Let t = p + -1. Let u(v) = t*z(v) - 3*m(v). Factor u(d).
2*d*(d - 1)
Let q(y) = y**2 - 10*y - 19. Let n be 