erivative of -4*t**2 + 24 + 1/2*t**4 - 2/5*t**5 + 0*t + 8/3*t**3. Factor h(q).
-2*q*(q - 2)*(q - 1)*(q + 2)
Let t(b) be the first derivative of 5*b**6/9 + 26*b**5/5 + 12*b**4 - 32*b**3/9 + 585. Factor t(m).
2*m**2*(m + 4)**2*(5*m - 1)/3
Let p(j) be the second derivative of 0 - 2*j - 1/78*j**4 - 2/39*j**3 + 0*j**2. Factor p(c).
-2*c*(c + 2)/13
Let p(t) be the second derivative of t**4/12 - 3*t**3/2 - 4*t**2 - 18*t. Let y be p(10). Factor -1/6*c**y + 1/3*c + 0.
-c*(c - 2)/6
Let n(a) be the second derivative of -a**10/105840 + a**8/11760 - a**6/2520 + 3*a**4/2 + 15*a. Let q(k) be the third derivative of n(k). Factor q(b).
-2*b*(b - 1)**2*(b + 1)**2/7
Let n(y) be the first derivative of y**6/6 + 7*y**5/5 + 13*y**4/4 + y**3/3 - 7*y**2 - 8*y - 114. Suppose n(b) = 0. Calculate b.
-4, -2, -1, 1
Let l be (32 + -36)/(2/(-1)). Let y = -210 - -421/2. Factor 3/2 + y*w**l + 2*w.
(w + 1)*(w + 3)/2
Let p(z) be the first derivative of z**6/10 - 3*z**5/20 + 9*z + 12. Let n(t) be the first derivative of p(t). What is r in n(r) = 0?
0, 1
Let h(t) be the second derivative of -3/14*t**3 + 0*t**4 - 2*t + 0 + 3/140*t**5 + 3/7*t**2. Factor h(u).
3*(u - 1)**2*(u + 2)/7
Let x(v) be the first derivative of -v**4/16 + 3*v**3/2 - 81*v**2/8 - 15. What is a in x(a) = 0?
0, 9
Let k(u) be the third derivative of -u**6/360 - u**5/15 - 11*u**4/72 - 467*u**2. Factor k(b).
-b*(b + 1)*(b + 11)/3
Let k(f) be the second derivative of f**9/3780 - f**7/210 - f**6/90 + 13*f**4/12 - 12*f. Let q(l) be the third derivative of k(l). Let q(h) = 0. Calculate h.
-1, 0, 2
Factor -v - 1/2 - 1/2*v**2.
-(v + 1)**2/2
Let 73*d**2 + 3*d - 3*d**3 + 2*d**3 + 3*d - 76*d**2 - 2*d**3 = 0. Calculate d.
-2, 0, 1
Determine f, given that -12/17 + 4/17*f**2 - 10/17*f + 2/17*f**3 = 0.
-3, -1, 2
Solve 47/2*a**3 - 15/2*a**4 + 0*a + 1/2*a**5 - 33/2*a**2 + 0 = 0 for a.
0, 1, 3, 11
Let g be (-2 + 1)*0 + 38 + -35. Let n(b) be the second derivative of 0 + 3*b + 1/6*b**g - 1/20*b**5 + 0*b**2 + 0*b**4. Factor n(y).
-y*(y - 1)*(y + 1)
Let c(b) be the first derivative of -5*b**3/3 + 15*b**2/2 + 50*b + 74. Find p such that c(p) = 0.
-2, 5
Let m(d) be the second derivative of -d**6/12 + 19*d**5/24 + 35*d**4/36 + 106*d. Determine w, given that m(w) = 0.
-2/3, 0, 7
Let f(x) = x**3 + 4*x**2 + 2*x + 3 - 4*x + 5*x + 0*x**3. Let k be f(-3). Suppose -11*p**3 + 14*p**2 + 7*p**4 - 2*p**3 - 2*p - k*p**3 - 3*p**2 = 0. Calculate p.
0, 2/7, 1
Let 104*s**3 + 288*s**2 - 7*s + 287*s + 92 - 269*s**4 + 273*s**4 = 0. What is s?
-23, -1
Let n(p) be the second derivative of -p**7/63 - p**6/9 + 20*p**4/9 + 80*p**3/9 + 16*p**2 + 225*p. Suppose n(t) = 0. What is t?
-2, 3
Let h(j) be the second derivative of -121*j**5/10 - 88*j**4 - 60*j**3 - 16*j**2 + 156*j. Solve h(w) = 0.
-4, -2/11
Let k(w) = 3*w**2 + 7*w - 16. Suppose 6*c + 19 = -5. Let m be k(c). Suppose 3/4*x**3 + 0*x + 0 + 3/8*x**2 + 3/8*x**m = 0. Calculate x.
-1, 0
Let s(c) be the third derivative of c**8/112 - 3*c**7/5 + 81*c**6/40 - 2*c**5 - 88*c**2. Factor s(n).
3*n**2*(n - 40)*(n - 1)**2
Let g = 27 + -24. Factor -138*v**g + 2*v**4 - 4 + 136*v**3 - 6*v**2 + 2*v + 8*v.
2*(v - 1)**3*(v + 2)
Let -81792/5*r - 27/5*r**4 - 58764/5*r**2 + 2556/5*r**3 - 27648/5 = 0. What is r?
-2/3, 48
Let f(b) be the first derivative of 85*b**3/3 + 415*b**2/2 - 50*b - 122. Factor f(q).
5*(q + 5)*(17*q - 2)
Suppose -3*m**2 - 22*m**4 + 14*m**3 - 147*m - 8*m**5 + 69*m + 13*m**2 + 12*m**2 + 72*m = 0. What is m?
-3, -1, 0, 1/4, 1
Let a(g) be the third derivative of -g**7/350 + 3*g**5/100 - g**4/20 - 11*g**2 - g. Let a(k) = 0. What is k?
-2, 0, 1
Suppose 0 = -8*z + 10*z - 6. Suppose 5*n - 7 = 2*g, 4*g - z*g - n = 1. Determine b, given that g*b**2 - 2*b**2 - 81*b**5 + 3*b**3 + 80*b**5 = 0.
-1, 0, 2
Let o(c) be the third derivative of -1/220*c**6 + 0*c + 1/1155*c**7 + 0*c**3 + 0 + 1/110*c**5 - 8*c**2 - 1/132*c**4. Factor o(b).
2*b*(b - 1)**3/11
Suppose -2*w + 9 = -i, 2*w - 5*i - 5 = 16. Factor 2/13*c**2 + 0 - 2/13*c**4 + 0*c + 0*c**w.
-2*c**2*(c - 1)*(c + 1)/13
Let b be ((-345)/(-46))/(5/2). Find d such that -3/2*d + 0 - 21/4*d**2 + 27/4*d**b = 0.
-2/9, 0, 1
Solve 92 - 30*j**2 + 97 - 25*j**3 + 20*j - 5*j**4 - 149 = 0 for j.
-2, 1
Let u(s) be the third derivative of 0*s**6 + 1/420*s**7 + 0 + 1/12*s**3 - 2*s + 36*s**2 + 0*s**4 - 1/60*s**5. Factor u(p).
(p - 1)**2*(p + 1)**2/2
Let s(v) be the third derivative of -v**7/840 - v**6/160 + v**5/60 + v**4/8 + 74*v**2. Factor s(n).
-n*(n - 2)*(n + 2)*(n + 3)/4
Let g be 4/8*-1 - 42/(-12). Let q be 12/((-9)/g) - (-72)/8. Factor 12/7*w**3 + 0 + 8/7*w**2 - 16/7*w + 2/7*w**q - 10/7*w**4.
2*w*(w - 2)**3*(w + 1)/7
Let -96/5 + 1/5*b**4 - 6*b**2 - 3/5*b**3 + 128/5*b = 0. Calculate b.
-6, 1, 4
Suppose 719*k - 40 = 709*k. Let b(t) be the first derivative of 0*t**3 + 1/6*t**2 - 1/30*t**5 - k - 1/12*t**4 + 1/6*t. Factor b(h).
-(h - 1)*(h + 1)**3/6
Suppose s + 3*m = -3, 2*s = 5*m + 46 - 19. Let v(t) be the second derivative of -1/20*t**5 + 0*t**2 + 0 + 0*t**3 + 1/60*t**s + 1/24*t**4 + 3*t. Solve v(a) = 0.
0, 1
Factor 32/3 - 4/3*r**3 + 4/3*r**2 + 40/3*r.
-4*(r - 4)*(r + 1)*(r + 2)/3
Let l be ((-6)/14)/((-24)/(-8480)). Let v = 152 + l. Determine n so that 2/7*n**2 + 2/7*n**4 + v*n**3 + 0 + 0*n = 0.
-1, 0
Let t(r) be the second derivative of r**6/80 - 3*r**4/16 + r**3/2 - 5*r**2 - 20*r. Let y(g) be the first derivative of t(g). Determine v, given that y(v) = 0.
-2, 1
Let v(w) be the second derivative of -3*w**5/140 + 10*w**4/21 - 17*w**3/6 - 7*w**2 - 24*w. Determine c, given that v(c) = 0.
-2/3, 7
Let t be (20*4/10)/(-5 + 11). Solve -1/6*x**2 - t*x - 8/3 = 0 for x.
-4
Let z be 0 - -6 - -1 - (-26 - 49)/(-15). Determine a, given that z*a**5 - 22/3*a**4 + 8/3 + 6*a**3 + 14/3*a**2 - 8*a = 0.
-1, 2/3, 1, 2
Let m(g) = -g**2 - 7*g + 5. Let l be m(-7). Factor 3*u**l - 3*u**5 + 3*u**5 - 3*u**3 + 0*u**5.
3*u**3*(u - 1)*(u + 1)
Let n be 1/(-4) - 121/(-484). Suppose n - 3/5*b**5 + 3/5*b + 6/5*b**2 + 0*b**3 - 6/5*b**4 = 0. What is b?
-1, 0, 1
Let i(q) be the first derivative of q**5/5 + 7*q**4/4 + 5*q**3/3 - 7*q**2/2 - 6*q + 62. Let i(x) = 0. Calculate x.
-6, -1, 1
Suppose -39*a + 42 = -95 + 20. Factor 3/2*m**2 - 3/4*m**a - 6 + 3*m.
-3*(m - 2)**2*(m + 2)/4
Let k(z) = -z**2 + 13*z - 42. Let m be k(7). Let n(v) be the third derivative of m + 1/240*v**5 - 1/48*v**4 + 0*v**3 + 0*v + 6*v**2. Factor n(w).
w*(w - 2)/4
Factor -8 - 632/3*v + 110/3*v**2 + 106/3*v**3.
2*(v - 2)*(v + 3)*(53*v + 2)/3
Let k(g) be the second derivative of 3*g**5/5 - 110*g**4/9 + 232*g**3/3 - 48*g**2 + 10*g - 3. Factor k(z).
4*(z - 6)**2*(9*z - 2)/3
Suppose -6*c = -4*c + 16. Let b be (66/c)/((-12)/8 - 0). Determine j so that -b*j - 1 + 8*j**4 + 7/2*j**5 - 7*j**2 + 2*j**3 = 0.
-1, -2/7, 1
Factor 6/7*f**2 - 6/7 - 2/7*f + 2/7*f**3.
2*(f - 1)*(f + 1)*(f + 3)/7
Let n(x) be the second derivative of 7*x - 1/6*x**4 + x**2 - 1/42*x**7 - 1/2*x**3 + 1/5*x**5 + 0*x**6 + 0. Find s, given that n(s) = 0.
-2, -1, 1
Factor 1/3*g**3 - 52/3*g - 10/3*g**2 - 56/3.
(g - 14)*(g + 2)**2/3
Let a(d) be the third derivative of -d**7/2520 + d**6/270 - d**5/90 + 7*d**3/6 + 11*d**2. Let z(y) be the first derivative of a(y). Factor z(k).
-k*(k - 2)**2/3
Let 55 + 74*g**2 - 28*g**2 + 60*g - 41*g**2 = 0. Calculate g.
-11, -1
Suppose -14*b = -17*b + 9. Let f(x) = 1 + x + 1 + 2 - 3 + x**4 - x**2. Let o(j) = -4*j**4 + 3*j**2 - 3*j - 3. Let w(a) = b*f(a) + o(a). Let w(l) = 0. What is l?
0
Determine t, given that 5*t + 20*t**4 + 0*t**5 + t**5 - t**5 - 5*t**5 + 30 + 57*t**2 - 107*t**2 = 0.
-1, 1, 2, 3
Let a(k) = -k**2 + 17*k - 13. Let d(u) = u**2 + 4*u - 24. Let x be d(-7). Let g(z) = 16*z - 12. Let h(l) = x*g(l) + 4*a(l). Factor h(v).
-4*(v - 4)*(v - 1)
Let c(u) be the third derivative of u**9/5040 + 9*u**8/2240 + 9*u**7/280 + 9*u**6/80 - u**4/4 - 13*u**2. Let z(k) be the second derivative of c(k). Factor z(b).
3*b*(b + 3)**3
Let t(s) be the third derivative of -s**7/420 + s**6/30 - s**5/10 + s**2 + 327*s. Let t(a) = 0. Calculate a.
0, 2, 6
Let j = 852 - 852. Let z(w) be the third derivative of 7*w**2 + 0 + 1/8*w**4 + 3/10*w**6 - 3/10*w**5 + 3/112*w**8 - 1/7*w**7 + 0*w + j*w**3. Factor z(a).
3*a*(a - 1)**3*(3*a - 1)
Let b be -2*(-47)/70 + 4/(-28). Find o, given that -6/5*o + 6/5*o**3 - b*o**4 + 0 + 6/5*o**2 = 0.
-1, 0, 1
Let j(h) be the second derivative of -h**5/60 - h**4/