- 2/63*b**7 + 0*b**5 + 0*b**2 - 8*b. Factor k(s).
-4*s*(s - 1)**3*(s + 1)/3
Let i(m) be the second derivative of -m**5/40 - 3*m**4/8 - 7*m**3/6 + 6*m**2 + 126*m. Let i(h) = 0. What is h?
-6, -4, 1
Suppose 3*l + 2*f + 1 = 0, 34 - 14 = 5*l - f. Factor -4/9*i**2 - 2/9*i**4 + 0*i + 0 + 2/3*i**l.
-2*i**2*(i - 2)*(i - 1)/9
Let n(w) be the third derivative of -1/300*w**6 + 0 + 0*w**3 + 0*w + 8/75*w**5 - 16/15*w**4 - 28*w**2. Solve n(f) = 0.
0, 8
Let p(m) be the second derivative of m**4/12 + 20*m**3/3 + 200*m**2 - m + 10. Factor p(u).
(u + 20)**2
Let a(l) = -10*l**3 + 268*l**2 + 498*l + 212. Let i(q) = -3*q**3 + 89*q**2 + 166*q + 71. Let u(f) = -3*a(f) + 8*i(f). Let u(d) = 0. What is d?
-1, -2/3, 17
Let d(k) be the third derivative of -k**5/240 + 3*k**3/8 - 169*k**2. Suppose d(u) = 0. Calculate u.
-3, 3
Suppose -3/7*w**3 - 9/7*w - 15/7*w**2 + 0 + 3/7*w**4 = 0. Calculate w.
-1, 0, 3
Let l(p) be the third derivative of -p**7/630 + p**6/40 - 3*p**5/20 + 3*p**4/8 - 57*p**2. Factor l(x).
-x*(x - 3)**3/3
Let m(d) be the second derivative of d**4/3 + 284*d**3/3 + 282*d**2 - 210*d. Determine q, given that m(q) = 0.
-141, -1
Let d(v) be the first derivative of -4*v**3/9 + 8*v**2/3 + 28*v + 28. Factor d(q).
-4*(q - 7)*(q + 3)/3
Suppose i = -3*u + 18, 5*i + 16*u - 14*u = 25. Let n be 1 + (-38)/(-14) - 2. Factor 0*b - 10/7*b**4 - n*b**i - 2/7*b**2 + 0.
-2*b**2*(b + 1)*(5*b + 1)/7
Let w(v) = v**2 - 7*v + 2. Suppose -10*z + 42 = -28. Let f be w(z). Factor 50/3*p**3 + 2/3 - 6*p + 10*p**f.
2*(p + 1)*(5*p - 1)**2/3
Let s(w) = w**2 + 10*w + 15. Let t be s(-12). Let a = t + -36. Suppose -12*f**4 + 10*f**2 + 10*f**a + 3*f**5 - 3*f**4 - 1 + 2*f**5 - 15*f + 6 = 0. Calculate f.
-1, 1
Suppose 12 = 3*p - 2*q, p - 4 - 4 = 2*q. Let i(d) be the first derivative of 5 + 1/25*d**5 + 1/5*d**4 + 1/5*d + 2/5*d**p + 2/5*d**3. Factor i(k).
(k + 1)**4/5
Let v(n) be the first derivative of 4/27*n**3 + 25 + 1/3*n**2 + 1/45*n**5 - 1/6*n**4 - 5/9*n. Suppose v(z) = 0. What is z?
-1, 1, 5
Suppose a = 2*z + 3*z + 29, 4*a + 3*z = 1. Solve a*w**2 + 90*w**4 - 126*w**4 + 28*w**5 - 76*w**3 + 40*w**2 - 16 + 8*w**2 + 48*w = 0 for w.
-1, 2/7, 1, 2
Find j such that 1 + 11 - 12 + j**4 - 64*j**3 + j**4 - 66*j**2 = 0.
-1, 0, 33
Let d(m) = -12*m**2 - 608*m + 6920. Let i(h) = 7*h**2 + 404*h - 4613. Let y(z) = 5*d(z) + 8*i(z). Factor y(v).
-4*(v - 24)**2
Solve 32/7 + 2/7*k**4 - 18/7*k**3 + 8*k**2 - 72/7*k = 0 for k.
1, 2, 4
Let o(q) be the second derivative of q**7/231 - 2*q**6/15 + 11*q**5/10 + 147*q. Factor o(x).
2*x**3*(x - 11)**2/11
Let z(s) be the first derivative of -s**7/280 - 7*s**6/480 + s**5/40 - 15*s**2 - 41. Let f(b) be the second derivative of z(b). Factor f(j).
-j**2*(j + 3)*(3*j - 2)/4
Suppose o = -4*j + 28, 0 = 2*o + 4*j - 79 + 31. Suppose -107*l**4 + 4*l**5 - 15*l**3 + l**5 - 20*l**2 + 117*l**4 + o*l = 0. Calculate l.
-2, 0, 1
Let p(k) be the third derivative of -k**5/10 + 25*k**4/24 - 2*k**3/3 - 2*k**2 + 30*k. Let p(s) = 0. What is s?
1/6, 4
Let m be -1*6*(140/(-30) + 4) + 0. Find u such that -19/2*u**2 + 13/2*u**3 - 3/2*u**m + 11/2*u - 1 = 0.
1/3, 1, 2
Let t(s) be the third derivative of -s**8/168 - 11*s**7/105 + 6*s**6/5 - 62*s**5/15 + 16*s**4/3 - s**2 - 487*s. Suppose t(i) = 0. Calculate i.
-16, 0, 1, 2
Factor 153*a**3 + 311/2*a + 232*a**2 + 39 + 37*a**4 - 1/2*a**5.
-(a - 78)*(a + 1)**4/2
Factor -69*n**2 - 275*n - 21*n**2 - 4*n**3 + 368*n + n**3.
-3*n*(n - 1)*(n + 31)
Let t = 1071 - 19277/18. Let q(w) be the third derivative of -1/24*w**4 + 0*w + 14*w**2 + 1/315*w**7 + 1/120*w**6 + 0 - t*w**3 - 1/180*w**5. Factor q(x).
(x - 1)*(x + 1)**2*(2*x + 1)/3
Let j(o) be the third derivative of o**5/60 - o**4/6 + 2*o**3/3 - 5*o**2. Let h(s) = -5 + s + 4*s + 0*s - s**2 - s**2. Let i(q) = 4*h(q) + 5*j(q). Factor i(d).
-3*d**2
Let s(v) = -3*v**3 + v**2. Let z be s(-1). Determine n so that 151*n + n**3 - 100*n - 558*n - z*n**3 - 78*n**2 = 0.
-13, 0
Factor -24*v - 4*v**3 + 38 - 19 - 19 + 20*v**2.
-4*v*(v - 3)*(v - 2)
Let w = 135 + -118. Let j be 1 + (-7 - -4) + 92/w. Suppose 24/17*s**5 + 0 + 2/17*s**2 - 4/17*s + j*s**4 + 40/17*s**3 = 0. Calculate s.
-1, -2/3, 0, 1/4
Suppose -q + 120 = 2*q. Factor -6 + 7 + 7*j**4 - q*j**3 - 9 + 86*j**2 - 10*j - 35*j**2.
(j - 4)*(j - 1)**2*(7*j + 2)
Let d(l) be the first derivative of l**5/5 - 11*l**4/20 - l**3/5 + 11*l**2/10 - 2*l/5 + 63. Find r such that d(r) = 0.
-1, 1/5, 1, 2
Let q(i) be the second derivative of 0 + 3/40*i**5 + 5/2*i**2 + 1/4*i**3 + 7*i - 2/3*i**4. Let q(j) = 0. Calculate j.
-2/3, 1, 5
Suppose -3*t = -d + 9, 68*t + 19 = 5*d + 66*t. Solve -8/5 - 1/5*b**d + 2*b**2 - 1/5*b**5 + 4/5*b - 4/5*b**4 = 0.
-2, 1
Let j(i) be the second derivative of -i**6/80 - 243*i**5/40 - 19683*i**4/16 - 531441*i**3/4 - 129140163*i**2/16 + i + 106. Suppose j(u) = 0. What is u?
-81
Let k = -93 - -81. Let h(b) = b**3 + b + 1. Let y(a) = -4*a**4 - 8*a**3 + 12*a**2 - 32*a - 4. Let s(r) = k*h(r) - y(r). Solve s(l) = 0.
-2, 1
Let f be (36/216)/(10/9 - 1). Let x = 877/586 - -1/293. Factor -3/2 + 3/2*m**2 - x*m + f*m**3.
3*(m - 1)*(m + 1)**2/2
Let g(w) be the third derivative of -w**5/15 + 23*w**4/3 - 30*w**3 + 264*w**2. What is j in g(j) = 0?
1, 45
Factor 0*a + 174/5*a**2 - a**4 + 433/5*a**3 + 0.
-a**2*(a - 87)*(5*a + 2)/5
Let u = -125 + 127. Suppose -24*s**4 - 4*s - 84*s**3 - 20*s**5 - 4*s - 12*s**2 - 44*s**4 - 32*s**u = 0. What is s?
-1, -2/5, 0
Let d(a) be the first derivative of -3 + 1/720*a**5 + 0*a + 0*a**2 + 0*a**4 - 1/360*a**6 + 2/3*a**3. Let u(c) be the third derivative of d(c). Factor u(b).
-b*(6*b - 1)/6
Let d(j) be the first derivative of j**6/63 + 8*j**5/105 + 2*j**4/21 - 4*j**3/63 - 5*j**2/21 - 4*j/21 - 946. Solve d(r) = 0.
-2, -1, 1
Let y(x) be the first derivative of -3*x**5/35 + 9*x**4/28 + 4*x**3 - 272. Factor y(i).
-3*i**2*(i - 7)*(i + 4)/7
Let w be (17822/(-140))/(-67) + (-1)/(-2). What is m in w*m**2 + 4/5*m**3 + 4/5 + 12/5*m = 0?
-1
Determine d, given that 3/4*d**2 - 1/4*d**4 + 0*d**3 + 1/2*d + 0 = 0.
-1, 0, 2
Solve -19 + 5*f**3 + 10*f**2 + 9 + 51*f - 56*f = 0.
-2, -1, 1
Let f(x) be the second derivative of -1/28*x**7 + 0 + 1/20*x**6 + 7*x - 1/8*x**4 + 3/40*x**5 + 0*x**2 + 0*x**3. Factor f(k).
-3*k**2*(k - 1)**2*(k + 1)/2
Let a(p) = 12*p + 4. Let u be a(2). Let s = u - 26. Let 0 - 2/9*r**3 - 4/9*r**s + 0*r = 0. What is r?
-2, 0
Suppose -4*h + 3*q = -0*q - 84, 2*h + 3*q = 24. Let u = h + -18. Let u + 0*l**2 + 2/3*l - 2/3*l**3 = 0. What is l?
-1, 0, 1
Let p(b) be the first derivative of -2*b**3/3 - 3*b**2 - 19. Factor p(w).
-2*w*(w + 3)
Let k(a) = -a**4 - 2*a**3 - a. Let f(u) = -6*u**4 + 3*u**3 + 48*u**2 + 27*u. Let t(x) = f(x) - 9*k(x). Suppose t(b) = 0. What is b?
-3, -2, 0
Let x(n) = 3*n**2 - 110*n - 2841. Let k(d) = -d**2 + d + 8. Let q(m) = -4*k(m) - x(m). Determine h so that q(h) = 0.
-53
Let a(y) be the second derivative of -y**5/4 + 25*y**4/6 - 235*y. Let a(v) = 0. Calculate v.
0, 10
Let v(y) be the first derivative of -1/6*y**6 + 0*y + 6/5*y**5 - 31 - 3*y**4 + 10/3*y**3 - 3/2*y**2. Factor v(z).
-z*(z - 3)*(z - 1)**3
Suppose 5 = -22*b + 19*b - p, -3*b = -5*p - 25. Factor 0 - 1/3*w**3 + 0*w + b*w**2.
-w**3/3
Suppose 13*u = 15*u - 4*o - 6, -5*u - 5*o + 75 = 0. Let l be (-22)/(-45) - u/(-99). Determine f, given that -3/5*f**3 - l*f**2 + 3/5*f + 3/5 = 0.
-1, 1
Let x be (1 - (-4 - -8))/(-1). Suppose x - k**4 - 5 + 7*k + 0*k**2 - 9*k**2 + 5*k**3 = 0. Calculate k.
1, 2
Let -2/3*w**2 + 2/3*w**3 - 2 - 10/3*w = 0. What is w?
-1, 3
Suppose d - 5*j = -6 + 1, 2*d - 14 = 2*j. Let c = 12 - d. Find z, given that -10/7*z**3 - 2/7*z**4 - 4/7 - 2*z - 18/7*z**c = 0.
-2, -1
Let o(g) = 34*g - 133. Let j be o(4). Let z(c) be the second derivative of -1/120*c**5 + 0 + c + 1/36*c**j - 1/12*c**2 + 1/72*c**4. What is x in z(x) = 0?
-1, 1
Let d(i) be the first derivative of -4913*i**4/40 - 867*i**3/2 - 2295*i**2/4 - 675*i/2 + 494. Factor d(n).
-(17*n + 15)**3/10
Suppose -f = 3*s - 5, 4*s + 4 = 8*s. Let a = -1/8 - -3/8. Factor -a + 5/4*w**f - w.
(w - 1)*(5*w + 1)/4
Suppose q - 1 = 2*q. Let h be -5*(3 - 4)/(-1). Let v(c) = -c - 1. Let u(g) = -3*g**3 + 9*g**2 + 5*g + 5. Let k(a) = h*v(a) + q*u(a). Factor k(x).
3*x**2*(x - 3)
Suppose 4*g - 7*g = -6. Suppose -n + 19 = 5*m, n - 12 = -g*n. Factor -2/13*i + 2/13*i**m - 4/13 + 4/13*i**2.
2*(i - 1)*(i + 1)*(i + 2)/13
Let q(z) be the firs