Let h(a) = j*m(a) - 4*p(a). Factor h(o).
-5*(o - 3)*(o + 2)
Solve 24 + 117/5*b - 3/5*b**2 = 0.
-1, 40
Let h(o) be the second derivative of o**7/210 + o**6/30 + o**5/10 + o**4/6 + 7*o**3/6 - 15*o. Let m(n) be the second derivative of h(n). Factor m(q).
4*(q + 1)**3
Let u(j) = -12*j**5 + 4*j**4 + 62*j**3 + 42*j**2 - 20*j - 18. Let g(i) = -i**5 - i**4 + i**3 - i**2 - i. Let f(m) = -2*g(m) + u(m). Solve f(c) = 0 for c.
-1, 3/5, 3
Let f be 8/24*(5 + (-11)/3). Factor f + 2/9*u - 2/9*u**2.
-2*(u - 2)*(u + 1)/9
Let z(o) be the third derivative of -1/12*o**5 + 0*o + 5/6*o**3 + 1/24*o**6 + 0 - 5/24*o**4 + 4*o**2. Determine t, given that z(t) = 0.
-1, 1
Let p(z) be the second derivative of -3*z**5/140 + 15*z**4/14 - 39*z**3/2 + 1014*z**2/7 + 207*z. Let p(w) = 0. What is w?
4, 13
Let j(y) be the second derivative of -y**5/30 + y**4/2 - 3*y**3 + 11*y**2/2 + 11*y. Let s(l) be the first derivative of j(l). Suppose s(i) = 0. What is i?
3
Let w(j) be the third derivative of -7*j**2 + 0 + 0*j**3 + 81/32*j**4 - 9/40*j**5 + 0*j + 1/160*j**6. Suppose w(p) = 0. Calculate p.
0, 9
Let c(m) be the first derivative of m**5/12 + 5*m**4/12 + 17*m**2/2 + 15. Let g(p) be the second derivative of c(p). Factor g(f).
5*f*(f + 2)
Let g = -66 + 6. Let t = 64 + g. Factor -j - 1/2*j**t + 0 - 2*j**3 - 5/2*j**2.
-j*(j + 1)**2*(j + 2)/2
Let m(z) be the second derivative of -z**6/90 + z**5/10 + 6*z. Factor m(i).
-i**3*(i - 6)/3
Determine r so that 12*r**2 - 106*r**2 + 3*r**4 + 18*r**3 + 22*r**2 - 27 + 78*r = 0.
-9, 1
Let r(c) be the third derivative of c**8/672 - 7*c**6/240 + c**5/20 - c**2 - 19*c. Factor r(d).
d**2*(d - 2)*(d - 1)*(d + 3)/2
Let n be 8*-1 + 55 + -42. Let m(h) be the first derivative of -21/20*h**n + 1/2*h**3 + 0*h + 0*h**2 - 13 - 15/16*h**4. What is b in m(b) = 0?
-1, 0, 2/7
Let a(y) = y**2 + y + 1. Let m(f) = -f**2 - 5*f - 2. Suppose -5*n = 20 + 10. Let w(s) = n*a(s) - 3*m(s). Factor w(h).
-3*h*(h - 3)
Let f(g) be the second derivative of -g**5/390 - g**4/52 + 4*g**3/39 + 5*g**2/2 + 28*g. Let d(o) be the first derivative of f(o). Solve d(j) = 0.
-4, 1
Let f = -142 + 150. Suppose -28*x + 32*x - f = 0. Factor 3/5*h**x + 0 + 1/5*h**3 + 2/5*h.
h*(h + 1)*(h + 2)/5
Let x = -290 + 293. Let q(z) be the second derivative of -1/5*z**2 + x*z + 0 + 1/20*z**4 + 1/30*z**3. Factor q(j).
(j + 1)*(3*j - 2)/5
Suppose -9*m + 5 = -49. Let i be (3/6)/(m/18). Suppose -9/4*v**2 - 1/4 + i*v = 0. What is v?
1/3
Let l(v) = -v**2 + v. Let j(b) = -2*b**2 + 3*b - 1. Suppose -2*o + 44 - 38 = 0. Let k(r) = o*l(r) - j(r). Find s, given that k(s) = 0.
-1, 1
Let r(m) = m**2 + 26*m - 21. Let z(f) = -14 + 15 + 51*f + f**2 - 42. Let v(l) = -11*r(l) + 6*z(l). Factor v(d).
-5*(d - 3)*(d - 1)
Let o(r) be the third derivative of -r**7/840 + 11*r**6/240 - 47*r**5/80 + 55*r**4/24 - 25*r**3/6 + 5*r**2 - 17. Let o(l) = 0. What is l?
1, 10
Let y = 1/4 - -1/4. Let v be ((-12)/9)/((-72)/162). Determine i, given that 0 + 15/4*i**5 + y*i**2 + i**4 - 9/4*i**v + 0*i = 0.
-1, 0, 1/3, 2/5
Let a be 7*1/14*6. Let h(n) be the second derivative of 1/9*n**a - 1/30*n**5 + 0 - 1/18*n**4 + 1/45*n**6 + 0*n**2 + 3*n. Factor h(x).
2*x*(x - 1)**2*(x + 1)/3
Let o(p) be the second derivative of 24*p + 1/9*p**3 + 0 - 1/6*p**2 - 1/36*p**4. Factor o(g).
-(g - 1)**2/3
Let l(g) be the first derivative of g**7/3360 + g**6/1440 - g**5/240 + 8*g**3/3 - 4. Let h(k) be the third derivative of l(k). Determine r so that h(r) = 0.
-2, 0, 1
Let c be -1*4/(-4) - -2. Suppose 13 = 5*z + c*j, 5*j - 3 = z - 0*j. Factor -4 - 9*l**2 + 13*l**z + 4 - 8*l.
4*l*(l - 2)
Solve -44*z**4 + 37*z**3 - 14*z**3 - 24*z**2 + 28*z**3 + 3*z**5 + 14*z**4 = 0 for z.
0, 1, 8
Let u = 12952/7 + -1782. Let o = u - 4246/63. Factor -2/9*i**2 - 8/9 - o*i.
-2*(i + 2)**2/9
Let d(i) = -i**2 + 12*i + 4. Let r(m) = -2*m - 1. Let f(q) = -4*d(q) - 36*r(q). Solve f(h) = 0 for h.
-5, -1
Let d = -703 + 42181/60. Let q(t) be the second derivative of 2/3*t**2 - 4*t - 1/36*t**4 + 0 + 2/9*t**3 - d*t**5. Factor q(m).
-(m - 2)*(m + 1)*(m + 2)/3
Suppose 421*j = 422*j - 3. Determine c so that 0 + 0*c - 2/9*c**4 - 2/3*c**j - 4/9*c**2 = 0.
-2, -1, 0
Suppose -3/2 + 3/2*o - 3/8*o**2 = 0. What is o?
2
Let o be (-4)/(-10) + (-4464)/60 - -1. Let l = o - -73. Factor 1/6*s**2 - 1/2*s**3 + 1/2*s**4 - 1/6*s**5 + 0 + l*s.
-s**2*(s - 1)**3/6
Let t(k) = k**3 + 7*k**2 - 9*k - 5. Let o be t(-8). Find a such that -o*a**2 + 3 - 5*a + 10*a + 2*a**2 - 3*a = 0.
-1, 3
Let h be (81*(-16)/720)/((-3)/5). Factor -3*t**h + 0 - 48/5*t**4 + 0*t - 27/5*t**5 + 6/5*t**2.
-3*t**2*(t + 1)**2*(9*t - 2)/5
Let q be (-16)/6*(-50484)/16. Factor 8414 - 2*n**3 - 8*n**2 - q.
-2*n**2*(n + 4)
Let t be (1426/(-345))/31 + (-44)/(-105). Suppose -2/7*i**3 + t*i - 2/7*i**2 + 2/7 = 0. Calculate i.
-1, 1
Let p(u) = 36*u + 60. Let i(j) = -j**2 + 37*j + 59. Let o(g) = 4*i(g) - 5*p(g). Find s, given that o(s) = 0.
-4
Let w(q) be the first derivative of 0*q - 4 + 0*q**3 + 0*q**2 - 2/3*q**6 + q**4 + 0*q**5. What is c in w(c) = 0?
-1, 0, 1
Let b(l) be the second derivative of -5*l**4/12 - 115*l**3/3 - 2645*l**2/2 - 2*l - 51. Factor b(i).
-5*(i + 23)**2
Let y(j) be the first derivative of 121*j**4/2 - 396*j**3 + 972*j**2 - 11664*j/11 + 81. Factor y(l).
2*(11*l - 18)**3/11
Let j be 5 - 5 - 3 - (-10 - -1). Let c(m) = m**3 + m**2 + 1. Let x(z) = 2*z**4 + 6*z**3 + 18*z**2 + 20*z. Let h(a) = j*c(a) + x(a). Factor h(i).
2*(i + 1)**3*(i + 3)
Let o(i) = -i**3 + 3*i**2 - i + 60. Let l be o(5). Factor 0 + 0*b + 18/5*b**3 + 12/5*b**4 + 8/5*b**2 + 2/5*b**l.
2*b**2*(b + 1)**2*(b + 4)/5
Suppose p + p = 8, 6 = u + p. Let -2*j**2 + j**2 + 4*j**u + 2*j**2 - 5 = 0. Calculate j.
-1, 1
Let v(w) = -2*w**3 - 69*w**2 - 97*w + 68. Let t be v(-33). Let -2/3*f**t - 4*f - 16/3 = 0. What is f?
-4, -2
Let g(b) = -b**3 + 6*b**2 + 8*b - 7. Let z be g(7). Let m be (-2 - z - -18)/(12 - -2). What is v in 2/7*v**4 - 10/7*v**2 - 2/7*v**5 + m - 8/7*v + 10/7*v**3 = 0?
-2, -1, 1, 2
Factor 32*i**3 + 42*i**2 + 6*i**2 + 2*i**5 - 68*i**3 + i**5.
3*i**2*(i - 2)**2*(i + 4)
Let j(q) be the first derivative of 7*q**5/20 + q**4/2 - q**3/6 + 9*q - 5. Let s(u) be the first derivative of j(u). Suppose s(g) = 0. What is g?
-1, 0, 1/7
Let t(r) be the first derivative of -r**6/21 + 2*r**4/7 - 4*r**3/21 - 3*r**2/7 + 4*r/7 - 314. Solve t(m) = 0.
-2, -1, 1
Let h(z) be the first derivative of 9 - 4/21*z**3 + 1/14*z**4 + 4/7*z - 1/7*z**2. Suppose h(f) = 0. Calculate f.
-1, 1, 2
Let s(g) = -g**2 + 3*g + 3. Let q be s(3). Suppose -q*r + 0*w + 17 = -2*w, -3*w - 27 = -5*r. Factor r*d**3 + 21 + 14*d + d + 12*d**2 - 15.
3*(d + 1)**2*(d + 2)
Let i be 2 + (-4)/(-8)*2. Let v = -70 - -72. Factor f + 4*f**2 - 16*f + i*f - f**v.
3*f*(f - 4)
Find f such that 285/7*f**2 + 0 - f**3 + 82/7*f = 0.
-2/7, 0, 41
Let q(j) = -3*j**4 + 5*j**2 + 2. Let m(f) be the second derivative of f**5/20 - f**4/12 - f**3/6 - f**2/2 - 7*f. Let l(i) = -2*m(i) - q(i). Factor l(a).
a*(a - 1)*(a + 1)*(3*a - 2)
Let k(q) = -4*q**2 - 40*q + 243. Let l(f) = -f**2 - 14*f + 81. Let m(v) = -6*k(v) + 21*l(v). Factor m(p).
3*(p - 9)**2
Let c be (-6)/4 - (-945)/14. Suppose -c*u = -61*u - 20. Find r, given that 32/7*r**3 - 12/7*r**2 - 8/7*r - 12/7*r**u + 0 = 0.
-1/3, 0, 1, 2
Factor -13*m**3 + 3/4*m**4 + 20 - 48*m + 1/4*m**5 + 40*m**2.
(m - 2)**3*(m - 1)*(m + 10)/4
Suppose -4*f + 2 = -3*y + 4, 0 = -3*y - 4*f + 10. Suppose 21*r - 50*r = -18*r. Find w, given that 6/5*w + r + 3/5*w**y = 0.
-2, 0
Let u(m) = -14*m**3 + 20*m**2 + 86*m + 88. Let j(v) = -30*v**3 + 41*v**2 + 173*v + 176. Let h(k) = 6*j(k) - 13*u(k). Determine q so that h(q) = 0.
-2, 11
Let o(s) be the first derivative of -81*s**5/40 - 63*s**4/16 - 13*s**3/24 + 7*s**2/4 - s/2 + 502. Factor o(v).
-(v + 1)**2*(9*v - 2)**2/8
Let x be (-946)/(-1210) - (-22)/(-121). What is u in 6/5*u**2 - 6/5*u**4 + 0 - x*u**5 + 3/5*u**3 + 0*u = 0?
-2, -1, 0, 1
Let v(d) = 5*d**3 - 24*d**2 + 25*d - 2. Let x(w) = -10*w**3 + 49*w**2 - 50*w + 2. Let p(o) = 9*v(o) + 4*x(o). Solve p(y) = 0.
1, 2
Let y(o) be the third derivative of 7*o**5/120 + 5*o**4/48 - o**3/6 + 12*o**2 + 4. Suppose y(s) = 0. Calculate s.
-1, 2/7
Let m be (-952)/(-5) + 0 - (3 - 1). Let n = 189 - m. Factor 0 + 0*l - n*l**3 - 3/5*l**5 + 6/5*l**4 + 0*l**2.
-3*l**3*(l - 1)**2/5
Let k(g) be the third derivative of -g**7/1050 + g**6/150 - g**5/100 - g**4/30 + 2*g*