. Determine d so that -9*d**3 + 4*d**3 - 4*d**2 - 4*d + 0*d - v*d**2 = 0.
-2, -2/5, 0
Let d(i) be the second derivative of -3*i**6/70 - 33*i**5/70 + 50*i**4/7 - 141*i**3/7 - 351*i**2/14 + 448*i - 1. Suppose d(a) = 0. Calculate a.
-13, -1/3, 3
Let o(w) be the third derivative of -83*w**2 + 1/15*w**5 + 0 + 1/6*w**3 - 5/24*w**4 + 0*w. Factor o(x).
(x - 1)*(4*x - 1)
Let z be (-56)/(-196 - 84)*-1*(-15)/4. Let j = 47 + -47. Factor -c**4 + 0*c + z*c**3 + 9/2*c**2 + j - 1/4*c**5.
-c**2*(c - 2)*(c + 3)**2/4
Factor 2/7*u**4 - 90/7*u - 18/7*u**2 + 10/7*u**3 + 0.
2*u*(u - 3)*(u + 3)*(u + 5)/7
Let f(b) be the third derivative of -b**6/40 - 33*b**5/10 + 69*b**4/8 + 67*b**3 + 1747*b**2. Find p such that f(p) = 0.
-67, -1, 2
Let q = -20 - -24. Let s = 187 + -184. Factor 4*l**q + 7*l**s + 5*l**3 + 125*l**2 - 117*l**2.
4*l**2*(l + 1)*(l + 2)
Let n(o) = -9*o**2 + 63*o + 65. Let r(w) = -3*w**2 + 11 + 5 + 6 + 21*w. Let h(a) = 2*n(a) - 7*r(a). Factor h(k).
3*(k - 8)*(k + 1)
Let j be ((-1)/4)/(-9 + (-19755)/(-2196)). Factor 5*p**3 + 155*p + j*p**2 - 17*p**2 + 6*p**2 + 150.
5*(p + 2)*(p + 3)*(p + 5)
Let t(q) = -q**2 + 4147*q - 4162. Let s(w) = -2*w**2 + 4149*w - 4159. Let k(l) = 4*s(l) - 3*t(l). Factor k(x).
-5*(x - 830)*(x - 1)
Factor 3/4*x**2 + 688323/4 + 1437/2*x.
3*(x + 479)**2/4
Suppose 5*z = -3*d + 4*d - 6, -4*z - 5 = -d. Let o(t) = 10*t**5 + 20*t**4 + 25*t**3 + 15*t**2. Let r(v) = v**5 + v**2. Let f(p) = z*o(p) + 5*r(p). Factor f(a).
-5*a**2*(a + 1)**2*(a + 2)
Suppose 0 = -24*j + 138 - 90. Factor 0 + 0*c - 1/8*c**3 + 3/8*c**j.
-c**2*(c - 3)/8
Suppose 0 = 14*k - k - 104. Let j be (0/2 + 4 - k) + 10. Solve -4/3*s + 0 - 14/3*s**2 - 10/3*s**4 - j*s**3 - 2/3*s**5 = 0.
-2, -1, 0
Let h(t) = -4*t**2 + 3477*t - 753429. Let j(g) = -g + 1. Let f(q) = h(q) + 5*j(q). Find y such that f(y) = 0.
434
Suppose -657*c = 768*c - 188*c - 2474. What is u in -80/3*u - 64/3 - 17/3*u**c - 1/3*u**3 = 0?
-8, -1
Let x(d) = -95*d**2 + 5*d. Let u be x(1). Let h be ((-24)/u)/(30/45). Factor -1/5*m**5 + h*m**4 + 0*m**2 + 0 + 0*m - 1/5*m**3.
-m**3*(m - 1)**2/5
Let r(y) be the first derivative of y + 2/3*y**2 + 1/27*y**4 + 3 + 8/27*y**3. Let v(f) be the first derivative of r(f). Factor v(k).
4*(k + 1)*(k + 3)/9
Let f = -53 - -67. Factor 49*n - 139 - f*n + 49 - n**2 + 6*n**2.
5*(n - 2)*(n + 9)
Let s be -5 + -2 - -5 - (-8)/2. Factor 0*m**3 + m**3 + 2*m - 14*m + 10*m - m**s.
m*(m - 2)*(m + 1)
Let l(c) be the second derivative of 1/63*c**4 - 2 - 2/7*c**2 + 5/63*c**3 - 1/210*c**5 - 3*c. Find b, given that l(b) = 0.
-2, 1, 3
Suppose -4*g + 10 = g. Let o be (10/36)/((-23135)/(-111048)). Solve -2*j + 2/3*j**g + o = 0 for j.
1, 2
Let s(b) be the third derivative of b**5/210 + 11*b**4/21 + 160*b**3/21 - 2*b**2 - 2. Factor s(t).
2*(t + 4)*(t + 40)/7
Let w(q) be the second derivative of -q**7/5670 + q**6/90 + 29*q**4/6 + 97*q. Let j(h) be the third derivative of w(h). Factor j(y).
-4*y*(y - 18)/9
Let o(y) = 5*y + 1. Let z(c) = -20*c**2 + c + 1. Let s = -302 + 305. Let m(b) = s*o(b) + z(b). Factor m(t).
-4*(t - 1)*(5*t + 1)
Suppose -581 - 859 = -32*y. Let n be 40/y*(21/6)/7. Factor -2/9*r + n + 2/9*r**3 - 4/9*r**2.
2*(r - 2)*(r - 1)*(r + 1)/9
Suppose 6*t = -0*t + 24. Let 23 + 10*n - 18 + t*n**2 + n**2 = 0. What is n?
-1
Let n = -207 + 1039/5. Let o be (-4)/10*(-3 + (-10 - -12)). Factor n*q + 0 + o*q**2.
2*q*(q + 2)/5
Let p(b) be the second derivative of 0*b**2 + 1/30*b**4 - 19/15*b**3 + 0 - 44*b. What is t in p(t) = 0?
0, 19
Let t = 1524 + -1522. Suppose -3 + t = -2*k + 5*c, 3*k - 5 = 4*c. Let 0*n**4 - 4/5*n**2 + 0 - 2/5*n**5 + 6/5*n**k + 0*n = 0. What is n?
-2, 0, 1
Let p = -153 - -152. Let z be (-6)/(-9)*-6*p. Factor 0 - 1/3*q**2 + 1/3*q**z - 1/3*q**3 + 1/3*q.
q*(q - 1)**2*(q + 1)/3
Let n(q) be the second derivative of q**5/45 + 11*q**4/27 - 80*q**3/27 + 56*q**2/9 + 5*q - 18. Let n(i) = 0. Calculate i.
-14, 1, 2
Let l(i) be the second derivative of -9*i - 19/2*i**2 + 0 + 1/210*i**5 + 0*i**4 - 1/21*i**3. Let h(b) be the first derivative of l(b). Factor h(a).
2*(a - 1)*(a + 1)/7
Let q = -389035 + 389107. Find i, given that -q + 8*i - 2/9*i**2 = 0.
18
Factor -9967*i - 7*i**2 + 5*i**2 + 9735*i - 456.
-2*(i + 2)*(i + 114)
Let c(t) be the third derivative of t**8/1176 - 2*t**7/245 - 4*t**6/105 - t**5/105 + 5*t**4/28 + 8*t**3/21 - 1801*t**2. Factor c(s).
2*(s - 8)*(s - 1)*(s + 1)**3/7
Let y(m) be the third derivative of -m**5/180 + m**4/12 - 59*m**2. Factor y(b).
-b*(b - 6)/3
Let s be (0 - 1/(-2))*(6 - 2). Suppose d - 15 = -5*l, -5 - 9 = -l + s*d. Let -5*f**4 + 5*f**l + 5*f**3 - 5*f**4 = 0. What is f?
0, 1
Let o(h) = 41*h**2 + 2*h + 1. Let f(p) = p**3 + 2*p**2 - 4*p - 4. Let n be f(-3). Let t be o(n). Find q, given that 3*q**2 - 43*q + t*q + 0*q**2 = 0.
0, 1
Let n(u) be the second derivative of u**6/15 + 19*u**5/10 + 44*u**4/3 - 472*u. Solve n(o) = 0.
-11, -8, 0
Let l = -63302 - -506421/8. Determine w, given that l*w**2 + 2*w + 3/8 = 0.
-3, -1/5
Suppose 18*j - n = 15*j - 3743, 3747 = -3*j - 3*n. Let b = j - -1251. Let 2/3*i**4 + 2*i**b - 2/3*i**5 - 10/3*i**2 + 4/3*i + 0 = 0. What is i?
-2, 0, 1
Let j(m) = m**3 - 137*m**2 - 103*m - 4812. Let o be j(138). Let 3/5*b**2 - o - 3/5*b = 0. Calculate b.
-5, 6
Let q be (6/(-40))/(432/(-2290)). Let p = q - -3/32. Factor p*c - 8/9*c**2 + 0 + 2/9*c**3.
2*c*(c - 2)**2/9
Let w(s) be the first derivative of -s**6/54 + 4*s**4/3 + 128*s**3/27 - 1873. Factor w(x).
-x**2*(x - 8)*(x + 4)**2/9
Let s = 88 - 84. Let q be 38/10 - (s - 112/35). Determine n so that -76*n**q - 4*n**5 - 17*n + 16 + 8*n**4 + 20*n**4 + 2*n + 100*n**2 - 49*n = 0.
1, 2
What is r in -452/3*r**2 + 2/3*r**3 + 26840/3*r - 48400 = 0?
6, 110
Let g(q) = 6*q**2 - 12*q + 21. Let z(r) = r**2 + 9*r + 14. Let t be z(-8). Let m(w) = 7*w**2 - 11*w + 22. Let p(a) = t*g(a) - 5*m(a). What is h in p(h) = 0?
1, 16
Let f(a) = -3*a**3 + a**2 + a + 3. Let r(o) = 8*o**3 - 282*o**2 - 2*o - 6. Let t(c) = -2*f(c) - r(c). Factor t(v).
-2*v**2*(v - 140)
Let x(m) be the third derivative of -m**7/1260 - 7*m**6/360 + m**5/18 + 25*m**4/6 + 1322*m**2. What is a in x(a) = 0?
-10, 0, 6
Let p(n) = -n**3 + 16*n**2 - 15*n + 13. Let s be p(15). Determine j so that -s*j**3 - 8 - 36*j**2 + 72 + 9*j**3 - 24*j = 0.
-8, -2, 1
Let h(i) be the second derivative of i**5/50 - 43*i**4/15 + 83*i**3/15 + 34*i**2 + 7*i - 78. Let h(q) = 0. Calculate q.
-1, 2, 85
Suppose 150 = -16*k + 182. What is a in 64*a**2 - 51*a**4 + 3*a**3 + 83*a**2 - 34 - 12*a**k - 21 + 12*a + 9*a**5 - 5 = 0?
-1, 2/3, 2, 5
Let p = -450961 + 450963. Factor 42/5*f + 1/5*f**p + 41/5.
(f + 1)*(f + 41)/5
Let u(v) be the third derivative of -13*v**5/20 - 16*v**4 + 141*v**2. Let r(m) = 7*m**2 + 64*m. Let f(b) = 34*r(b) + 6*u(b). Factor f(z).
4*z*(z - 32)
Let y(w) = -7*w**3 - 129*w**2 - 4086*w - 7685. Let j(v) = -9*v**3 - 130*v**2 - 4084*v - 7684. Let g(p) = 3*j(p) - 4*y(p). Factor g(c).
(c + 2)*(c + 62)**2
Let h(d) = -d**3 - 2. Let x be h(-3). Let a = 28 - x. Factor 3 + 3/2*l + 15/2*l**a - 12*l**2.
3*(l - 1)**2*(5*l + 2)/2
Suppose -4*z + 5 + 3 = 0. Suppose -62*m + 171 + 31 = 39*m. What is w in -m*w**3 + 16/7*w + 10/7*w**4 - 2/7*w**5 - 2/7*w**z - 8/7 = 0?
-1, 1, 2
Let d(u) be the first derivative of u**4/10 + 468*u**3/5 + 164268*u**2/5 + 25625808*u/5 - 598. Factor d(g).
2*(g + 234)**3/5
Let p(a) be the first derivative of 43 + 351/14*a**2 + 3/28*a**4 - 20/7*a**3 - 486/7*a. Factor p(j).
3*(j - 9)**2*(j - 2)/7
Factor -93/2*l - 28/3 + 5/6*l**3 + l**2.
(l - 7)*(l + 8)*(5*l + 1)/6
Let n(j) be the third derivative of -j**8/2184 - 2*j**7/91 - 7*j**6/78 + 10*j**5/13 + 71*j**4/156 - 90*j**3/13 - 23*j**2 - 32. Determine a so that n(a) = 0.
-27, -5, -1, 1, 2
Suppose 521667/2*i**2 - 72511713/4*i**3 + 2 - 1251*i = 0. What is i?
2/417
Let f = -301983/5 + 60397. Factor -38/5*j + 36/5 + f*j**2.
2*(j - 18)*(j - 1)/5
Suppose 77 - 5 = 9*i. Let 20*t - 56*t - 17*t**3 + i + 48*t**2 - 3*t**3 = 0. What is t?
2/5, 1
Let k(c) be the third derivative of -3*c**7/14 + 21*c**6/8 - 53*c**5/12 - 35*c**4/24 + 5*c**3 - 741*c**2. Suppose k(s) = 0. What is s?
-1/3, 1/3, 1, 6
Let s(r) be the third derivative of 3*r**6/10 + 172*r**5/5 + 28525*r**4/24 - 30625*r**3/6 + 27*r**2 - 6. Factor s(o).
(o - 1)*(6*o + 175)**2
Let x(h) = -2*h**4 - h**3 + h**2 + 1. Let y(b) = -11*b**4 + 83*b**3 + 949*b**2 + 2997*b + 3082. Let m(r) = -4*x(r) 