lculate a.
-2, -1
Let g(x) be the first derivative of x**6/21 + 2*x**5/35 - x**4/14 - 2*x**3/21 + 23. Determine q so that g(q) = 0.
-1, 0, 1
Let d(f) = f**3 - 8*f**2 + 13*f - 32. Let g be d(7). Let y be 50/g + (-14)/4. Factor 3/4*k**2 - 3/4*k - y.
3*(k - 2)*(k + 1)/4
Let p be (-40)/(-5) + 18/(5 - 8). Solve 0 - 2/5*k**5 + 4/5*k**p + 4/3*k**4 - 8/5*k**3 - 2/15*k = 0.
0, 1/3, 1
Let t(v) be the third derivative of 4/5*v**5 + 0*v + 12*v**2 - 17/40*v**6 - 1/2*v**4 + 0*v**3 + 1/14*v**7 + 0. Factor t(j).
3*j*(j - 2)*(j - 1)*(5*j - 2)
Let x be 438/(-146) - 3/((-54)/57). Let r be (-6)/(-54) - 2/(-9). What is j in -x*j**2 - 1/3*j**3 + r*j + 0 + 1/6*j**4 = 0?
-1, 0, 1, 2
Solve -3*n - 12/5 - 3/5*n**2 = 0 for n.
-4, -1
Let r(q) be the third derivative of -1/24*q**4 + 2/15*q**3 + 0 + 3*q**2 + 0*q + 1/300*q**5. Factor r(f).
(f - 4)*(f - 1)/5
Suppose 2*w + 145*b + 12 = 142*b, 5*b = w - 20. Factor -1/4*k**5 + w + 0*k - 13/4*k**3 + 3/2*k**2 + 2*k**4.
-k**2*(k - 6)*(k - 1)**2/4
Suppose 8*s - 30*s + 155 = 111. Factor 10/7*o**3 + 0 - 2/7*o - 8/7*o**s.
2*o*(o - 1)*(5*o + 1)/7
Let i(l) = 24*l**4 + 71*l**3 + 40*l**2 - 11*l - 20. Let s(k) = 47*k**4 + 143*k**3 + 80*k**2 - 23*k - 35. Let a(y) = -7*i(y) + 4*s(y). Factor a(v).
5*v*(v + 1)*(v + 3)*(4*v - 1)
Let f = -37 + 39. Find o, given that -4 + 20*o**2 - 12*o**f + 24*o + 20*o**2 = 0.
-1, 1/7
Solve -2/3*z**2 + 46/3*z + 100/3 = 0.
-2, 25
Let s be ((-6)/21 - (-96)/42) + -2. Let u be (s + 90/220)*4/3. Let 6/11*p**2 + u*p + 2/11 + 2/11*p**3 = 0. What is p?
-1
Let x(f) be the first derivative of 6 + 0*f**2 + 1/54*f**4 - 1/90*f**5 + 0*f**3 + 8*f. Let d(l) be the first derivative of x(l). Suppose d(u) = 0. What is u?
0, 1
Factor 3*q**3 + 7/3*q**2 + 4 - 56/3*q.
(q - 2)*(q + 3)*(9*q - 2)/3
Suppose 5445*i + 4*i**3 + 115*i**2 - 15*i**2 + 122*i**2 + i**3 + 108*i**2 = 0. What is i?
-33, 0
Let f(w) be the second derivative of -w**5/120 + 5*w**4/72 + 2*w**3/9 - w**2 - w + 9. Factor f(y).
-(y - 6)*(y - 1)*(y + 2)/6
Let y(f) be the second derivative of f**4/16 - 285*f. Factor y(j).
3*j**2/4
Let c(i) = i**3. Let y(h) be the second derivative of 0 + 7/20*h**5 + 1/6*h**3 + 1/2*h**2 - 8*h - 1/12*h**4. Let p(l) = 24*c(l) - 3*y(l). Factor p(f).
3*(f - 1)*(f + 1)**2
Let z be ((0/2)/(-19 - -17))/2. Solve z + 0*y + 2/9*y**2 = 0.
0
Let y be (2/5)/(8/220). Let d(c) = -44*c - 5*c - 2*c + 69 + 16*c**2. Let r(l) = -3*l**2 + 10*l - 14. Let n(v) = y*r(v) + 2*d(v). Factor n(u).
-(u - 4)**2
Solve -14/3*l - 14/3*l**2 - 2/3*l**3 + 10 = 0.
-5, -3, 1
Let v(j) be the second derivative of j**7/357 - j**6/255 - j**5/85 + j**4/51 + j**3/51 - j**2/17 - 11*j - 10. Suppose v(s) = 0. Calculate s.
-1, 1
Let t(m) be the second derivative of -m**6/30 + m**5/20 + 235*m. Factor t(d).
-d**3*(d - 1)
Let s(y) be the second derivative of -1/24*y**5 - y + 1/252*y**7 - 3/8*y**4 - 8/9*y**3 - y**2 + 12 + 1/60*y**6. Find b such that s(b) = 0.
-2, -1, 3
Let q(t) = 6*t**3 - 6*t**2 + 3*t + 3. Let g be (-1)/(-1) - (-3 + 0). Let w(y) = -7*y**3 + 6*y**2 - 4*y - 4. Let r(u) = g*q(u) + 3*w(u). Factor r(k).
3*k**2*(k - 2)
Find u such that -76/3*u - 4/3*u**2 + 80/3 = 0.
-20, 1
Let p(d) be the third derivative of -d**6/420 - 17*d**5/42 - 22*d**4 - 84*d**3 - 22*d**2. Let p(b) = 0. What is b?
-42, -1
Let j be 7 - ((-45)/20 - (-3)/12). Find b such that -21*b**2 + j*b**2 + 7*b**2 + 30*b = 0.
0, 6
Determine m so that -156 - 9*m**3 + 511*m**2 - 244*m**2 - 321*m - 6 + 225*m**2 = 0.
-1/3, 1, 54
Solve -1/2*v**4 + 9/2 - 3*v**3 + 3*v - 4*v**2 = 0 for v.
-3, -1, 1
Let x(a) be the third derivative of 37*a**2 + 0 + 0*a - 5/12*a**4 + 5/6*a**3 + 1/12*a**5. Factor x(d).
5*(d - 1)**2
Let d(z) be the third derivative of 0*z + 1/540*z**5 + 1/27*z**3 + 0 + 1/72*z**4 - 19*z**2. Find p, given that d(p) = 0.
-2, -1
Let h(o) be the first derivative of o**5/80 - o**4/32 - o**3/4 - 5*o**2/2 - 6. Let v(t) be the second derivative of h(t). Factor v(u).
3*(u - 2)*(u + 1)/4
Suppose -2*f = 2*m + 10, 21*m = -2*f + 23*m + 14. Determine o, given that -1/4*o**2 - 5/4*o - f = 0.
-4, -1
Let s = -187 - -314. Let f = 132 - s. Solve 320*n + 256 + 160*n**2 + 1/4*n**f + 5*n**4 + 40*n**3 = 0 for n.
-4
Suppose 14/3*r**4 + 10/3*r**2 + 2/3*r**5 - 32/3*r + 10*r**3 - 8 = 0. What is r?
-3, -2, -1, 1
Suppose -263 - 61 = -81*w. Let o(f) be the third derivative of 0 - 1/9*f**3 - 1/18*f**w - 1/72*f**5 + 0*f - 7*f**2 - 1/720*f**6. Determine x so that o(x) = 0.
-2, -1
Suppose 8*f - 9 = -1. Let n(w) be the first derivative of -1/2*w**2 - 2/3*w + f - 1/9*w**3. Factor n(k).
-(k + 1)*(k + 2)/3
Suppose 3*k = 5*d - 305, -101 = 2*k - k - d. Let x be k/(-24) - 5/3. Suppose -x*a**3 - 6*a**2 - 2*a + 0 = 0. What is a?
-2, -2/5, 0
Factor 117*g + 21/2*g**3 + 48 - 351/2*g**2.
3*(g - 16)*(g - 1)*(7*g + 2)/2
Suppose -94*c + 145 + 378 = -41. Solve c*v**4 - 3/2*v**5 + 0 + 0*v**2 + 0*v - 9/2*v**3 = 0.
0, 1, 3
Let -2/9*s**5 + 206/9*s**2 - 2*s**3 - 260/9*s - 22/9*s**4 + 32/3 = 0. Calculate s.
-8, -6, 1
Let y be 6/9 - (-110)/6. Let d = -16 + y. Factor -21*u - 19*u**2 + 4*u**2 - d*u**3 - 1 - 8.
-3*(u + 1)**2*(u + 3)
Let t be ((-108)/(-234))/(-2 + (-60)/(-26)). Find c, given that -1/3*c**2 - t*c - 3/2 = 0.
-3, -3/2
Let w(o) be the second derivative of -o**5/50 + 7*o**4/15 + o**3/15 - 14*o**2/5 + 65*o. Suppose w(s) = 0. What is s?
-1, 1, 14
Let y be (((-2548)/39)/14)/(-1). Let y*a**3 + 0 + 0*a + 10/3*a**4 + 4/3*a**2 = 0. What is a?
-1, -2/5, 0
Let t(c) be the third derivative of c**7/1260 + c**6/240 - c**5/120 - 7*c**4/144 + c**3/6 + 165*c**2. Solve t(j) = 0.
-3, -2, 1
Let s(g) be the second derivative of g**5/270 + 5*g**4/108 - 21*g**2/2 - 8*g. Let t(a) be the first derivative of s(a). Factor t(k).
2*k*(k + 5)/9
Let 24 + 4*g - g**2 + 8*g - 10*g = 0. Calculate g.
-4, 6
Let w(p) = -p**2 + 7*p - 1. Let g be (-2)/10 - 31/(-5). Let t be w(g). Factor 0*f**t + 3*f + 5*f**2 - 3*f**5 - 6*f**4 + f**2.
-3*f*(f - 1)*(f + 1)**3
Let d(p) = p**3 - 40*p**2 - 159*p - 114. Let v(f) = -3*f**3 + 80*f**2 + 317*f + 227. Let b(k) = 7*d(k) + 4*v(k). Factor b(r).
-5*(r - 11)*(r + 1)*(r + 2)
Let q(j) be the third derivative of j**8/672 - 2*j**7/105 + 7*j**6/240 - 25*j**2 - j. Factor q(u).
u**3*(u - 7)*(u - 1)/2
Let w(t) be the second derivative of t**4/18 - t**3/18 - t**2/6 - 84*t. Determine q so that w(q) = 0.
-1/2, 1
Let f(r) be the first derivative of r**5/10 - 3*r**4/2 + 9*r**3 - 27*r**2 + 10*r + 1. Let a(p) be the first derivative of f(p). Find n, given that a(n) = 0.
3
Let r = 19 + -4. Suppose 4*i + 3*a = r, 0*i - 3*a - 6 = -3*i. Factor -i*f**2 - f**3 - 1 + 2*f - 4*f - f.
-(f + 1)**3
Solve 40*p**2 - 4*p**3 - 88 + 3*p - 8*p + 10*p + 47*p = 0 for p.
-2, 1, 11
Let z(o) be the third derivative of -o**7/105 - o**6/20 + o**4/3 + 2*o**2 - 24*o. Suppose z(a) = 0. Calculate a.
-2, 0, 1
Let n(d) = -3*d**2 + 33*d - 82. Let f be n(7). Let o(c) be the first derivative of -4/13*c**3 + 9/13*c**f - 1 + 1/26*c**4 + 0*c. Factor o(m).
2*m*(m - 3)**2/13
Let t be 18/5 - (-567)/405. Let b(y) be the second derivative of 0 + 9*y - 3/2*y**2 - 3/4*y**4 + 3/2*y**3 + 3/20*y**t. Let b(v) = 0. Calculate v.
1
Let z(y) be the first derivative of y**6/900 + 2*y**5/75 + 4*y**4/15 + y**3 - 14. Let k(b) be the third derivative of z(b). Factor k(i).
2*(i + 4)**2/5
Let c(o) be the second derivative of -o**6/240 + o**5/24 - o**4/16 - 3*o**3/4 - 7*o**2/2 - 4*o. Let h(x) be the first derivative of c(x). Factor h(u).
-(u - 3)**2*(u + 1)/2
Let u(z) be the second derivative of 2*z**2 + 22*z + z**3 + 0 + 1/6*z**4. Suppose u(k) = 0. Calculate k.
-2, -1
Let q(t) be the second derivative of t**4/16 - 3*t**3/2 + 27*t**2/2 + 39*t. Factor q(y).
3*(y - 6)**2/4
Let o(q) = 47*q**3 - 175*q**2 - 36*q + 164. Let h(z) = -9*z**3 + 35*z**2 + 7*z - 33. Let f(v) = 11*h(v) + 2*o(v). Solve f(m) = 0.
-1, 1, 7
Suppose -14*n = -10*n - 232. Let y = n + -58. Determine f, given that 4/5*f**2 + y + 1/5*f**3 + 4/5*f = 0.
-2, 0
Let l(f) be the second derivative of 13/90*f**5 + 1/189*f**7 + 0 - 2/45*f**6 - 2/9*f**4 + 2*f + 4/27*f**3 + 0*f**2. Find k such that l(k) = 0.
0, 1, 2
Let m(v) be the first derivative of -3*v**5/25 - 9*v**4/20 + 6*v**3/5 + 42*v**2/5 + 72*v/5 - 2. Let m(i) = 0. What is i?
-2, 3
Suppose 5*w = 20, 0 = o - 3*o - 2*w + 14. Let h = 13826 - 55303/4. Determine r so that -3/8*r**2 + 0 + 3/8*r**o + 1/4*r**4 - h*r = 0.
-2, -1/2, 0, 1
Let d(k) 