Calculate h.
-1, 1
Let w = -1 + 5. Let t(u) be the first derivative of 17*u**3 + u**5 + 13*u**3 - 135*u - 17 + 3*u**4 + 7*u**w. Factor t(v).
5*(v - 1)*(v + 3)**3
Let i = -24 + -82. Let y = i - -150. Factor 3 + 44*h - y*h - 3*h**2.
-3*(h - 1)*(h + 1)
Let r(k) be the first derivative of k**5/20 - k**3 - 2*k**2 + 583. Factor r(o).
o*(o - 4)*(o + 2)**2/4
Let f(g) be the second derivative of 4*g**7/21 - 59*g**6/30 + 117*g**5/20 - 3*g**4 + 310*g. Determine b so that f(b) = 0.
0, 3/8, 3, 4
Suppose d + 3*o = 8, -5*d + 4*o = o - 22. Let -d*m**3 + 8*m**3 + 4*m**2 - 16 - 3*m - 5*m - m**3 = 0. What is m?
-2, 2
Let d(f) be the third derivative of -f**8/40 + 22*f**7/175 + 3*f**6/5 - 17*f**5/5 + 107*f**4/20 - 12*f**3/5 + 905*f**2. Determine s so that d(s) = 0.
-3, 1/7, 1, 4
Let -760384/11 + 1/11*x**3 - 1745/11*x**2 + 762128/11*x = 0. What is x?
1, 872
Let l(k) be the second derivative of -k**4/12 - 25*k**3/3 + 168*k**2 + 1165*k. Factor l(u).
-(u - 6)*(u + 56)
Let m(b) = 2*b**3 - 444*b**2 + 10077*b - 26463. Let v(r) = 5*r**3 - 885*r**2 + 20155*r - 52925. Let z(g) = 5*m(g) - 3*v(g). Solve z(c) = 0 for c.
3, 42
Let d(g) = 35*g**3 - 5 - 32*g**3 - g**2 + 6. Let r(k) = 2*k**3 + 5*k**2 + 16*k + 1. Let s(o) = -d(o) + r(o). Factor s(p).
-p*(p - 8)*(p + 2)
Determine l so that 2539/2*l**3 - 5*l**4 + 1387*l - 252 - 4799/2*l**2 = 0.
2/5, 1/2, 1, 252
Let v(x) = 2*x**3 - x**2 + 210. Let d be v(0). Let -30*u**2 - d*u - 12*u**2 - 111 - 3*u**2 - 134 = 0. What is u?
-7/3
Let a(s) be the first derivative of 5*s**3/3 - 1490*s**2 + 5940*s - 6687. Solve a(y) = 0 for y.
2, 594
Suppose -11*k + 5614 = -25*k. Let f = 401 + k. Factor 1/7*i**2 + f*i - 1/7.
(i - 1)*(i + 1)/7
Suppose -20*g = -16*g - 1932. Suppose g = 9*k + 12*k. Solve 11*x**2 - 2*x - 2*x + k*x**2 + 38*x**3 = 0.
-1, 0, 2/19
Let j be 3419/91 + 4 + -41. Suppose 354/7*t**2 + j + 562/7*t**4 - 10*t - 24*t**5 - 682/7*t**3 = 0. Calculate t.
2/21, 1/4, 1
Let u(t) be the second derivative of -t**5/30 + 17*t**4/3 + 35*t**3/3 - 206*t**2/3 - 2*t + 58. Factor u(h).
-2*(h - 103)*(h - 1)*(h + 2)/3
Suppose 0 = u + 227 - 227. Let k(j) be the first derivative of u*j**2 + 0*j + 12/35*j**5 + 3/7*j**4 + 19 + 4/21*j**3 + 2/21*j**6. Factor k(h).
4*h**2*(h + 1)**3/7
Let t = 485 - 473. Determine y, given that -2*y**4 + 653*y + 78*y**2 + 6*y**2 - t*y**3 - 749*y - y**4 = 0.
-8, 0, 2
Let a(g) be the first derivative of 2*g**6/3 - 16*g**5/5 - 24*g**4 + 344*g**3/3 - 178*g**2 + 120*g + 869. Factor a(p).
4*(p - 6)*(p - 1)**3*(p + 5)
Let c(o) = -3*o**2 - o**2 - 5*o + o**2 + 22 + 2*o**2. Let a be c(-6). Factor -j**5 - a - 40*j**4 - 4*j**5 + 20*j**2 - 3*j**5 - 50*j**3 + 40*j.
-2*(j + 2)**3*(2*j - 1)**2
Suppose -5*z = 3*x + 3, 10*z = 3*x + 8*z - 18. Suppose -5*q + x = -t, -3*t - 20 = 2*t. Factor -24/7*y**4 + 92/7*y**3 + 2/7*y**5 + q - 120/7*y**2 + 50/7*y.
2*y*(y - 5)**2*(y - 1)**2/7
Suppose -89*f - 9 = -92*f. Factor 1774*t**3 + 28*t**4 - f*t**2 - 1810*t**3 + 11*t**2.
4*t**2*(t - 1)*(7*t - 2)
Let u(w) = w**2 - 26*w + 82. Let m be u(22). Let x be (-19)/(-57) - (-2)/m. Factor 9/2*o**3 + x - 3*o**2 + 0*o.
3*o**2*(3*o - 2)/2
Let l(o) = -4*o**2 - 870*o + 886. Let d(f) = 12*f**2 + 2615*f - 2661. Let g(y) = 6*d(y) + 17*l(y). Determine m, given that g(m) = 0.
-226, 1
Let r(x) be the first derivative of 9*x**5 + 40*x**4 - 175*x**3/6 + 15*x**2/2 - 54*x + 34. Let b(a) be the first derivative of r(a). What is p in b(p) = 0?
-3, 1/6
Suppose 4*w - 3152 = -4*w. Factor -5*u**3 + 400*u**2 - w*u**2 + 8*u**3 + 3*u.
3*u*(u + 1)**2
Let o(g) = -2996*g - 44937. Let v be o(-15). Factor -6*x + 2/7*x**v - 18/7*x**2 - 22/7.
2*(x - 11)*(x + 1)**2/7
Let p be -5 + 3 + (-6 - -2) + 12. Let b be p/9*120/640. Factor -3/4*a + 5/8 + b*a**2.
(a - 5)*(a - 1)/8
Let m(y) be the first derivative of 0*y + 1/2*y**2 + 0*y**3 + 1/6*y**6 + 0*y**5 + 20 - 1/2*y**4. Find f, given that m(f) = 0.
-1, 0, 1
Factor 707*q**2 - 3790809 - 2952829*q - q**3 + 1397*q**2 + 1789*q**2 - 834086*q.
-(q - 1947)**2*(q + 1)
Suppose 918*a - 15*a = 1806. Factor 0*c - 2/11*c**a + 2/11.
-2*(c - 1)*(c + 1)/11
Let c(t) = -19*t**3 - 822*t**2 - 7860*t + 719. Let j(i) = -284*i**3 - 12326*i**2 - 117898*i + 10784. Let p(y) = 92*c(y) - 6*j(y). Let p(m) = 0. What is m?
-19, 1/11
Let s(q) = -9*q**2 + 3*q + 5. Let d = 115 + -118. Let v(z) = 5*z**2 - z - 3. Let m(x) = d*s(x) - 5*v(x). Find b, given that m(b) = 0.
0, 2
Suppose 300*i**3 + 160*i**2 - 48 + 150*i**4 - 6*i**5 - 294*i + 0*i**5 - 256*i**4 - 56 + 50*i**4 = 0. Calculate i.
-13, -1, -1/3, 1, 4
Let d(u) be the first derivative of -1/19*u**2 - 48 + 16/19*u**3 + 0*u. Determine r so that d(r) = 0.
0, 1/24
What is h in -2/3*h**2 - 7372/3 - 2458*h = 0?
-3686, -1
Suppose -14*p + 36 = 148. Let f be (p/80)/((-2)/16). Suppose 0*l - 4/5*l**3 + 0 + 0*l**2 + f*l**4 = 0. Calculate l.
0, 1
Let q(k) be the second derivative of k**8/11200 - k**7/1400 + k**6/600 + 32*k**4/3 + k + 6. Let a(j) be the third derivative of q(j). Factor a(s).
3*s*(s - 2)*(s - 1)/5
Let o(i) be the second derivative of i**5/110 + 29*i**4/33 - 181*i**3/33 + 122*i**2/11 - 15963*i. Solve o(p) = 0.
-61, 1, 2
Let c(y) be the second derivative of y**4/3 - 332*y**3 - 2000*y**2 - 598*y. Factor c(r).
4*(r - 500)*(r + 2)
Factor -21771 - 64*q**2 + q**5 + 32*q**4 - 2*q**3 + q + 10910 + 10893.
(q - 1)**2*(q + 1)**2*(q + 32)
Let t = -81 + 118. Suppose -2*h + 3*x = -48, -3*h + 4*x + 35 = -t. Factor 8 - 17*j**2 + h*j**2 - 15*j + 1 - j**3.
-(j - 3)**2*(j - 1)
Let u(i) = -15*i**2 - i. Let j(y) = 254*y**2 + 653*y - 101124. Let q(g) = -2*j(g) - 34*u(g). Solve q(t) = 0 for t.
318
Let p be 3341/(-7) + -6*5/(-105). Let y = -474 - p. Suppose 0*t + 4/9*t**y + 2/3*t**4 + 2/9*t**5 + 0 + 0*t**2 = 0. What is t?
-2, -1, 0
Let l = -589750/9 + 65655. Let j = -127 + l. Factor 0 + 4/9*a**3 - 2/9*a**2 + j*a**4 - 4/9*a.
2*a*(a - 1)*(a + 1)*(a + 2)/9
Suppose 8*d + 125 = 13*d. Let r = -15 + d. Let a(q) = -q + 1. Let c(k) = 6*k**2 - 14*k + 8. Let h(i) = r*a(i) - c(i). Factor h(y).
-2*(y - 1)*(3*y + 1)
Determine g so that -4802/9*g - 4/9*g**5 + 398/9*g**4 + 14602/9*g**2 + 0 - 3398/3*g**3 = 0.
0, 1/2, 1, 49
Let r be -2 - 2*(12 - 15). Let y(q) be the second derivative of r*q + 0 + 1/6*q**4 - 1/6*q**3 + 0*q**2 - 1/20*q**5. Factor y(h).
-h*(h - 1)**2
Let c(l) = 2*l**4 + l**3 - 1. Let h(u) = 6*u**4 - 7*u - 9*u**2 + 5 - 11*u**3 - 17*u**4 + 3*u. Let k(j) = 5*c(j) + h(j). Factor k(r).
-r*(r + 1)**2*(r + 4)
Let s = 15191 + -15189. Let y(w) be the first derivative of -7/18*w**3 - 1/3*w + 4 + 7/12*w**s + 1/12*w**4. Solve y(u) = 0 for u.
1/2, 1, 2
Suppose -12*s - 912 = -0*s. Let o be (6 + -1)*s/(-190). Factor 1/3*r**o + 16/3 + 8/3*r.
(r + 4)**2/3
Suppose -9*u = -0*u - 81. Suppose 4 = 3*n - 14. Solve 27*o**4 - 15*o - n - u*o**2 + 3*o**3 - 13*o**4 - 11*o**4 = 0.
-1, 2
Let p(r) be the third derivative of 10/3*r**3 + 1/12*r**5 - 5/6*r**4 - 24 + 0*r - 2*r**2. Factor p(y).
5*(y - 2)**2
Let d = 434 + -431. Let c be (-60)/(-9) - (d - 7)*1. Determine u so that -c*u**2 + 40/9*u - 4/9 = 0.
1/6, 1/4
Let l = -7941 + 7941. Let n(x) be the third derivative of 0*x + 0*x**3 + 12*x**2 + l + 1/15*x**6 + 2/105*x**7 + 0*x**4 + 1/15*x**5. Factor n(q).
4*q**2*(q + 1)**2
Let q(d) be the third derivative of -d**11/831600 + d**9/50400 - d**8/25200 + 13*d**5/15 + 34*d**2 + 1. Let a(h) be the third derivative of q(h). Factor a(g).
-2*g**2*(g - 1)**2*(g + 2)/5
Solve -15*y**3 - 21*y**3 - 8*y**3 - 72*y - 17*y**3 + 3*y**4 + 4*y**4 - 270*y**2 = 0 for y.
-3, -2/7, 0, 12
Let r(s) = s + 3. Let u = -28 - -29. Let g be r(u). Suppose -4*o**2 - 7 + 6*o**3 - 4*o**g + o + o**5 + 7 = 0. Calculate o.
0, 1
Let f = 4219 + -4219. Let m(t) be the second derivative of 0*t**3 + 1/3*t**4 + f*t**2 + 7*t + 0 + 1/5*t**5 + 1/30*t**6. Factor m(r).
r**2*(r + 2)**2
Determine p, given that 38/3*p + 3/2*p**5 - 19/6*p**2 - 10/3 + 9/2*p**4 - 97/6*p**3 = 0.
-5, -1, 1/3, 2/3, 2
Let p(u) be the first derivative of 3/5*u**5 + 0*u**2 - 192 - 3*u**3 - 3*u**4 + u**6 + 0*u. Factor p(w).
3*w**2*(w + 1)**2*(2*w - 3)
Suppose -250/3 + 251/3*m - 1/3*m**2 = 0. What is m?
1, 250
Let x(p) be the second derivative of 1/6*p**3 + 0 - 6*p**2 + 131*p + 1/12*p**4. Factor x(r).
(r - 3)*(r + 4)
Let s be 393/3 - 4*4/8. Factor -17 - 2*n**2 + 117*n - s*n - 1.
-2*(n + 3)**2
Let a(n) be the third derivative of n**7/735 - 9*n**5/70 + 9*n**4/14 + 1126*n**2. Factor 